id	sid	tid	token	lemma	pos
ejpam-6204	1	1	european	european	PROPN
ejpam-6204	1	2	journal	journal	PROPN
ejpam-6204	1	3	of	of	ADP
ejpam-6204	1	4	pure	pure	ADJ
ejpam-6204	1	5	and	and	CCONJ
ejpam-6204	1	6	applied	applied	ADJ
ejpam-6204	1	7	mathematics	mathematic	NOUN
ejpam-6204	1	8	2025	2025	NUM
ejpam-6204	1	9	,	,	PUNCT
ejpam-6204	1	10	vol	vol	NOUN
ejpam-6204	1	11	.	.	PROPN
ejpam-6204	1	12	18	18	NUM
ejpam-6204	1	13	,	,	PUNCT
ejpam-6204	1	14	issue	issue	NOUN
ejpam-6204	1	15	3	3	NUM
ejpam-6204	1	16	,	,	PUNCT
ejpam-6204	1	17	article	article	NOUN
ejpam-6204	1	18	number	number	NOUN
ejpam-6204	1	19	6204	6204	NUM
ejpam-6204	1	20	issn	issn	VERB
ejpam-6204	1	21	1307	1307	NUM
ejpam-6204	1	22	-	-	SYM
ejpam-6204	1	23	5543	5543	NUM
ejpam-6204	1	24	–	–	PUNCT
ejpam-6204	1	25	ejpam.com	ejpam.com	X
ejpam-6204	1	26	published	publish	VERB
ejpam-6204	1	27	by	by	ADP
ejpam-6204	1	28	new	new	PROPN
ejpam-6204	1	29	york	york	PROPN
ejpam-6204	1	30	business	business	PROPN
ejpam-6204	1	31	global	global	ADJ
ejpam-6204	1	32	general	general	ADJ
ejpam-6204	1	33	deformations	deformation	NOUN
ejpam-6204	1	34	of	of	ADP
ejpam-6204	1	35	sprays	spray	NOUN
ejpam-6204	1	36	on	on	ADP
ejpam-6204	1	37	finsler	finsler	NOUN
ejpam-6204	1	38	manifolds	manifold	NOUN
ejpam-6204	1	39	s.	s.	PROPN
ejpam-6204	1	40	g.	g.	PROPN
ejpam-6204	1	41	elgendi1,∗	elgendi1,∗	PROPN
ejpam-6204	1	42	,	,	PUNCT
ejpam-6204	1	43	a.	a.	NOUN
ejpam-6204	1	44	soleiman2	soleiman2	NOUN
ejpam-6204	2	1	1	1	NUM
ejpam-6204	2	2	department	department	NOUN
ejpam-6204	2	3	of	of	ADP
ejpam-6204	2	4	mathematics	mathematic	NOUN
ejpam-6204	2	5	,	,	PUNCT
ejpam-6204	2	6	faculty	faculty	NOUN
ejpam-6204	2	7	of	of	ADP
ejpam-6204	2	8	science	science	NOUN
ejpam-6204	2	9	,	,	PUNCT
ejpam-6204	2	10	islamic	islamic	PROPN
ejpam-6204	2	11	university	university	PROPN
ejpam-6204	2	12	of	of	ADP
ejpam-6204	2	13	madinah	madinah	PROPN
ejpam-6204	2	14	,	,	PUNCT
ejpam-6204	2	15	madinah	madinah	PROPN
ejpam-6204	2	16	,	,	PUNCT
ejpam-6204	2	17	saudi	saudi	PROPN
ejpam-6204	2	18	arabia	arabia	PROPN
ejpam-6204	2	19	2	2	NUM
ejpam-6204	2	20	department	department	NOUN
ejpam-6204	2	21	of	of	ADP
ejpam-6204	2	22	mathematics	mathematic	NOUN
ejpam-6204	2	23	,	,	PUNCT
ejpam-6204	2	24	college	college	NOUN
ejpam-6204	2	25	of	of	ADP
ejpam-6204	2	26	science	science	NOUN
ejpam-6204	2	27	,	,	PUNCT
ejpam-6204	2	28	jouf	jouf	PROPN
ejpam-6204	2	29	university	university	PROPN
ejpam-6204	2	30	,	,	PUNCT
ejpam-6204	2	31	skaka	skaka	PROPN
ejpam-6204	2	32	,	,	PUNCT
ejpam-6204	2	33	saudi	saudi	PROPN
ejpam-6204	2	34	arabia	arabia	PROPN
ejpam-6204	2	35	abstract	abstract	NOUN
ejpam-6204	2	36	.	.	PUNCT
ejpam-6204	3	1	in	in	ADP
ejpam-6204	3	2	this	this	DET
ejpam-6204	3	3	paper	paper	NOUN
ejpam-6204	3	4	,	,	PUNCT
ejpam-6204	3	5	we	we	PRON
ejpam-6204	3	6	investigate	investigate	VERB
ejpam-6204	3	7	the	the	DET
ejpam-6204	3	8	concept	concept	NOUN
ejpam-6204	3	9	of	of	ADP
ejpam-6204	3	10	general	general	ADJ
ejpam-6204	3	11	deformations	deformation	NOUN
ejpam-6204	3	12	of	of	ADP
ejpam-6204	3	13	a	a	DET
ejpam-6204	3	14	spray	spray	NOUN
ejpam-6204	3	15	s	s	VERB
ejpam-6204	3	16	on	on	ADP
ejpam-6204	3	17	a	a	DET
ejpam-6204	3	18	manifoldm	manifoldm	NOUN
ejpam-6204	3	19	.	.	PUNCT
ejpam-6204	4	1	we	we	PRON
ejpam-6204	4	2	then	then	ADV
ejpam-6204	4	3	focus	focus	VERB
ejpam-6204	4	4	on	on	ADP
ejpam-6204	4	5	a	a	DET
ejpam-6204	4	6	specific	specific	ADJ
ejpam-6204	4	7	case	case	NOUN
ejpam-6204	4	8	,	,	PUNCT
ejpam-6204	4	9	which	which	PRON
ejpam-6204	4	10	we	we	PRON
ejpam-6204	4	11	call	call	VERB
ejpam-6204	4	12	a	a	DET
ejpam-6204	4	13	projective	projective	ADJ
ejpam-6204	4	14	-	-	PUNCT
ejpam-6204	4	15	like	like	ADJ
ejpam-6204	4	16	deformation	deformation	NOUN
ejpam-6204	4	17	.	.	PUNCT
ejpam-6204	5	1	this	this	DET
ejpam-6204	5	2	type	type	NOUN
ejpam-6204	5	3	of	of	ADP
ejpam-6204	5	4	deformation	deformation	NOUN
ejpam-6204	5	5	extends	extend	VERB
ejpam-6204	5	6	the	the	DET
ejpam-6204	5	7	notion	notion	NOUN
ejpam-6204	5	8	of	of	ADP
ejpam-6204	5	9	projective	projective	ADJ
ejpam-6204	5	10	deformation	deformation	NOUN
ejpam-6204	5	11	but	but	CCONJ
ejpam-6204	5	12	,	,	PUNCT
ejpam-6204	5	13	unlike	unlike	ADP
ejpam-6204	5	14	projective	projective	ADJ
ejpam-6204	5	15	deformation	deformation	NOUN
ejpam-6204	5	16	,	,	PUNCT
ejpam-6204	5	17	it	it	PRON
ejpam-6204	5	18	does	do	AUX
ejpam-6204	5	19	not	not	PART
ejpam-6204	5	20	necessarily	necessarily	ADV
ejpam-6204	5	21	preserve	preserve	VERB
ejpam-6204	5	22	geodesics	geodesic	NOUN
ejpam-6204	5	23	.	.	PUNCT
ejpam-6204	6	1	we	we	PRON
ejpam-6204	6	2	derive	derive	VERB
ejpam-6204	6	3	an	an	DET
ejpam-6204	6	4	explicit	explicit	ADJ
ejpam-6204	6	5	formula	formula	NOUN
ejpam-6204	6	6	for	for	ADP
ejpam-6204	6	7	the	the	DET
ejpam-6204	6	8	jacobi	jacobi	PROPN
ejpam-6204	6	9	endomorphism	endomorphism	PROPN
ejpam-6204	6	10	under	under	ADP
ejpam-6204	6	11	projective	projective	ADJ
ejpam-6204	6	12	-	-	PUNCT
ejpam-6204	6	13	like	like	ADJ
ejpam-6204	6	14	deformations	deformation	NOUN
ejpam-6204	6	15	and	and	CCONJ
ejpam-6204	6	16	analyze	analyze	VERB
ejpam-6204	6	17	the	the	DET
ejpam-6204	6	18	conditions	condition	NOUN
ejpam-6204	6	19	under	under	ADP
ejpam-6204	6	20	which	which	PRON
ejpam-6204	6	21	it	it	PRON
ejpam-6204	6	22	remains	remain	VERB
ejpam-6204	6	23	invariant	invariant	ADJ
ejpam-6204	6	24	.	.	PUNCT
ejpam-6204	7	1	as	as	ADP
ejpam-6204	7	2	applications	application	NOUN
ejpam-6204	7	3	,	,	PUNCT
ejpam-6204	7	4	we	we	PRON
ejpam-6204	7	5	consider	consider	VERB
ejpam-6204	7	6	(	(	PUNCT
ejpam-6204	7	7	α	α	NOUN
ejpam-6204	7	8	,	,	PUNCT
ejpam-6204	7	9	β)-metrics	β)-metrics	PUNCT
ejpam-6204	7	10	and	and	CCONJ
ejpam-6204	7	11	spherically	spherically	NOUN
ejpam-6204	7	12	symmetric	symmetric	ADJ
ejpam-6204	7	13	metrics	metric	NOUN
ejpam-6204	7	14	.	.	PUNCT
ejpam-6204	8	1	we	we	PRON
ejpam-6204	8	2	find	find	VERB
ejpam-6204	8	3	a	a	DET
ejpam-6204	8	4	necessary	necessary	ADJ
ejpam-6204	8	5	and	and	CCONJ
ejpam-6204	8	6	sufficient	sufficient	ADJ
ejpam-6204	8	7	condition	condition	NOUN
ejpam-6204	8	8	for	for	ADP
ejpam-6204	8	9	an	an	DET
ejpam-6204	8	10	(	(	PUNCT
ejpam-6204	8	11	α	α	NOUN
ejpam-6204	8	12	,	,	PUNCT
ejpam-6204	8	13	β)-metric	β)-metric	PUNCT
ejpam-6204	8	14	and	and	CCONJ
ejpam-6204	8	15	the	the	DET
ejpam-6204	8	16	riemannian	riemannian	ADJ
ejpam-6204	8	17	metric	metric	PROPN
ejpam-6204	8	18	α	α	PROPN
ejpam-6204	8	19	to	to	PART
ejpam-6204	8	20	be	be	AUX
ejpam-6204	8	21	projectively	projectively	ADV
ejpam-6204	8	22	related	relate	VERB
ejpam-6204	8	23	.	.	PUNCT
ejpam-6204	9	1	additionally	additionally	ADV
ejpam-6204	9	2	,	,	PUNCT
ejpam-6204	9	3	we	we	PRON
ejpam-6204	9	4	provide	provide	VERB
ejpam-6204	9	5	and	and	CCONJ
ejpam-6204	9	6	examine	examine	VERB
ejpam-6204	9	7	several	several	ADJ
ejpam-6204	9	8	explicit	explicit	ADJ
ejpam-6204	9	9	examples	example	NOUN
ejpam-6204	9	10	.	.	PUNCT
ejpam-6204	10	1	2020	2020	NUM
ejpam-6204	10	2	mathematics	mathematic	NOUN
ejpam-6204	10	3	subject	subject	NOUN
ejpam-6204	10	4	classifications	classification	NOUN
ejpam-6204	10	5	:	:	PUNCT
ejpam-6204	10	6	53c60	53c60	NUM
ejpam-6204	10	7	,	,	PUNCT
ejpam-6204	10	8	53b40	53b40	NUM
ejpam-6204	10	9	,	,	PUNCT
ejpam-6204	10	10	58b20	58b20	NUM
ejpam-6204	10	11	.	.	PUNCT
ejpam-6204	11	1	key	key	ADJ
ejpam-6204	11	2	words	word	NOUN
ejpam-6204	11	3	and	and	CCONJ
ejpam-6204	11	4	phrases	phrase	NOUN
ejpam-6204	11	5	:	:	PUNCT
ejpam-6204	11	6	sprays	spray	NOUN
ejpam-6204	11	7	,	,	PUNCT
ejpam-6204	11	8	projective	projective	ADJ
ejpam-6204	11	9	deformation	deformation	NOUN
ejpam-6204	11	10	,	,	PUNCT
ejpam-6204	11	11	projective	projective	ADJ
ejpam-6204	11	12	-	-	PUNCT
ejpam-6204	11	13	like	like	ADJ
ejpam-6204	11	14	deformation	deformation	NOUN
ejpam-6204	11	15	,	,	PUNCT
ejpam-6204	11	16	jacobi	jacobi	PROPN
ejpam-6204	11	17	endomorphism	endomorphism	PROPN
ejpam-6204	11	18	1	1	NUM
ejpam-6204	11	19	.	.	PUNCT
ejpam-6204	11	20	introduction	introduction	NOUN
ejpam-6204	11	21	in	in	ADP
ejpam-6204	11	22	finsler	finsler	NOUN
ejpam-6204	11	23	geometry	geometry	NOUN
ejpam-6204	11	24	,	,	PUNCT
ejpam-6204	11	25	the	the	DET
ejpam-6204	11	26	concepts	concept	NOUN
ejpam-6204	11	27	of	of	ADP
ejpam-6204	11	28	sprays	spray	NOUN
ejpam-6204	11	29	and	and	CCONJ
ejpam-6204	11	30	its	its	PRON
ejpam-6204	11	31	projective	projective	ADJ
ejpam-6204	11	32	deformation	deformation	NOUN
ejpam-6204	11	33	play	play	VERB
ejpam-6204	11	34	a	a	DET
ejpam-6204	11	35	crucial	crucial	ADJ
ejpam-6204	11	36	role	role	NOUN
ejpam-6204	11	37	in	in	ADP
ejpam-6204	11	38	understanding	understand	VERB
ejpam-6204	11	39	how	how	SCONJ
ejpam-6204	11	40	the	the	DET
ejpam-6204	11	41	geodesic	geodesic	ADJ
ejpam-6204	11	42	structure	structure	NOUN
ejpam-6204	11	43	of	of	ADP
ejpam-6204	11	44	a	a	DET
ejpam-6204	11	45	manifold	manifold	ADJ
ejpam-6204	11	46	changes	change	NOUN
ejpam-6204	11	47	under	under	ADP
ejpam-6204	11	48	transformations	transformation	NOUN
ejpam-6204	11	49	that	that	PRON
ejpam-6204	11	50	preserve	preserve	VERB
ejpam-6204	11	51	the	the	DET
ejpam-6204	11	52	projective	projective	ADJ
ejpam-6204	11	53	class	class	NOUN
ejpam-6204	11	54	of	of	ADP
ejpam-6204	11	55	paths	path	NOUN
ejpam-6204	11	56	.	.	PUNCT
ejpam-6204	12	1	a	a	DET
ejpam-6204	12	2	projective	projective	ADJ
ejpam-6204	12	3	deformation	deformation	NOUN
ejpam-6204	12	4	of	of	ADP
ejpam-6204	12	5	a	a	DET
ejpam-6204	12	6	spray	spray	NOUN
ejpam-6204	12	7	refers	refer	VERB
ejpam-6204	12	8	to	to	ADP
ejpam-6204	12	9	a	a	DET
ejpam-6204	12	10	modification	modification	NOUN
ejpam-6204	12	11	of	of	ADP
ejpam-6204	12	12	the	the	DET
ejpam-6204	12	13	spray	spray	NOUN
ejpam-6204	12	14	such	such	ADJ
ejpam-6204	12	15	that	that	SCONJ
ejpam-6204	12	16	the	the	DET
ejpam-6204	12	17	new	new	ADJ
ejpam-6204	12	18	spray	spray	NOUN
ejpam-6204	12	19	generates	generate	VERB
ejpam-6204	12	20	the	the	DET
ejpam-6204	12	21	same	same	ADJ
ejpam-6204	12	22	set	set	NOUN
ejpam-6204	12	23	of	of	ADP
ejpam-6204	12	24	unparameterized	unparameterized	ADJ
ejpam-6204	12	25	geodesics	geodesic	NOUN
ejpam-6204	12	26	as	as	ADP
ejpam-6204	12	27	the	the	DET
ejpam-6204	12	28	original	original	ADJ
ejpam-6204	12	29	one	one	NUM
ejpam-6204	12	30	.	.	PUNCT
ejpam-6204	13	1	this	this	DET
ejpam-6204	13	2	concept	concept	NOUN
ejpam-6204	13	3	is	be	AUX
ejpam-6204	13	4	closely	closely	ADV
ejpam-6204	13	5	related	relate	VERB
ejpam-6204	13	6	to	to	ADP
ejpam-6204	13	7	projective	projective	ADJ
ejpam-6204	13	8	geometry	geometry	NOUN
ejpam-6204	13	9	,	,	PUNCT
ejpam-6204	13	10	where	where	SCONJ
ejpam-6204	13	11	only	only	ADV
ejpam-6204	13	12	the	the	DET
ejpam-6204	13	13	direction	direction	NOUN
ejpam-6204	13	14	of	of	ADP
ejpam-6204	13	15	geodesics	geodesic	NOUN
ejpam-6204	13	16	matters	matter	VERB
ejpam-6204	13	17	rather	rather	ADV
ejpam-6204	13	18	than	than	ADP
ejpam-6204	13	19	their	their	PRON
ejpam-6204	13	20	specific	specific	ADJ
ejpam-6204	13	21	parameterization	parameterization	NOUN
ejpam-6204	13	22	.	.	PUNCT
ejpam-6204	14	1	for	for	ADP
ejpam-6204	14	2	example	example	NOUN
ejpam-6204	14	3	,	,	PUNCT
ejpam-6204	14	4	see	see	VERB
ejpam-6204	14	5	[	[	X
ejpam-6204	14	6	1–11	1–11	X
ejpam-6204	14	7	]	]	PUNCT
ejpam-6204	14	8	.	.	PUNCT
ejpam-6204	15	1	a	a	DET
ejpam-6204	15	2	projective	projective	ADJ
ejpam-6204	15	3	deformation	deformation	NOUN
ejpam-6204	15	4	[	[	X
ejpam-6204	15	5	5	5	NUM
ejpam-6204	15	6	,	,	PUNCT
ejpam-6204	15	7	7	7	NUM
ejpam-6204	15	8	,	,	PUNCT
ejpam-6204	15	9	10	10	NUM
ejpam-6204	15	10	,	,	PUNCT
ejpam-6204	15	11	12	12	NUM
ejpam-6204	15	12	]	]	PUNCT
ejpam-6204	15	13	of	of	ADP
ejpam-6204	15	14	s	s	PROPN
ejpam-6204	15	15	results	result	NOUN
ejpam-6204	15	16	in	in	ADP
ejpam-6204	15	17	a	a	DET
ejpam-6204	15	18	new	new	ADJ
ejpam-6204	15	19	spray	spray	NOUN
ejpam-6204	15	20	s	s	AUX
ejpam-6204	15	21	given	give	VERB
ejpam-6204	15	22	by	by	ADP
ejpam-6204	15	23	:	:	PUNCT
ejpam-6204	15	24	s	s	X
ejpam-6204	15	25	=	=	X
ejpam-6204	15	26	s	s	PART
ejpam-6204	15	27	−	−	PROPN
ejpam-6204	15	28	2p(x	2p(x	PROPN
ejpam-6204	15	29	,	,	PUNCT
ejpam-6204	15	30	y)c	y)c	NOUN
ejpam-6204	15	31	,	,	PUNCT
ejpam-6204	15	32	(	(	PUNCT
ejpam-6204	15	33	1	1	X
ejpam-6204	15	34	)	)	PUNCT
ejpam-6204	15	35	∗corresponding	∗corresponde	VERB
ejpam-6204	15	36	author	author	NOUN
ejpam-6204	15	37	.	.	PUNCT
ejpam-6204	16	1	doi	doi	NOUN
ejpam-6204	16	2	:	:	PUNCT
ejpam-6204	16	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6204	https://doi.org/10.29020/nybg.ejpam.v18i3.6204	NOUN
ejpam-6204	16	4	email	email	NOUN
ejpam-6204	16	5	addresses	address	NOUN
ejpam-6204	16	6	:	:	PUNCT
ejpam-6204	16	7	salah.ali@fsc.bu.edu.eg	salah.ali@fsc.bu.edu.eg	NUM
ejpam-6204	16	8	,	,	PUNCT
ejpam-6204	16	9	salahelgendi@yahoo.com	salahelgendi@yahoo.com	X
ejpam-6204	16	10	(	(	PUNCT
ejpam-6204	16	11	s.	s.	PROPN
ejpam-6204	16	12	g.	g.	PROPN
ejpam-6204	16	13	elgendi	elgendi	PROPN
ejpam-6204	16	14	)	)	PUNCT
ejpam-6204	16	15	,	,	PUNCT
ejpam-6204	16	16	asoliman@ju.edu.sa	asoliman@ju.edu.sa	PROPN
ejpam-6204	16	17	,	,	PUNCT
ejpam-6204	16	18	amrsoleiman@yahoo.com	amrsoleiman@yahoo.com	X
ejpam-6204	16	19	(	(	PUNCT
ejpam-6204	16	20	a.	a.	NOUN
ejpam-6204	16	21	soleiman	soleiman	PROPN
ejpam-6204	16	22	)	)	PUNCT
ejpam-6204	16	23	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6204	17	1	1	1	NUM
ejpam-6204	17	2	copyright	copyright	NOUN
ejpam-6204	17	3	:	:	PUNCT
ejpam-6204	17	4	©	©	PROPN
ejpam-6204	17	5	2025	2025	NUM
ejpam-6204	17	6	the	the	DET
ejpam-6204	17	7	author(s	author(s	NOUN
ejpam-6204	17	8	)	)	PUNCT
ejpam-6204	17	9	.	.	PUNCT
ejpam-6204	18	1	(	(	PUNCT
ejpam-6204	18	2	cc	cc	NOUN
ejpam-6204	18	3	by	by	ADP
ejpam-6204	18	4	-	-	PUNCT
ejpam-6204	18	5	nc	nc	PROPN
ejpam-6204	18	6	4.0	4.0	NUM
ejpam-6204	18	7	)	)	PUNCT
ejpam-6204	18	8	s.	s.	PROPN
ejpam-6204	18	9	g.	g.	PROPN
ejpam-6204	18	10	elgendi	elgendi	PROPN
ejpam-6204	18	11	,	,	PUNCT
ejpam-6204	18	12	a.	a.	NOUN
ejpam-6204	18	13	soleiman	soleiman	PROPN
ejpam-6204	18	14	/	/	SYM
ejpam-6204	18	15	eur	eur	PROPN
ejpam-6204	18	16	.	.	PUNCT
ejpam-6204	19	1	j.	j.	PROPN
ejpam-6204	19	2	pure	pure	PROPN
ejpam-6204	19	3	appl	appl	PROPN
ejpam-6204	19	4	.	.	PROPN
ejpam-6204	19	5	math	math	PROPN
ejpam-6204	19	6	,	,	PUNCT
ejpam-6204	19	7	18	18	NUM
ejpam-6204	19	8	(	(	PUNCT
ejpam-6204	19	9	3	3	NUM
ejpam-6204	19	10	)	)	PUNCT
ejpam-6204	19	11	(	(	PUNCT
ejpam-6204	19	12	2025	2025	NUM
ejpam-6204	19	13	)	)	PUNCT
ejpam-6204	19	14	,	,	PUNCT
ejpam-6204	19	15	6204	6204	NUM
ejpam-6204	19	16	2	2	NUM
ejpam-6204	19	17	of	of	ADP
ejpam-6204	19	18	18	18	NUM
ejpam-6204	19	19	where	where	SCONJ
ejpam-6204	19	20	p(x	p(x	PROPN
ejpam-6204	19	21	,	,	PUNCT
ejpam-6204	19	22	y	y	NOUN
ejpam-6204	19	23	)	)	PUNCT
ejpam-6204	19	24	is	be	AUX
ejpam-6204	19	25	a	a	DET
ejpam-6204	19	26	scalar	scalar	ADJ
ejpam-6204	19	27	function	function	NOUN
ejpam-6204	19	28	known	know	VERB
ejpam-6204	19	29	as	as	ADP
ejpam-6204	19	30	the	the	DET
ejpam-6204	19	31	projective	projective	ADJ
ejpam-6204	19	32	factor	factor	NOUN
ejpam-6204	19	33	,	,	PUNCT
ejpam-6204	19	34	and	and	CCONJ
ejpam-6204	19	35	c	c	NOUN
ejpam-6204	19	36	is	be	AUX
ejpam-6204	19	37	the	the	DET
ejpam-6204	19	38	canonical	canonical	ADJ
ejpam-6204	19	39	liouville	liouville	NOUN
ejpam-6204	19	40	vector	vector	NOUN
ejpam-6204	19	41	field	field	NOUN
ejpam-6204	19	42	.	.	PUNCT
ejpam-6204	20	1	this	this	DET
ejpam-6204	20	2	transformation	transformation	NOUN
ejpam-6204	20	3	ensures	ensure	VERB
ejpam-6204	20	4	that	that	SCONJ
ejpam-6204	20	5	the	the	DET
ejpam-6204	20	6	integral	integral	ADJ
ejpam-6204	20	7	curves	curve	NOUN
ejpam-6204	20	8	of	of	ADP
ejpam-6204	20	9	s	s	PRON
ejpam-6204	20	10	and	and	CCONJ
ejpam-6204	20	11	s	s	VERB
ejpam-6204	20	12	remain	remain	VERB
ejpam-6204	20	13	the	the	DET
ejpam-6204	20	14	same	same	ADJ
ejpam-6204	20	15	up	up	ADP
ejpam-6204	20	16	to	to	ADP
ejpam-6204	20	17	reparameterization	reparameterization	NOUN
ejpam-6204	20	18	,	,	PUNCT
ejpam-6204	20	19	meaning	mean	VERB
ejpam-6204	20	20	the	the	DET
ejpam-6204	20	21	geodesics	geodesic	NOUN
ejpam-6204	20	22	of	of	ADP
ejpam-6204	20	23	the	the	DET
ejpam-6204	20	24	manifold	manifold	NOUN
ejpam-6204	20	25	remain	remain	VERB
ejpam-6204	20	26	unchanged	unchanged	ADJ
ejpam-6204	20	27	as	as	ADP
ejpam-6204	20	28	point	point	NOUN
ejpam-6204	20	29	sets	set	NOUN
ejpam-6204	20	30	.	.	PUNCT
ejpam-6204	21	1	projective	projective	ADJ
ejpam-6204	21	2	deformations	deformation	NOUN
ejpam-6204	21	3	[	[	X
ejpam-6204	21	4	1	1	NUM
ejpam-6204	21	5	,	,	PUNCT
ejpam-6204	21	6	7	7	NUM
ejpam-6204	21	7	]	]	PUNCT
ejpam-6204	21	8	are	be	AUX
ejpam-6204	21	9	particularly	particularly	ADV
ejpam-6204	21	10	useful	useful	ADJ
ejpam-6204	21	11	in	in	ADP
ejpam-6204	21	12	finsler	finsler	NOUN
ejpam-6204	21	13	geometry	geometry	NOUN
ejpam-6204	21	14	for	for	ADP
ejpam-6204	21	15	studying	study	VERB
ejpam-6204	21	16	conditions	condition	NOUN
ejpam-6204	21	17	under	under	ADP
ejpam-6204	21	18	which	which	PRON
ejpam-6204	21	19	a	a	DET
ejpam-6204	21	20	given	give	VERB
ejpam-6204	21	21	finsler	finsler	NOUN
ejpam-6204	21	22	metric	metric	NOUN
ejpam-6204	21	23	can	can	AUX
ejpam-6204	21	24	be	be	AUX
ejpam-6204	21	25	related	relate	VERB
ejpam-6204	21	26	to	to	ADP
ejpam-6204	21	27	another	another	DET
ejpam-6204	21	28	one	one	NOUN
ejpam-6204	21	29	via	via	ADP
ejpam-6204	21	30	projectively	projectively	ADV
ejpam-6204	21	31	equivalent	equivalent	ADJ
ejpam-6204	21	32	sprays	spray	NOUN
ejpam-6204	21	33	.	.	PUNCT
ejpam-6204	22	1	these	these	DET
ejpam-6204	22	2	transformations	transformation	NOUN
ejpam-6204	22	3	are	be	AUX
ejpam-6204	22	4	fundamental	fundamental	ADJ
ejpam-6204	22	5	in	in	ADP
ejpam-6204	22	6	various	various	ADJ
ejpam-6204	22	7	areas	area	NOUN
ejpam-6204	22	8	,	,	PUNCT
ejpam-6204	22	9	including	include	VERB
ejpam-6204	22	10	the	the	DET
ejpam-6204	22	11	study	study	NOUN
ejpam-6204	22	12	of	of	ADP
ejpam-6204	22	13	curvature	curvature	NOUN
ejpam-6204	22	14	properties	property	NOUN
ejpam-6204	22	15	,	,	PUNCT
ejpam-6204	22	16	and	and	CCONJ
ejpam-6204	22	17	projective	projective	ADJ
ejpam-6204	22	18	flatness	flatness	NOUN
ejpam-6204	22	19	.	.	PUNCT
ejpam-6204	23	1	the	the	DET
ejpam-6204	23	2	theory	theory	NOUN
ejpam-6204	23	3	of	of	ADP
ejpam-6204	23	4	projective	projective	ADJ
ejpam-6204	23	5	changes	change	NOUN
ejpam-6204	23	6	in	in	ADP
ejpam-6204	23	7	riemannian	riemannian	ADJ
ejpam-6204	23	8	geometry	geometry	NOUN
ejpam-6204	23	9	has	have	AUX
ejpam-6204	23	10	been	be	AUX
ejpam-6204	23	11	deeply	deeply	ADV
ejpam-6204	23	12	studied	study	VERB
ejpam-6204	23	13	(	(	PUNCT
ejpam-6204	23	14	locally	locally	ADV
ejpam-6204	23	15	and	and	CCONJ
ejpam-6204	23	16	intrinsically	intrinsically	ADV
ejpam-6204	23	17	)	)	PUNCT
ejpam-6204	23	18	by	by	ADP
ejpam-6204	23	19	many	many	ADJ
ejpam-6204	23	20	authors	author	NOUN
ejpam-6204	23	21	.	.	PUNCT
ejpam-6204	24	1	as	as	SCONJ
ejpam-6204	24	2	regards	regard	NOUN
ejpam-6204	24	3	to	to	ADP
ejpam-6204	24	4	finsler	finsler	NOUN
ejpam-6204	24	5	geometry	geometry	NOUN
ejpam-6204	24	6	,	,	PUNCT
ejpam-6204	24	7	a	a	DET
ejpam-6204	24	8	complete	complete	ADJ
ejpam-6204	24	9	local	local	ADJ
ejpam-6204	24	10	theory	theory	NOUN
ejpam-6204	24	11	of	of	ADP
ejpam-6204	24	12	projective	projective	ADJ
ejpam-6204	24	13	changes	change	NOUN
ejpam-6204	24	14	has	have	AUX
ejpam-6204	24	15	been	be	AUX
ejpam-6204	24	16	established	establish	VERB
ejpam-6204	24	17	(	(	PUNCT
ejpam-6204	24	18	[	[	X
ejpam-6204	24	19	5	5	NUM
ejpam-6204	24	20	,	,	PUNCT
ejpam-6204	24	21	7	7	NUM
ejpam-6204	24	22	,	,	PUNCT
ejpam-6204	24	23	8	8	NUM
ejpam-6204	24	24	,	,	PUNCT
ejpam-6204	24	25	13	13	NUM
ejpam-6204	24	26	,	,	PUNCT
ejpam-6204	24	27	14	14	NUM
ejpam-6204	24	28	]	]	PUNCT
ejpam-6204	24	29	)	)	PUNCT
ejpam-6204	24	30	.	.	PUNCT
ejpam-6204	25	1	moreover	moreover	ADV
ejpam-6204	25	2	,	,	PUNCT
ejpam-6204	25	3	an	an	DET
ejpam-6204	25	4	intrinsic	intrinsic	ADJ
ejpam-6204	25	5	theory	theory	NOUN
ejpam-6204	25	6	of	of	ADP
ejpam-6204	25	7	projective	projective	ADJ
ejpam-6204	25	8	changes	change	NOUN
ejpam-6204	25	9	(	(	PUNCT
ejpam-6204	25	10	resp	resp	NOUN
ejpam-6204	25	11	.	.	PUNCT
ejpam-6204	26	1	semi	semi	ADJ
ejpam-6204	26	2	-	-	ADJ
ejpam-6204	26	3	projective	projective	ADJ
ejpam-6204	26	4	changes	change	NOUN
ejpam-6204	26	5	)	)	PUNCT
ejpam-6204	26	6	has	have	AUX
ejpam-6204	26	7	been	be	AUX
ejpam-6204	26	8	investigated	investigate	VERB
ejpam-6204	26	9	in	in	ADP
ejpam-6204	26	10	[	[	X
ejpam-6204	26	11	10	10	NUM
ejpam-6204	26	12	,	,	PUNCT
ejpam-6204	26	13	15	15	NUM
ejpam-6204	26	14	]	]	PUNCT
ejpam-6204	26	15	)	)	PUNCT
ejpam-6204	26	16	following	follow	VERB
ejpam-6204	26	17	the	the	DET
ejpam-6204	26	18	kg	kg	NOUN
ejpam-6204	26	19	-	-	NOUN
ejpam-6204	26	20	approach	approach	NOUN
ejpam-6204	26	21	.	.	PUNCT
ejpam-6204	27	1	in	in	ADP
ejpam-6204	27	2	this	this	DET
ejpam-6204	27	3	paper	paper	NOUN
ejpam-6204	27	4	,	,	PUNCT
ejpam-6204	27	5	considering	consider	VERB
ejpam-6204	27	6	two	two	NUM
ejpam-6204	27	7	sprays	spray	NOUN
ejpam-6204	27	8	s1	s1	NOUN
ejpam-6204	27	9	and	and	CCONJ
ejpam-6204	27	10	s2	s2	NOUN
ejpam-6204	27	11	on	on	ADP
ejpam-6204	27	12	a	a	DET
ejpam-6204	27	13	manifold	manifold	ADJ
ejpam-6204	27	14	m	m	NOUN
ejpam-6204	27	15	,	,	PUNCT
ejpam-6204	27	16	and	and	CCONJ
ejpam-6204	27	17	using	use	VERB
ejpam-6204	27	18	the	the	DET
ejpam-6204	27	19	fact	fact	NOUN
ejpam-6204	27	20	that	that	SCONJ
ejpam-6204	27	21	that	that	SCONJ
ejpam-6204	27	22	the	the	DET
ejpam-6204	27	23	difference	difference	NOUN
ejpam-6204	27	24	s1	s1	NOUN
ejpam-6204	27	25	−	−	PROPN
ejpam-6204	27	26	s2	s2	NOUN
ejpam-6204	27	27	is	be	AUX
ejpam-6204	27	28	always	always	ADV
ejpam-6204	27	29	vertical	vertical	ADJ
ejpam-6204	27	30	,	,	PUNCT
ejpam-6204	27	31	we	we	PRON
ejpam-6204	27	32	introduce	introduce	VERB
ejpam-6204	27	33	the	the	DET
ejpam-6204	27	34	general	general	ADJ
ejpam-6204	27	35	deformation	deformation	NOUN
ejpam-6204	27	36	of	of	ADP
ejpam-6204	27	37	a	a	DET
ejpam-6204	27	38	spray	spray	NOUN
ejpam-6204	27	39	s	s	PRON
ejpam-6204	27	40	as	as	SCONJ
ejpam-6204	27	41	follows	follow	VERB
ejpam-6204	27	42	:	:	PUNCT
ejpam-6204	27	43	s̃	s̃	PROPN
ejpam-6204	27	44	=	=	SYM
ejpam-6204	27	45	s	s	PART
ejpam-6204	27	46	−	−	NOUN
ejpam-6204	27	47	2ζ	2ζ	NOUN
ejpam-6204	27	48	,	,	PUNCT
ejpam-6204	27	49	where	where	SCONJ
ejpam-6204	27	50	ζ	ζ	NOUN
ejpam-6204	27	51	is	be	AUX
ejpam-6204	27	52	a	a	DET
ejpam-6204	27	53	vertical	vertical	ADJ
ejpam-6204	27	54	vector	vector	NOUN
ejpam-6204	27	55	field	field	NOUN
ejpam-6204	27	56	ζ	ζ	NOUN
ejpam-6204	27	57	∈	∈	PROPN
ejpam-6204	27	58	xv(tm	xv(tm	PROPN
ejpam-6204	27	59	)	)	PUNCT
ejpam-6204	27	60	.	.	PUNCT
ejpam-6204	28	1	then	then	ADV
ejpam-6204	28	2	,	,	PUNCT
ejpam-6204	28	3	we	we	PRON
ejpam-6204	28	4	focus	focus	VERB
ejpam-6204	28	5	our	our	PRON
ejpam-6204	28	6	attentions	attention	NOUN
ejpam-6204	28	7	to	to	ADP
ejpam-6204	28	8	an	an	DET
ejpam-6204	28	9	interesting	interesting	ADJ
ejpam-6204	28	10	special	special	ADJ
ejpam-6204	28	11	case	case	NOUN
ejpam-6204	28	12	.	.	PUNCT
ejpam-6204	29	1	that	that	PRON
ejpam-6204	29	2	is	is	ADV
ejpam-6204	29	3	,	,	PUNCT
ejpam-6204	29	4	we	we	PRON
ejpam-6204	29	5	introduce	introduce	VERB
ejpam-6204	29	6	what	what	PRON
ejpam-6204	29	7	we	we	PRON
ejpam-6204	29	8	called	call	VERB
ejpam-6204	29	9	projective	projective	ADJ
ejpam-6204	29	10	-	-	PUNCT
ejpam-6204	29	11	like	like	ADJ
ejpam-6204	29	12	deformation	deformation	NOUN
ejpam-6204	29	13	.	.	PUNCT
ejpam-6204	30	1	precisely	precisely	ADV
ejpam-6204	30	2	,	,	PUNCT
ejpam-6204	30	3	let	let	VERB
ejpam-6204	30	4	s	s	PRON
ejpam-6204	30	5	be	be	AUX
ejpam-6204	30	6	a	a	DET
ejpam-6204	30	7	spray	spray	NOUN
ejpam-6204	30	8	on	on	ADP
ejpam-6204	30	9	a	a	DET
ejpam-6204	30	10	manifold	manifold	ADJ
ejpam-6204	30	11	m	m	NOUN
ejpam-6204	30	12	,	,	PUNCT
ejpam-6204	30	13	and	and	CCONJ
ejpam-6204	30	14	consider	consider	VERB
ejpam-6204	30	15	any	any	DET
ejpam-6204	30	16	vertical	vertical	ADJ
ejpam-6204	30	17	vector	vector	NOUN
ejpam-6204	30	18	field	field	NOUN
ejpam-6204	30	19	ξ	ξ	PROPN
ejpam-6204	30	20	∈	∈	PROPN
ejpam-6204	30	21	xv(tm	xv(tm	PROPN
ejpam-6204	30	22	)	)	PUNCT
ejpam-6204	30	23	.	.	PUNCT
ejpam-6204	31	1	the	the	DET
ejpam-6204	31	2	projective	projective	NOUN
ejpam-6204	31	3	-	-	PUNCT
ejpam-6204	31	4	like	like	ADJ
ejpam-6204	31	5	deformation	deformation	NOUN
ejpam-6204	31	6	of	of	ADP
ejpam-6204	31	7	s	s	PRON
ejpam-6204	31	8	is	be	AUX
ejpam-6204	31	9	given	give	VERB
ejpam-6204	31	10	by	by	ADP
ejpam-6204	31	11	s̃	s̃	PROPN
ejpam-6204	31	12	=	=	SYM
ejpam-6204	31	13	s	s	PART
ejpam-6204	31	14	−	−	PROPN
ejpam-6204	31	15	2p(x	2p(x	PROPN
ejpam-6204	31	16	,	,	PUNCT
ejpam-6204	31	17	y)ξ	y)ξ	NOUN
ejpam-6204	31	18	,	,	PUNCT
ejpam-6204	31	19	where	where	SCONJ
ejpam-6204	31	20	p(x	p(x	PROPN
ejpam-6204	31	21	,	,	PUNCT
ejpam-6204	31	22	y	y	NOUN
ejpam-6204	31	23	)	)	PUNCT
ejpam-6204	31	24	∈	∈	PROPN
ejpam-6204	31	25	c∞(t	c∞(t	PROPN
ejpam-6204	31	26	m	m	NOUN
ejpam-6204	31	27	)	)	PUNCT
ejpam-6204	31	28	is	be	AUX
ejpam-6204	31	29	a	a	DET
ejpam-6204	31	30	smooth	smooth	ADJ
ejpam-6204	31	31	,	,	PUNCT
ejpam-6204	31	32	and	and	CCONJ
ejpam-6204	31	33	positively	positively	ADV
ejpam-6204	31	34	homogeneous	homogeneous	ADJ
ejpam-6204	31	35	function	function	NOUN
ejpam-6204	31	36	of	of	ADP
ejpam-6204	31	37	degree	degree	NOUN
ejpam-6204	31	38	1	1	NUM
ejpam-6204	31	39	in	in	ADP
ejpam-6204	31	40	y	y	PROPN
ejpam-6204	31	41	,	,	PUNCT
ejpam-6204	31	42	and	and	CCONJ
ejpam-6204	31	43	called	call	VERB
ejpam-6204	31	44	the	the	DET
ejpam-6204	31	45	deformation	deformation	NOUN
ejpam-6204	31	46	factor	factor	NOUN
ejpam-6204	31	47	.	.	PUNCT
ejpam-6204	32	1	we	we	PRON
ejpam-6204	32	2	consider	consider	VERB
ejpam-6204	32	3	two	two	NUM
ejpam-6204	32	4	special	special	ADJ
ejpam-6204	32	5	classes	class	NOUN
ejpam-6204	32	6	of	of	ADP
ejpam-6204	32	7	finsler	finsler	NOUN
ejpam-6204	32	8	metrics	metric	NOUN
ejpam-6204	32	9	,	,	PUNCT
ejpam-6204	32	10	namely	namely	ADV
ejpam-6204	32	11	,	,	PUNCT
ejpam-6204	32	12	the	the	DET
ejpam-6204	32	13	class	class	NOUN
ejpam-6204	32	14	of	of	ADP
ejpam-6204	32	15	(	(	PUNCT
ejpam-6204	32	16	α	α	NOUN
ejpam-6204	32	17	,	,	PUNCT
ejpam-6204	32	18	β)-metrics	β)-metrics	PUNCT
ejpam-6204	32	19	and	and	CCONJ
ejpam-6204	32	20	the	the	DET
ejpam-6204	32	21	class	class	NOUN
ejpam-6204	32	22	of	of	ADP
ejpam-6204	32	23	spherically	spherically	NOUN
ejpam-6204	32	24	symmetric	symmetric	ADJ
ejpam-6204	32	25	metrics	metric	NOUN
ejpam-6204	32	26	.	.	PUNCT
ejpam-6204	33	1	for	for	ADP
ejpam-6204	33	2	these	these	DET
ejpam-6204	33	3	classes	class	NOUN
ejpam-6204	33	4	,	,	PUNCT
ejpam-6204	33	5	we	we	PRON
ejpam-6204	33	6	figure	figure	VERB
ejpam-6204	33	7	out	out	ADP
ejpam-6204	33	8	the	the	DET
ejpam-6204	33	9	relation	relation	NOUN
ejpam-6204	33	10	between	between	ADP
ejpam-6204	33	11	the	the	DET
ejpam-6204	33	12	background	background	NOUN
ejpam-6204	33	13	spray	spray	NOUN
ejpam-6204	33	14	and	and	CCONJ
ejpam-6204	33	15	the	the	DET
ejpam-6204	33	16	new	new	ADJ
ejpam-6204	33	17	one	one	NOUN
ejpam-6204	33	18	showing	show	VERB
ejpam-6204	33	19	the	the	DET
ejpam-6204	33	20	explicit	explicit	ADJ
ejpam-6204	33	21	formula	formula	NOUN
ejpam-6204	33	22	of	of	ADP
ejpam-6204	33	23	the	the	DET
ejpam-6204	33	24	vertical	vertical	ADJ
ejpam-6204	33	25	vector	vector	NOUN
ejpam-6204	33	26	which	which	PRON
ejpam-6204	33	27	identifies	identify	VERB
ejpam-6204	33	28	the	the	DET
ejpam-6204	33	29	difference	difference	NOUN
ejpam-6204	33	30	between	between	ADP
ejpam-6204	33	31	the	the	DET
ejpam-6204	33	32	two	two	NUM
ejpam-6204	33	33	sprays	spray	NOUN
ejpam-6204	33	34	.	.	PUNCT
ejpam-6204	34	1	moreover	moreover	ADV
ejpam-6204	34	2	,	,	PUNCT
ejpam-6204	34	3	as	as	ADP
ejpam-6204	34	4	by	by	ADP
ejpam-6204	34	5	-	-	PUNCT
ejpam-6204	34	6	product	product	NOUN
ejpam-6204	34	7	,	,	PUNCT
ejpam-6204	34	8	we	we	PRON
ejpam-6204	34	9	discuss	discuss	VERB
ejpam-6204	34	10	when	when	SCONJ
ejpam-6204	34	11	the	the	DET
ejpam-6204	34	12	background	background	NOUN
ejpam-6204	34	13	spray	spray	VERB
ejpam-6204	34	14	and	and	CCONJ
ejpam-6204	34	15	new	new	ADJ
ejpam-6204	34	16	one	one	NOUN
ejpam-6204	34	17	are	be	AUX
ejpam-6204	34	18	projective	projective	ADJ
ejpam-6204	34	19	.	.	PUNCT
ejpam-6204	35	1	for	for	ADP
ejpam-6204	35	2	example	example	NOUN
ejpam-6204	35	3	,	,	PUNCT
ejpam-6204	35	4	for	for	ADP
ejpam-6204	35	5	an	an	DET
ejpam-6204	35	6	(	(	PUNCT
ejpam-6204	35	7	α	α	NOUN
ejpam-6204	35	8	,	,	PUNCT
ejpam-6204	35	9	β)-metric	β)-metric	PUNCT
ejpam-6204	35	10	f	f	NOUN
ejpam-6204	35	11	=	=	PUNCT
ejpam-6204	35	12	αϕ(s	αϕ(s	PROPN
ejpam-6204	35	13	)	)	PUNCT
ejpam-6204	35	14	,	,	PUNCT
ejpam-6204	35	15	then	then	ADV
ejpam-6204	35	16	the	the	DET
ejpam-6204	35	17	associated	associated	ADJ
ejpam-6204	35	18	sprays	spray	NOUN
ejpam-6204	35	19	with	with	ADP
ejpam-6204	35	20	f	f	PROPN
ejpam-6204	35	21	and	and	CCONJ
ejpam-6204	35	22	the	the	DET
ejpam-6204	35	23	riemannian	riemannian	ADJ
ejpam-6204	35	24	metric	metric	PROPN
ejpam-6204	35	25	α	α	PROPN
ejpam-6204	35	26	are	be	AUX
ejpam-6204	35	27	projectively	projectively	ADV
ejpam-6204	35	28	related	relate	VERB
ejpam-6204	35	29	if	if	SCONJ
ejpam-6204	35	30	and	and	CCONJ
ejpam-6204	35	31	only	only	ADV
ejpam-6204	35	32	if	if	SCONJ
ejpam-6204	35	33	2αϕ′si0	2αϕ′si0	NUM
ejpam-6204	35	34	+	+	NUM
ejpam-6204	35	35	r00ϕ	r00ϕ	PROPN
ejpam-6204	35	36	′′bi	′′bi	PROPN
ejpam-6204	35	37	−	−	PROPN
ejpam-6204	35	38	r00ϕ	r00ϕ	VERB
ejpam-6204	36	1	′′	′′	PROPN
ejpam-6204	36	2	β	β	PROPN
ejpam-6204	36	3	α2	α2	PROPN
ejpam-6204	36	4	yi	yi	PROPN
ejpam-6204	36	5	=	=	PUNCT
ejpam-6204	36	6	0	0	X
ejpam-6204	36	7	.	.	PUNCT
ejpam-6204	37	1	under	under	ADP
ejpam-6204	37	2	the	the	DET
ejpam-6204	37	3	projective	projective	ADJ
ejpam-6204	37	4	-	-	PUNCT
ejpam-6204	37	5	like	like	ADJ
ejpam-6204	37	6	deformation	deformation	NOUN
ejpam-6204	37	7	,	,	PUNCT
ejpam-6204	37	8	we	we	PRON
ejpam-6204	37	9	establish	establish	VERB
ejpam-6204	37	10	the	the	DET
ejpam-6204	37	11	relation	relation	NOUN
ejpam-6204	37	12	between	between	ADP
ejpam-6204	37	13	the	the	DET
ejpam-6204	37	14	two	two	NUM
ejpam-6204	37	15	associated	associated	ADJ
ejpam-6204	37	16	jacobi	jacobi	PROPN
ejpam-6204	37	17	endomorphisms	endomorphism	NOUN
ejpam-6204	37	18	.	.	PUNCT
ejpam-6204	38	1	moreover	moreover	ADV
ejpam-6204	38	2	,	,	PUNCT
ejpam-6204	38	3	we	we	PRON
ejpam-6204	38	4	discuss	discuss	VERB
ejpam-6204	38	5	the	the	DET
ejpam-6204	38	6	invariance	invariance	NOUN
ejpam-6204	38	7	property	property	NOUN
ejpam-6204	38	8	of	of	ADP
ejpam-6204	38	9	the	the	DET
ejpam-6204	38	10	jacobi	jacobi	PROPN
ejpam-6204	38	11	endomorphism	endomorphism	PROPN
ejpam-6204	38	12	.	.	PUNCT
ejpam-6204	39	1	some	some	DET
ejpam-6204	39	2	explicit	explicit	ADJ
ejpam-6204	39	3	examples	example	NOUN
ejpam-6204	39	4	are	be	AUX
ejpam-6204	39	5	studied	study	VERB
ejpam-6204	39	6	.	.	PUNCT
ejpam-6204	40	1	s.	s.	PROPN
ejpam-6204	40	2	g.	g.	PROPN
ejpam-6204	40	3	elgendi	elgendi	PROPN
ejpam-6204	40	4	,	,	PUNCT
ejpam-6204	40	5	a.	a.	NOUN
ejpam-6204	40	6	soleiman	soleiman	PROPN
ejpam-6204	40	7	/	/	SYM
ejpam-6204	40	8	eur	eur	PROPN
ejpam-6204	40	9	.	.	PUNCT
ejpam-6204	41	1	j.	j.	PROPN
ejpam-6204	41	2	pure	pure	PROPN
ejpam-6204	41	3	appl	appl	PROPN
ejpam-6204	41	4	.	.	PROPN
ejpam-6204	41	5	math	math	PROPN
ejpam-6204	41	6	,	,	PUNCT
ejpam-6204	41	7	18	18	NUM
ejpam-6204	41	8	(	(	PUNCT
ejpam-6204	41	9	3	3	NUM
ejpam-6204	41	10	)	)	PUNCT
ejpam-6204	41	11	(	(	PUNCT
ejpam-6204	41	12	2025	2025	NUM
ejpam-6204	41	13	)	)	PUNCT
ejpam-6204	41	14	,	,	PUNCT
ejpam-6204	41	15	6204	6204	NUM
ejpam-6204	41	16	3	3	NUM
ejpam-6204	41	17	of	of	ADP
ejpam-6204	41	18	18	18	NUM
ejpam-6204	41	19	2	2	NUM
ejpam-6204	41	20	.	.	PUNCT
ejpam-6204	42	1	preliminaries	preliminary	NOUN
ejpam-6204	42	2	let	let	VERB
ejpam-6204	42	3	m	m	PRON
ejpam-6204	42	4	be	be	AUX
ejpam-6204	42	5	an	an	DET
ejpam-6204	42	6	n	n	ADV
ejpam-6204	42	7	-	-	PUNCT
ejpam-6204	42	8	dimensional	dimensional	ADJ
ejpam-6204	42	9	differentiable	differentiable	ADJ
ejpam-6204	42	10	manifold	manifold	NOUN
ejpam-6204	42	11	with	with	ADP
ejpam-6204	42	12	its	its	PRON
ejpam-6204	42	13	tangent	tangent	NOUN
ejpam-6204	42	14	bundle	bundle	NOUN
ejpam-6204	42	15	represented	represent	VERB
ejpam-6204	42	16	by	by	ADP
ejpam-6204	42	17	(	(	PUNCT
ejpam-6204	42	18	tm	tm	PROPN
ejpam-6204	42	19	,	,	PUNCT
ejpam-6204	42	20	πm	πm	INTJ
ejpam-6204	42	21	,	,	PUNCT
ejpam-6204	42	22	m	m	NOUN
ejpam-6204	42	23	)	)	PUNCT
ejpam-6204	42	24	,	,	PUNCT
ejpam-6204	42	25	and	and	CCONJ
ejpam-6204	42	26	let	let	VERB
ejpam-6204	42	27	(	(	PUNCT
ejpam-6204	42	28	t	t	NOUN
ejpam-6204	42	29	m	m	PROPN
ejpam-6204	42	30	,	,	PUNCT
ejpam-6204	42	31	π	π	PROPN
ejpam-6204	42	32	,	,	PUNCT
ejpam-6204	42	33	m	m	NOUN
ejpam-6204	42	34	)	)	PUNCT
ejpam-6204	42	35	denote	denote	VERB
ejpam-6204	42	36	the	the	DET
ejpam-6204	42	37	subbundle	subbundle	NOUN
ejpam-6204	42	38	comprising	comprise	VERB
ejpam-6204	42	39	nonzero	nonzero	PROPN
ejpam-6204	42	40	tangent	tangent	ADJ
ejpam-6204	42	41	vectors	vector	NOUN
ejpam-6204	42	42	.	.	PUNCT
ejpam-6204	43	1	the	the	DET
ejpam-6204	43	2	local	local	ADJ
ejpam-6204	43	3	coordinates	coordinate	NOUN
ejpam-6204	43	4	onm	onm	NOUN
ejpam-6204	43	5	are	be	AUX
ejpam-6204	43	6	expressed	express	VERB
ejpam-6204	43	7	as	as	ADP
ejpam-6204	43	8	(	(	PUNCT
ejpam-6204	43	9	xi	xi	PROPN
ejpam-6204	43	10	)	)	PUNCT
ejpam-6204	43	11	,	,	PUNCT
ejpam-6204	43	12	while	while	SCONJ
ejpam-6204	43	13	the	the	DET
ejpam-6204	43	14	associated	associated	ADJ
ejpam-6204	43	15	coordinates	coordinate	NOUN
ejpam-6204	43	16	on	on	ADP
ejpam-6204	43	17	tm	tm	PROPN
ejpam-6204	43	18	are	be	AUX
ejpam-6204	43	19	(	(	PUNCT
ejpam-6204	43	20	xi	xi	PROPN
ejpam-6204	43	21	,	,	PUNCT
ejpam-6204	43	22	yi	yi	PROPN
ejpam-6204	43	23	)	)	PUNCT
ejpam-6204	43	24	,	,	PUNCT
ejpam-6204	43	25	where	where	SCONJ
ejpam-6204	43	26	yi	yi	PROPN
ejpam-6204	43	27	are	be	AUX
ejpam-6204	43	28	the	the	DET
ejpam-6204	43	29	components	component	NOUN
ejpam-6204	43	30	of	of	ADP
ejpam-6204	43	31	the	the	DET
ejpam-6204	43	32	tangent	tangent	ADJ
ejpam-6204	43	33	vectors	vector	NOUN
ejpam-6204	43	34	.	.	PUNCT
ejpam-6204	44	1	the	the	DET
ejpam-6204	44	2	tangent	tangent	PROPN
ejpam-6204	44	3	bundle	bundle	PROPN
ejpam-6204	44	4	tm	tm	PROPN
ejpam-6204	44	5	is	be	AUX
ejpam-6204	44	6	naturally	naturally	ADV
ejpam-6204	44	7	equipped	equip	VERB
ejpam-6204	44	8	with	with	ADP
ejpam-6204	44	9	an	an	DET
ejpam-6204	44	10	almost	almost	ADV
ejpam-6204	44	11	-	-	PUNCT
ejpam-6204	44	12	tangent	tangent	ADJ
ejpam-6204	44	13	structure	structure	NOUN
ejpam-6204	44	14	j	j	PROPN
ejpam-6204	44	15	,	,	PUNCT
ejpam-6204	44	16	locally	locally	ADV
ejpam-6204	44	17	given	give	VERB
ejpam-6204	44	18	by	by	ADP
ejpam-6204	44	19	j	j	PROPN
ejpam-6204	44	20	=	=	SYM
ejpam-6204	44	21	∂	∂	PROPN
ejpam-6204	44	22	∂yi	∂yi	PROPN
ejpam-6204	44	23	⊗	⊗	PROPN
ejpam-6204	44	24	dxi	dxi	PROPN
ejpam-6204	44	25	.	.	PUNCT
ejpam-6204	45	1	let	let	VERB
ejpam-6204	45	2	’s	’s	NOUN
ejpam-6204	45	3	recall	recall	VERB
ejpam-6204	45	4	some	some	DET
ejpam-6204	45	5	basics	basic	NOUN
ejpam-6204	45	6	and	and	CCONJ
ejpam-6204	45	7	properties	property	NOUN
ejpam-6204	45	8	of	of	ADP
ejpam-6204	45	9	the	the	DET
ejpam-6204	45	10	klein	klein	PROPN
ejpam-6204	45	11	-	-	PUNCT
ejpam-6204	45	12	grifone	grifone	ADJ
ejpam-6204	45	13	approach	approach	NOUN
ejpam-6204	45	14	to	to	ADP
ejpam-6204	45	15	finsler	finsler	NOUN
ejpam-6204	45	16	geometry	geometry	NOUN
ejpam-6204	45	17	.	.	PUNCT
ejpam-6204	46	1	the	the	DET
ejpam-6204	46	2	canonical	canonical	ADJ
ejpam-6204	46	3	(	(	PUNCT
ejpam-6204	46	4	or	or	CCONJ
ejpam-6204	46	5	liouville	liouville	NOUN
ejpam-6204	46	6	)	)	PUNCT
ejpam-6204	46	7	vector	vector	NOUN
ejpam-6204	46	8	field	field	NOUN
ejpam-6204	46	9	c	c	PROPN
ejpam-6204	46	10	on	on	ADP
ejpam-6204	46	11	tm	tm	PROPN
ejpam-6204	46	12	is	be	AUX
ejpam-6204	46	13	a	a	DET
ejpam-6204	46	14	vertical	vertical	ADJ
ejpam-6204	46	15	vector	vector	NOUN
ejpam-6204	46	16	field	field	NOUN
ejpam-6204	46	17	defined	define	VERB
ejpam-6204	46	18	as	as	ADP
ejpam-6204	46	19	:	:	PUNCT
ejpam-6204	46	20	c	c	NOUN
ejpam-6204	46	21	=	=	SYM
ejpam-6204	46	22	yi	yi	PROPN
ejpam-6204	46	23	∂	∂	NOUN
ejpam-6204	46	24	∂yi	∂yi	PROPN
ejpam-6204	46	25	.	.	PUNCT
ejpam-6204	47	1	(	(	PUNCT
ejpam-6204	47	2	2	2	X
ejpam-6204	47	3	)	)	PUNCT
ejpam-6204	47	4	more	more	ADJ
ejpam-6204	47	5	details	detail	NOUN
ejpam-6204	47	6	can	can	AUX
ejpam-6204	47	7	be	be	AUX
ejpam-6204	47	8	found	find	VERB
ejpam-6204	47	9	in	in	ADP
ejpam-6204	47	10	[	[	X
ejpam-6204	47	11	1	1	NUM
ejpam-6204	47	12	,	,	PUNCT
ejpam-6204	47	13	9	9	NUM
ejpam-6204	47	14	,	,	PUNCT
ejpam-6204	47	15	16	16	NUM
ejpam-6204	47	16	]	]	PUNCT
ejpam-6204	47	17	.	.	PUNCT
ejpam-6204	48	1	a	a	DET
ejpam-6204	48	2	spray	spray	NOUN
ejpam-6204	48	3	s	s	VERB
ejpam-6204	48	4	is	be	AUX
ejpam-6204	48	5	a	a	DET
ejpam-6204	48	6	vector	vector	NOUN
ejpam-6204	48	7	field	field	NOUN
ejpam-6204	48	8	s	s	PART
ejpam-6204	48	9	∈	∈	NOUN
ejpam-6204	48	10	x(t	x(t	PROPN
ejpam-6204	48	11	m	m	NOUN
ejpam-6204	48	12	)	)	PUNCT
ejpam-6204	48	13	that	that	PRON
ejpam-6204	48	14	satisfies	satisfy	VERB
ejpam-6204	48	15	js	js	PROPN
ejpam-6204	48	16	=	=	SYM
ejpam-6204	48	17	c	c	PROPN
ejpam-6204	48	18	and	and	CCONJ
ejpam-6204	48	19	[	[	X
ejpam-6204	48	20	c	c	X
ejpam-6204	48	21	,	,	PUNCT
ejpam-6204	48	22	s	s	X
ejpam-6204	48	23	]	]	X
ejpam-6204	48	24	=	=	PUNCT
ejpam-6204	48	25	s.	s.	PROPN
ejpam-6204	48	26	locally	locally	ADV
ejpam-6204	48	27	,	,	PUNCT
ejpam-6204	48	28	it	it	PRON
ejpam-6204	48	29	has	have	VERB
ejpam-6204	48	30	the	the	DET
ejpam-6204	48	31	expression	expression	NOUN
ejpam-6204	48	32	:	:	PUNCT
ejpam-6204	48	33	s	s	X
ejpam-6204	48	34	=	=	SYM
ejpam-6204	48	35	yi	yi	PROPN
ejpam-6204	48	36	∂	∂	NOUN
ejpam-6204	48	37	∂xi	∂xi	PROPN
ejpam-6204	48	38	−	−	PROPN
ejpam-6204	48	39	2gi	2gi	NOUN
ejpam-6204	48	40	∂	∂	NOUN
ejpam-6204	48	41	∂yi	∂yi	PROPN
ejpam-6204	48	42	,	,	PUNCT
ejpam-6204	48	43	(	(	PUNCT
ejpam-6204	48	44	3	3	X
ejpam-6204	48	45	)	)	PUNCT
ejpam-6204	48	46	wheregi	wheregi	NOUN
ejpam-6204	48	47	=	=	SYM
ejpam-6204	48	48	gi(x	gi(x	X
ejpam-6204	48	49	,	,	PUNCT
ejpam-6204	48	50	y	y	PROPN
ejpam-6204	48	51	)	)	PUNCT
ejpam-6204	48	52	,	,	PUNCT
ejpam-6204	48	53	known	know	VERB
ejpam-6204	48	54	as	as	ADP
ejpam-6204	48	55	the	the	DET
ejpam-6204	48	56	spray	spray	NOUN
ejpam-6204	48	57	coefficients	coefficient	NOUN
ejpam-6204	48	58	,	,	PUNCT
ejpam-6204	48	59	are	be	AUX
ejpam-6204	48	60	functions	function	NOUN
ejpam-6204	48	61	that	that	PRON
ejpam-6204	48	62	exhibit	exhibit	VERB
ejpam-6204	48	63	2	2	NUM
ejpam-6204	48	64	-	-	PUNCT
ejpam-6204	48	65	homogeneity	homogeneity	NOUN
ejpam-6204	48	66	in	in	ADP
ejpam-6204	48	67	y.	y.	PROPN
ejpam-6204	48	68	a	a	DET
ejpam-6204	48	69	nonlinear	nonlinear	ADJ
ejpam-6204	48	70	connection	connection	NOUN
ejpam-6204	48	71	is	be	AUX
ejpam-6204	48	72	an	an	DET
ejpam-6204	48	73	n	n	ADV
ejpam-6204	48	74	-	-	PUNCT
ejpam-6204	48	75	dimensional	dimensional	ADJ
ejpam-6204	48	76	distribution	distribution	NOUN
ejpam-6204	48	77	h(t	h(t	PROPN
ejpam-6204	48	78	m	m	VERB
ejpam-6204	48	79	)	)	PUNCT
ejpam-6204	48	80	that	that	PRON
ejpam-6204	48	81	serves	serve	VERB
ejpam-6204	48	82	as	as	ADP
ejpam-6204	48	83	a	a	DET
ejpam-6204	48	84	complement	complement	NOUN
ejpam-6204	48	85	to	to	ADP
ejpam-6204	48	86	the	the	DET
ejpam-6204	48	87	vertical	vertical	ADJ
ejpam-6204	48	88	distribution	distribution	NOUN
ejpam-6204	48	89	v	v	NOUN
ejpam-6204	48	90	(	(	PUNCT
ejpam-6204	48	91	t	t	NOUN
ejpam-6204	48	92	m	m	PROPN
ejpam-6204	48	93	)	)	PUNCT
ejpam-6204	48	94	:	:	PUNCT
ejpam-6204	49	1	=	=	PUNCT
ejpam-6204	49	2	kerπ∗.	kerπ∗.	PROPN
ejpam-6204	49	3	this	this	PRON
ejpam-6204	49	4	implies	imply	VERB
ejpam-6204	49	5	that	that	SCONJ
ejpam-6204	49	6	,	,	PUNCT
ejpam-6204	49	7	for	for	ADP
ejpam-6204	49	8	each	each	DET
ejpam-6204	49	9	z	z	PROPN
ejpam-6204	49	10	∈	∈	PROPN
ejpam-6204	49	11	t	t	PROPN
ejpam-6204	49	12	m	m	PRON
ejpam-6204	49	13	,	,	PUNCT
ejpam-6204	49	14	the	the	DET
ejpam-6204	49	15	tangent	tangent	ADJ
ejpam-6204	49	16	space	space	NOUN
ejpam-6204	49	17	at	at	ADP
ejpam-6204	49	18	z	z	NOUN
ejpam-6204	49	19	decomposes	decompose	NOUN
ejpam-6204	49	20	as	as	ADP
ejpam-6204	49	21	:	:	PUNCT
ejpam-6204	49	22	tz(t	tz(t	X
ejpam-6204	49	23	m	m	NOUN
ejpam-6204	49	24	)	)	PUNCT
ejpam-6204	49	25	=	=	PUNCT
ejpam-6204	49	26	hz(t	hz(t	X
ejpam-6204	49	27	m)⊕	m)⊕	NOUN
ejpam-6204	49	28	vz(t	vz(t	X
ejpam-6204	49	29	m	m	PROPN
ejpam-6204	49	30	)	)	PUNCT
ejpam-6204	49	31	.	.	PUNCT
ejpam-6204	50	1	(	(	PUNCT
ejpam-6204	50	2	4	4	X
ejpam-6204	50	3	)	)	PUNCT
ejpam-6204	50	4	each	each	DET
ejpam-6204	50	5	spray	spray	NOUN
ejpam-6204	50	6	s	s	PRON
ejpam-6204	50	7	naturally	naturally	ADV
ejpam-6204	50	8	induces	induce	VERB
ejpam-6204	50	9	a	a	DET
ejpam-6204	50	10	nonlinear	nonlinear	ADJ
ejpam-6204	50	11	connection	connection	NOUN
ejpam-6204	50	12	γ	γ	X
ejpam-6204	50	13	=	=	PROPN
ejpam-6204	51	1	[	[	AUX
ejpam-6204	51	2	j	j	X
ejpam-6204	51	3	,	,	PUNCT
ejpam-6204	51	4	s	s	X
ejpam-6204	51	5	]	]	X
ejpam-6204	51	6	(	(	PUNCT
ejpam-6204	51	7	see	see	VERB
ejpam-6204	51	8	[	[	X
ejpam-6204	51	9	16	16	NUM
ejpam-6204	51	10	]	]	PUNCT
ejpam-6204	51	11	)	)	PUNCT
ejpam-6204	51	12	characterized	characterize	VERB
ejpam-6204	51	13	by	by	ADP
ejpam-6204	51	14	horizontal	horizontal	ADJ
ejpam-6204	51	15	and	and	CCONJ
ejpam-6204	51	16	vertical	vertical	ADJ
ejpam-6204	51	17	projectors	projector	NOUN
ejpam-6204	51	18	:	:	PUNCT
ejpam-6204	51	19	h	h	NOUN
ejpam-6204	51	20	=	=	NOUN
ejpam-6204	51	21	1	1	NUM
ejpam-6204	51	22	2	2	NUM
ejpam-6204	51	23	(	(	PUNCT
ejpam-6204	51	24	i	i	NOUN
ejpam-6204	51	25	d	d	PROPN
ejpam-6204	52	1	+	+	PROPN
ejpam-6204	53	1	[	[	X
ejpam-6204	53	2	j	j	X
ejpam-6204	53	3	,	,	PUNCT
ejpam-6204	53	4	s	s	PROPN
ejpam-6204	53	5	]	]	X
ejpam-6204	53	6	)	)	PUNCT
ejpam-6204	53	7	,	,	PUNCT
ejpam-6204	53	8	v	v	NOUN
ejpam-6204	53	9	=	=	SYM
ejpam-6204	53	10	1	1	NUM
ejpam-6204	53	11	2	2	NUM
ejpam-6204	53	12	(	(	PUNCT
ejpam-6204	53	13	id−	id−	SYM
ejpam-6204	53	14	[	[	X
ejpam-6204	53	15	j	j	PROPN
ejpam-6204	53	16	,	,	PUNCT
ejpam-6204	53	17	s	s	PROPN
ejpam-6204	53	18	]	]	X
ejpam-6204	53	19	)	)	PUNCT
ejpam-6204	53	20	.	.	PUNCT
ejpam-6204	54	1	(	(	PUNCT
ejpam-6204	54	2	5	5	X
ejpam-6204	54	3	)	)	PUNCT
ejpam-6204	54	4	locally	locally	ADV
ejpam-6204	54	5	,	,	PUNCT
ejpam-6204	54	6	these	these	DET
ejpam-6204	54	7	projectors	projector	NOUN
ejpam-6204	54	8	take	take	VERB
ejpam-6204	54	9	the	the	DET
ejpam-6204	54	10	forms	form	NOUN
ejpam-6204	54	11	:	:	PUNCT
ejpam-6204	54	12	h	h	NOUN
ejpam-6204	54	13	=	=	PUNCT
ejpam-6204	54	14	δ	δ	PROPN
ejpam-6204	54	15	δxi	δxi	ADP
ejpam-6204	54	16	⊗	⊗	PROPN
ejpam-6204	54	17	dxi	dxi	PROPN
ejpam-6204	54	18	,	,	PUNCT
ejpam-6204	54	19	v	v	NOUN
ejpam-6204	54	20	=	=	SYM
ejpam-6204	54	21	∂	∂	NUM
ejpam-6204	54	22	∂yi	∂yi	PROPN
ejpam-6204	54	23	⊗	⊗	PROPN
ejpam-6204	54	24	δyi	δyi	PROPN
ejpam-6204	54	25	,	,	PUNCT
ejpam-6204	54	26	(	(	PUNCT
ejpam-6204	54	27	6	6	NUM
ejpam-6204	54	28	)	)	PUNCT
ejpam-6204	55	1	where	where	SCONJ
ejpam-6204	55	2	:	:	PUNCT
ejpam-6204	55	3	δ	δ	NOUN
ejpam-6204	55	4	δxi	δxi	ADP
ejpam-6204	55	5	=	=	NOUN
ejpam-6204	55	6	∂	∂	NUM
ejpam-6204	55	7	∂xi	∂xi	PROPN
ejpam-6204	55	8	−n	−n	NOUN
ejpam-6204	55	9	j	j	PROPN
ejpam-6204	56	1	i	i	PRON
ejpam-6204	56	2	(	(	PUNCT
ejpam-6204	56	3	x	x	NOUN
ejpam-6204	56	4	,	,	PUNCT
ejpam-6204	56	5	y	y	NOUN
ejpam-6204	56	6	)	)	PUNCT
ejpam-6204	56	7	∂	∂	NUM
ejpam-6204	56	8	∂yj	∂yj	NOUN
ejpam-6204	56	9	,	,	PUNCT
ejpam-6204	56	10	δyi	δyi	NOUN
ejpam-6204	56	11	=	=	PROPN
ejpam-6204	56	12	dyi	dyi	PROPN
ejpam-6204	56	13	+	+	PROPN
ejpam-6204	56	14	n	n	PROPN
ejpam-6204	56	15	j	j	NOUN
ejpam-6204	56	16	i	i	PRON
ejpam-6204	56	17	(	(	PUNCT
ejpam-6204	56	18	x	x	X
ejpam-6204	56	19	,	,	PUNCT
ejpam-6204	56	20	y)dx	y)dx	PROPN
ejpam-6204	56	21	i	i	PROPN
ejpam-6204	56	22	,	,	PUNCT
ejpam-6204	56	23	n	n	PROPN
ejpam-6204	56	24	j	j	PROPN
ejpam-6204	57	1	i	i	PRON
ejpam-6204	57	2	(	(	PUNCT
ejpam-6204	57	3	x	x	NOUN
ejpam-6204	57	4	,	,	PUNCT
ejpam-6204	57	5	y	y	NOUN
ejpam-6204	57	6	)	)	PUNCT
ejpam-6204	57	7	=	=	SYM
ejpam-6204	58	1	∂gj	∂gj	PROPN
ejpam-6204	58	2	∂yi	∂yi	PROPN
ejpam-6204	58	3	.	.	PUNCT
ejpam-6204	59	1	(	(	PUNCT
ejpam-6204	59	2	7	7	X
ejpam-6204	59	3	)	)	PUNCT
ejpam-6204	59	4	for	for	ADP
ejpam-6204	59	5	a	a	DET
ejpam-6204	59	6	vector	vector	NOUN
ejpam-6204	59	7	k	k	NOUN
ejpam-6204	59	8	-	-	NOUN
ejpam-6204	59	9	form	form	NOUN
ejpam-6204	59	10	k	k	PROPN
ejpam-6204	59	11	on	on	ADP
ejpam-6204	59	12	m	m	PROPN
ejpam-6204	59	13	,	,	PUNCT
ejpam-6204	59	14	the	the	DET
ejpam-6204	59	15	graded	grade	VERB
ejpam-6204	59	16	derivations	derivation	NOUN
ejpam-6204	59	17	ik	ik	X
ejpam-6204	59	18	and	and	CCONJ
ejpam-6204	59	19	dk	dk	PROPN
ejpam-6204	59	20	on	on	ADP
ejpam-6204	59	21	the	the	DET
ejpam-6204	59	22	grassmann	grassmann	PROPN
ejpam-6204	59	23	algebra	algebra	NOUN
ejpam-6204	59	24	of	of	ADP
ejpam-6204	59	25	m	m	NOUN
ejpam-6204	59	26	are	be	AUX
ejpam-6204	59	27	given	give	VERB
ejpam-6204	59	28	by	by	ADP
ejpam-6204	59	29	[	[	X
ejpam-6204	59	30	17	17	NUM
ejpam-6204	59	31	]	]	X
ejpam-6204	59	32	:	:	PUNCT
ejpam-6204	59	33	ikf	ikf	NOUN
ejpam-6204	59	34	=	=	SYM
ejpam-6204	59	35	0	0	NUM
ejpam-6204	59	36	,	,	PUNCT
ejpam-6204	59	37	ikdf	ikdf	NOUN
ejpam-6204	59	38	=	=	SYM
ejpam-6204	59	39	df	df	PROPN
ejpam-6204	59	40	◦	◦	PROPN
ejpam-6204	59	41	k	k	PROPN
ejpam-6204	59	42	,	,	PUNCT
ejpam-6204	59	43	(	(	PUNCT
ejpam-6204	59	44	8)	8)	NUM
ejpam-6204	59	45	s.	s.	PROPN
ejpam-6204	59	46	g.	g.	PROPN
ejpam-6204	59	47	elgendi	elgendi	PROPN
ejpam-6204	59	48	,	,	PUNCT
ejpam-6204	59	49	a.	a.	NOUN
ejpam-6204	59	50	soleiman	soleiman	PROPN
ejpam-6204	59	51	/	/	SYM
ejpam-6204	59	52	eur	eur	PROPN
ejpam-6204	59	53	.	.	PUNCT
ejpam-6204	60	1	j.	j.	PROPN
ejpam-6204	60	2	pure	pure	PROPN
ejpam-6204	60	3	appl	appl	PROPN
ejpam-6204	60	4	.	.	PROPN
ejpam-6204	60	5	math	math	PROPN
ejpam-6204	60	6	,	,	PUNCT
ejpam-6204	60	7	18	18	NUM
ejpam-6204	60	8	(	(	PUNCT
ejpam-6204	60	9	3	3	NUM
ejpam-6204	60	10	)	)	PUNCT
ejpam-6204	60	11	(	(	PUNCT
ejpam-6204	60	12	2025	2025	NUM
ejpam-6204	60	13	)	)	PUNCT
ejpam-6204	60	14	,	,	PUNCT
ejpam-6204	60	15	6204	6204	NUM
ejpam-6204	60	16	4	4	NUM
ejpam-6204	60	17	of	of	ADP
ejpam-6204	60	18	18	18	NUM
ejpam-6204	60	19	where	where	SCONJ
ejpam-6204	60	20	f	f	PROPN
ejpam-6204	60	21	∈	∈	PROPN
ejpam-6204	60	22	c∞(m	c∞(m	NOUN
ejpam-6204	60	23	)	)	PUNCT
ejpam-6204	60	24	and	and	CCONJ
ejpam-6204	60	25	df	df	NOUN
ejpam-6204	60	26	represents	represent	VERB
ejpam-6204	60	27	the	the	DET
ejpam-6204	60	28	exterior	exterior	ADJ
ejpam-6204	60	29	derivative	derivative	NOUN
ejpam-6204	60	30	of	of	ADP
ejpam-6204	60	31	f	f	PROPN
ejpam-6204	60	32	.	.	PUNCT
ejpam-6204	61	1	furthermore	furthermore	ADV
ejpam-6204	61	2	,	,	PUNCT
ejpam-6204	61	3	the	the	DET
ejpam-6204	61	4	derivation	derivation	NOUN
ejpam-6204	61	5	dk	dk	NOUN
ejpam-6204	61	6	is	be	AUX
ejpam-6204	61	7	defined	define	VERB
ejpam-6204	61	8	as	as	ADP
ejpam-6204	61	9	:	:	PUNCT
ejpam-6204	61	10	dk	dk	X
ejpam-6204	61	11	:	:	PUNCT
ejpam-6204	61	12	=	=	SYM
ejpam-6204	62	1	[	[	X
ejpam-6204	62	2	ik	ik	X
ejpam-6204	62	3	,	,	PUNCT
ejpam-6204	62	4	d	d	X
ejpam-6204	62	5	]	]	X
ejpam-6204	62	6	=	=	SYM
ejpam-6204	62	7	ik	ik	PROPN
ejpam-6204	62	8	◦	◦	NOUN
ejpam-6204	62	9	d−	d−	PROPN
ejpam-6204	62	10	(	(	PUNCT
ejpam-6204	62	11	−1)k−1dik	−1)k−1dik	NUM
ejpam-6204	62	12	.	.	PUNCT
ejpam-6204	63	1	(	(	PUNCT
ejpam-6204	63	2	9	9	X
ejpam-6204	63	3	)	)	PUNCT
ejpam-6204	63	4	the	the	DET
ejpam-6204	63	5	jacobi	jacobi	PROPN
ejpam-6204	63	6	endomorphism	endomorphism	PROPN
ejpam-6204	63	7	(	(	PUNCT
ejpam-6204	63	8	or	or	CCONJ
ejpam-6204	63	9	riemann	riemann	PROPN
ejpam-6204	63	10	curvature	curvature	NOUN
ejpam-6204	63	11	,	,	PUNCT
ejpam-6204	63	12	as	as	SCONJ
ejpam-6204	63	13	seen	see	VERB
ejpam-6204	63	14	in	in	ADP
ejpam-6204	63	15	[	[	X
ejpam-6204	63	16	9	9	NUM
ejpam-6204	63	17	]	]	PUNCT
ejpam-6204	63	18	)	)	PUNCT
ejpam-6204	63	19	φ	φ	PROPN
ejpam-6204	63	20	is	be	AUX
ejpam-6204	63	21	formulated	formulate	VERB
ejpam-6204	63	22	as	as	ADP
ejpam-6204	63	23	:	:	PUNCT
ejpam-6204	63	24	φ	φ	PROPN
ejpam-6204	63	25	=	=	PROPN
ejpam-6204	63	26	v	v	ADP
ejpam-6204	63	27	◦	◦	NOUN
ejpam-6204	64	1	[	[	X
ejpam-6204	64	2	s	s	X
ejpam-6204	64	3	,	,	PUNCT
ejpam-6204	64	4	h	h	NOUN
ejpam-6204	64	5	]	]	X
ejpam-6204	64	6	=	=	SYM
ejpam-6204	64	7	ri	ri	PROPN
ejpam-6204	64	8	j	j	PROPN
ejpam-6204	64	9	∂	∂	PROPN
ejpam-6204	64	10	∂yi	∂yi	PROPN
ejpam-6204	64	11	⊗	⊗	PROPN
ejpam-6204	64	12	dxj	dxj	PROPN
ejpam-6204	64	13	,	,	PUNCT
ejpam-6204	64	14	(	(	PUNCT
ejpam-6204	64	15	10	10	NUM
ejpam-6204	64	16	)	)	PUNCT
ejpam-6204	64	17	where	where	SCONJ
ejpam-6204	64	18	:	:	PUNCT
ejpam-6204	64	19	ri	ri	PROPN
ejpam-6204	64	20	j	j	PROPN
ejpam-6204	64	21	=	=	SYM
ejpam-6204	64	22	2	2	NUM
ejpam-6204	64	23	∂gi	∂gi	PROPN
ejpam-6204	64	24	∂xj	∂xj	NOUN
ejpam-6204	64	25	−	−	PROPN
ejpam-6204	64	26	s(n	s(n	PROPN
ejpam-6204	64	27	i	i	PRON
ejpam-6204	64	28	j)−n	j)−n	VERB
ejpam-6204	65	1	i	i	PRON
ejpam-6204	65	2	kn	kn	PROPN
ejpam-6204	66	1	k	k	PROPN
ejpam-6204	66	2	j	j	PROPN
ejpam-6204	66	3	.	.	PUNCT
ejpam-6204	67	1	(	(	PUNCT
ejpam-6204	67	2	11	11	NUM
ejpam-6204	67	3	)	)	PUNCT
ejpam-6204	67	4	the	the	DET
ejpam-6204	67	5	curvature	curvature	NOUN
ejpam-6204	67	6	tensor	tensor	NOUN
ejpam-6204	67	7	r	r	NOUN
ejpam-6204	67	8	of	of	ADP
ejpam-6204	67	9	a	a	DET
ejpam-6204	67	10	spray	spray	NOUN
ejpam-6204	67	11	s	s	VERB
ejpam-6204	67	12	is	be	AUX
ejpam-6204	67	13	given	give	VERB
ejpam-6204	67	14	by	by	ADP
ejpam-6204	67	15	:	:	PUNCT
ejpam-6204	67	16	r	r	NOUN
ejpam-6204	67	17	=	=	SYM
ejpam-6204	67	18	−1	−1	NOUN
ejpam-6204	67	19	2	2	NUM
ejpam-6204	67	20	[	[	X
ejpam-6204	67	21	h	h	X
ejpam-6204	67	22	,	,	PUNCT
ejpam-6204	67	23	h	h	NOUN
ejpam-6204	67	24	]	]	X
ejpam-6204	67	25	=	=	PUNCT
ejpam-6204	67	26	rℓ	rℓ	NOUN
ejpam-6204	67	27	ij	ij	NOUN
ejpam-6204	67	28	∂	∂	X
ejpam-6204	67	29	∂yℓ	∂yℓ	PROPN
ejpam-6204	67	30	⊗	⊗	PROPN
ejpam-6204	67	31	dxi	dxi	NOUN
ejpam-6204	67	32	⊗	⊗	PROPN
ejpam-6204	67	33	dxj	dxj	PROPN
ejpam-6204	67	34	,	,	PUNCT
ejpam-6204	67	35	with	with	ADP
ejpam-6204	67	36	:	:	PUNCT
ejpam-6204	67	37	rℓ	rℓ	NOUN
ejpam-6204	67	38	ij	ij	NOUN
ejpam-6204	67	39	=	=	NOUN
ejpam-6204	67	40	δgℓ	δgℓ	NOUN
ejpam-6204	68	1	i	i	PRON
ejpam-6204	68	2	δxj	δxj	VERB
ejpam-6204	68	3	−	−	PROPN
ejpam-6204	68	4	δgℓ	δgℓ	NOUN
ejpam-6204	68	5	j	j	NOUN
ejpam-6204	68	6	δxi	δxi	INTJ
ejpam-6204	68	7	.	.	PUNCT
ejpam-6204	69	1	(	(	PUNCT
ejpam-6204	69	2	12	12	NUM
ejpam-6204	69	3	)	)	PUNCT
ejpam-6204	69	4	the	the	DET
ejpam-6204	69	5	two	two	NUM
ejpam-6204	69	6	curvature	curvature	NOUN
ejpam-6204	69	7	tensors	tensor	NOUN
ejpam-6204	69	8	are	be	AUX
ejpam-6204	69	9	related	relate	VERB
ejpam-6204	69	10	as	as	SCONJ
ejpam-6204	69	11	follows	follow	VERB
ejpam-6204	69	12	(	(	PUNCT
ejpam-6204	69	13	see	see	VERB
ejpam-6204	69	14	,	,	PUNCT
ejpam-6204	69	15	for	for	ADP
ejpam-6204	69	16	example	example	NOUN
ejpam-6204	69	17	,	,	PUNCT
ejpam-6204	70	1	[	[	X
ejpam-6204	70	2	3	3	NUM
ejpam-6204	70	3	]	]	SYM
ejpam-6204	70	4	):	):	PUNCT
ejpam-6204	70	5	3r	3r	NUM
ejpam-6204	70	6	=	=	PUNCT
ejpam-6204	71	1	[	[	X
ejpam-6204	71	2	j	j	PROPN
ejpam-6204	71	3	,	,	PUNCT
ejpam-6204	71	4	φ	φ	PROPN
ejpam-6204	71	5	]	]	X
ejpam-6204	71	6	,	,	PUNCT
ejpam-6204	71	7	φ	φ	PROPN
ejpam-6204	71	8	=	=	SYM
ejpam-6204	71	9	isr	isr	PROPN
ejpam-6204	71	10	.	.	PUNCT
ejpam-6204	72	1	(	(	PUNCT
ejpam-6204	72	2	13	13	NUM
ejpam-6204	72	3	)	)	PUNCT
ejpam-6204	72	4	definition	definition	NOUN
ejpam-6204	72	5	1	1	NUM
ejpam-6204	72	6	.	.	PUNCT
ejpam-6204	73	1	a	a	DET
ejpam-6204	73	2	finsler	finsler	NOUN
ejpam-6204	73	3	manifold	manifold	NOUN
ejpam-6204	73	4	(	(	PUNCT
ejpam-6204	73	5	m	m	PROPN
ejpam-6204	73	6	,	,	PUNCT
ejpam-6204	73	7	f	f	PROPN
ejpam-6204	73	8	)	)	PUNCT
ejpam-6204	73	9	consists	consist	VERB
ejpam-6204	73	10	of	of	ADP
ejpam-6204	73	11	an	an	DET
ejpam-6204	73	12	n	n	ADV
ejpam-6204	73	13	-	-	PUNCT
ejpam-6204	73	14	dimensional	dimensional	ADJ
ejpam-6204	73	15	manifold	manifold	ADJ
ejpam-6204	73	16	m	m	NOUN
ejpam-6204	73	17	along	along	ADP
ejpam-6204	73	18	with	with	ADP
ejpam-6204	73	19	a	a	DET
ejpam-6204	73	20	function	function	NOUN
ejpam-6204	73	21	f	f	NOUN
ejpam-6204	73	22	:	:	PUNCT
ejpam-6204	73	23	tm	tm	PROPN
ejpam-6204	73	24	→	→	SYM
ejpam-6204	73	25	r	r	NOUN
ejpam-6204	73	26	that	that	PRON
ejpam-6204	73	27	meets	meet	VERB
ejpam-6204	73	28	the	the	DET
ejpam-6204	73	29	following	following	ADJ
ejpam-6204	73	30	conditions	condition	NOUN
ejpam-6204	73	31	:	:	PUNCT
ejpam-6204	73	32	a	a	X
ejpam-6204	73	33	)	)	PUNCT
ejpam-6204	73	34	f	f	PROPN
ejpam-6204	73	35	is	be	AUX
ejpam-6204	73	36	smooth	smooth	ADJ
ejpam-6204	73	37	and	and	CCONJ
ejpam-6204	73	38	strictly	strictly	ADV
ejpam-6204	73	39	positive	positive	ADJ
ejpam-6204	73	40	on	on	ADP
ejpam-6204	73	41	t	t	PROPN
ejpam-6204	73	42	m	m	PROPN
ejpam-6204	73	43	.	.	PUNCT
ejpam-6204	74	1	b	b	X
ejpam-6204	74	2	)	)	PUNCT
ejpam-6204	74	3	f	f	PROPN
ejpam-6204	74	4	is	be	AUX
ejpam-6204	74	5	positively	positively	ADV
ejpam-6204	74	6	homogeneous	homogeneous	ADJ
ejpam-6204	74	7	of	of	ADP
ejpam-6204	74	8	degree	degree	NOUN
ejpam-6204	74	9	1	1	NUM
ejpam-6204	74	10	in	in	ADP
ejpam-6204	74	11	y	y	PROPN
ejpam-6204	74	12	:	:	PUNCT
ejpam-6204	74	13	lcf	lcf	PROPN
ejpam-6204	74	14	=	=	SYM
ejpam-6204	74	15	f	f	PROPN
ejpam-6204	74	16	.	.	PUNCT
ejpam-6204	75	1	c	c	X
ejpam-6204	75	2	)	)	PUNCT
ejpam-6204	75	3	the	the	DET
ejpam-6204	75	4	hessian	hessian	ADJ
ejpam-6204	75	5	matrix	matrix	NOUN
ejpam-6204	75	6	gij	gij	NOUN
ejpam-6204	75	7	=	=	SYM
ejpam-6204	76	1	∂2e	∂2e	PROPN
ejpam-6204	76	2	∂yi∂yj	∂yi∂yj	NOUN
ejpam-6204	76	3	has	have	VERB
ejpam-6204	76	4	full	full	ADJ
ejpam-6204	76	5	rank	rank	NOUN
ejpam-6204	76	6	n	n	PROPN
ejpam-6204	76	7	on	on	ADP
ejpam-6204	76	8	t	t	PROPN
ejpam-6204	76	9	m	m	PROPN
ejpam-6204	76	10	,	,	PUNCT
ejpam-6204	76	11	where	where	SCONJ
ejpam-6204	76	12	e	e	NOUN
ejpam-6204	76	13	=	=	SYM
ejpam-6204	76	14	1	1	NUM
ejpam-6204	76	15	2f	2f	NUM
ejpam-6204	76	16	2	2	NUM
ejpam-6204	76	17	.	.	PUNCT
ejpam-6204	77	1	the	the	DET
ejpam-6204	77	2	geodesic	geodesic	ADJ
ejpam-6204	77	3	spray	spray	NOUN
ejpam-6204	77	4	s	s	AUX
ejpam-6204	77	5	associated	associate	VERB
ejpam-6204	77	6	with	with	ADP
ejpam-6204	77	7	f	f	PROPN
ejpam-6204	77	8	is	be	AUX
ejpam-6204	77	9	determined	determine	VERB
ejpam-6204	77	10	uniquely	uniquely	ADV
ejpam-6204	77	11	by	by	ADP
ejpam-6204	77	12	the	the	DET
ejpam-6204	77	13	euler	euler	PROPN
ejpam-6204	77	14	-	-	PUNCT
ejpam-6204	77	15	lagrange	lagrange	NOUN
ejpam-6204	77	16	equation	equation	NOUN
ejpam-6204	77	17	:	:	PUNCT
ejpam-6204	77	18	isddje	isddje	ADV
ejpam-6204	77	19	=	=	SYM
ejpam-6204	77	20	−de	−de	PROPN
ejpam-6204	77	21	.	.	PROPN
ejpam-6204	78	1	for	for	ADP
ejpam-6204	78	2	simplicity	simplicity	NOUN
ejpam-6204	78	3	,	,	PUNCT
ejpam-6204	78	4	we	we	PRON
ejpam-6204	78	5	use	use	VERB
ejpam-6204	78	6	the	the	DET
ejpam-6204	78	7	notations	notation	NOUN
ejpam-6204	78	8	δi	δi	ADP
ejpam-6204	78	9	:	:	PUNCT
ejpam-6204	78	10	=	=	SYM
ejpam-6204	78	11	δ	δ	NOUN
ejpam-6204	78	12	δxi	δxi	ADJ
ejpam-6204	78	13	,	,	PUNCT
ejpam-6204	78	14	∂i	∂i	PROPN
ejpam-6204	78	15	:	:	PUNCT
ejpam-6204	78	16	=	=	SYM
ejpam-6204	78	17	∂	∂	NUM
ejpam-6204	78	18	∂xi	∂xi	PROPN
ejpam-6204	78	19	,	,	PUNCT
ejpam-6204	78	20	∂̇i	∂̇i	NOUN
ejpam-6204	78	21	:	:	PUNCT
ejpam-6204	78	22	=	=	SYM
ejpam-6204	78	23	∂	∂	NUM
ejpam-6204	78	24	∂yi	∂yi	PROPN
ejpam-6204	78	25	.	.	PUNCT
ejpam-6204	79	1	for	for	ADP
ejpam-6204	79	2	a	a	DET
ejpam-6204	79	3	finsler	finsler	NOUN
ejpam-6204	79	4	manifold	manifold	NOUN
ejpam-6204	79	5	(	(	PUNCT
ejpam-6204	79	6	m	m	PROPN
ejpam-6204	79	7	,	,	PUNCT
ejpam-6204	79	8	f	f	PROPN
ejpam-6204	79	9	)	)	PUNCT
ejpam-6204	79	10	,	,	PUNCT
ejpam-6204	79	11	the	the	DET
ejpam-6204	79	12	coefficients	coefficient	NOUN
ejpam-6204	79	13	gi	gi	INTJ
ejpam-6204	79	14	of	of	ADP
ejpam-6204	79	15	the	the	DET
ejpam-6204	79	16	geodesic	geodesic	ADJ
ejpam-6204	79	17	spray	spray	NOUN
ejpam-6204	79	18	of	of	ADP
ejpam-6204	79	19	f	f	PROPN
ejpam-6204	79	20	are	be	AUX
ejpam-6204	79	21	given	give	VERB
ejpam-6204	79	22	by	by	ADP
ejpam-6204	79	23	gi	gi	NOUN
ejpam-6204	79	24	=	=	SYM
ejpam-6204	79	25	1	1	NUM
ejpam-6204	79	26	4	4	NUM
ejpam-6204	79	27	gih(yr∂r∂̇hf	gih(yr∂r∂̇hf	NOUN
ejpam-6204	79	28	2	2	NUM
ejpam-6204	79	29	−	−	NOUN
ejpam-6204	79	30	∂hf	∂hf	PROPN
ejpam-6204	79	31	2	2	NUM
ejpam-6204	79	32	)	)	PUNCT
ejpam-6204	79	33	,	,	PUNCT
ejpam-6204	79	34	(	(	PUNCT
ejpam-6204	79	35	14	14	NUM
ejpam-6204	79	36	)	)	PUNCT
ejpam-6204	79	37	where	where	SCONJ
ejpam-6204	79	38	gij	gij	PROPN
ejpam-6204	79	39	are	be	AUX
ejpam-6204	79	40	the	the	DET
ejpam-6204	79	41	components	component	NOUN
ejpam-6204	79	42	of	of	ADP
ejpam-6204	79	43	the	the	DET
ejpam-6204	79	44	inverse	inverse	ADJ
ejpam-6204	79	45	metric	metric	ADJ
ejpam-6204	79	46	tensor	tensor	NOUN
ejpam-6204	79	47	.	.	PUNCT
ejpam-6204	80	1	s.	s.	PROPN
ejpam-6204	80	2	g.	g.	PROPN
ejpam-6204	80	3	elgendi	elgendi	PROPN
ejpam-6204	80	4	,	,	PUNCT
ejpam-6204	80	5	a.	a.	NOUN
ejpam-6204	80	6	soleiman	soleiman	PROPN
ejpam-6204	80	7	/	/	SYM
ejpam-6204	80	8	eur	eur	PROPN
ejpam-6204	80	9	.	.	PUNCT
ejpam-6204	81	1	j.	j.	PROPN
ejpam-6204	81	2	pure	pure	PROPN
ejpam-6204	81	3	appl	appl	PROPN
ejpam-6204	81	4	.	.	PROPN
ejpam-6204	81	5	math	math	PROPN
ejpam-6204	81	6	,	,	PUNCT
ejpam-6204	81	7	18	18	NUM
ejpam-6204	81	8	(	(	PUNCT
ejpam-6204	81	9	3	3	NUM
ejpam-6204	81	10	)	)	PUNCT
ejpam-6204	81	11	(	(	PUNCT
ejpam-6204	81	12	2025	2025	NUM
ejpam-6204	81	13	)	)	PUNCT
ejpam-6204	81	14	,	,	PUNCT
ejpam-6204	81	15	6204	6204	NUM
ejpam-6204	81	16	5	5	NUM
ejpam-6204	81	17	of	of	ADP
ejpam-6204	81	18	18	18	NUM
ejpam-6204	81	19	2.1	2.1	NUM
ejpam-6204	81	20	.	.	PUNCT
ejpam-6204	82	1	projective	projective	ADJ
ejpam-6204	82	2	deformations	deformation	NOUN
ejpam-6204	82	3	of	of	ADP
ejpam-6204	82	4	sprays	spray	NOUN
ejpam-6204	82	5	the	the	DET
ejpam-6204	82	6	concepts	concept	NOUN
ejpam-6204	82	7	of	of	ADP
ejpam-6204	82	8	sprays	spray	NOUN
ejpam-6204	82	9	and	and	CCONJ
ejpam-6204	82	10	its	its	PRON
ejpam-6204	82	11	projective	projective	ADJ
ejpam-6204	82	12	deformation	deformation	NOUN
ejpam-6204	82	13	play	play	VERB
ejpam-6204	82	14	a	a	DET
ejpam-6204	82	15	crucial	crucial	ADJ
ejpam-6204	82	16	role	role	NOUN
ejpam-6204	82	17	in	in	ADP
ejpam-6204	82	18	understanding	understand	VERB
ejpam-6204	82	19	how	how	SCONJ
ejpam-6204	82	20	the	the	DET
ejpam-6204	82	21	geodesic	geodesic	ADJ
ejpam-6204	82	22	structure	structure	NOUN
ejpam-6204	82	23	of	of	ADP
ejpam-6204	82	24	a	a	DET
ejpam-6204	82	25	manifold	manifold	ADJ
ejpam-6204	82	26	changes	change	NOUN
ejpam-6204	82	27	under	under	ADP
ejpam-6204	82	28	transformations	transformation	NOUN
ejpam-6204	82	29	that	that	PRON
ejpam-6204	82	30	preserve	preserve	VERB
ejpam-6204	82	31	the	the	DET
ejpam-6204	82	32	projective	projective	ADJ
ejpam-6204	82	33	class	class	NOUN
ejpam-6204	82	34	of	of	ADP
ejpam-6204	82	35	paths	path	NOUN
ejpam-6204	82	36	.	.	PUNCT
ejpam-6204	83	1	a	a	DET
ejpam-6204	83	2	complete	complete	ADJ
ejpam-6204	83	3	local	local	ADJ
ejpam-6204	83	4	theory	theory	NOUN
ejpam-6204	83	5	of	of	ADP
ejpam-6204	83	6	projective	projective	ADJ
ejpam-6204	83	7	changes	change	NOUN
ejpam-6204	83	8	has	have	AUX
ejpam-6204	83	9	been	be	AUX
ejpam-6204	83	10	established	establish	VERB
ejpam-6204	83	11	(	(	PUNCT
ejpam-6204	83	12	[	[	X
ejpam-6204	83	13	5	5	NUM
ejpam-6204	83	14	,	,	PUNCT
ejpam-6204	83	15	7	7	NUM
ejpam-6204	83	16	,	,	PUNCT
ejpam-6204	83	17	8	8	NUM
ejpam-6204	83	18	,	,	PUNCT
ejpam-6204	83	19	13	13	NUM
ejpam-6204	83	20	,	,	PUNCT
ejpam-6204	83	21	14	14	NUM
ejpam-6204	83	22	]	]	PUNCT
ejpam-6204	83	23	)	)	PUNCT
ejpam-6204	83	24	.	.	PUNCT
ejpam-6204	84	1	a	a	DET
ejpam-6204	84	2	regular	regular	ADJ
ejpam-6204	84	3	curve	curve	NOUN
ejpam-6204	84	4	is	be	AUX
ejpam-6204	84	5	a	a	DET
ejpam-6204	84	6	curve	curve	NOUN
ejpam-6204	84	7	γ	γ	NOUN
ejpam-6204	84	8	:	:	PUNCT
ejpam-6204	84	9	i	i	PROPN
ejpam-6204	84	10	→	→	PUNCT
ejpam-6204	84	11	m	m	VERB
ejpam-6204	84	12	with	with	ADP
ejpam-6204	84	13	the	the	DET
ejpam-6204	84	14	tangent	tangent	NOUN
ejpam-6204	84	15	lift	lift	NOUN
ejpam-6204	84	16	γ′	γ′	PROPN
ejpam-6204	84	17	:	:	PUNCT
ejpam-6204	85	1	i	i	PRON
ejpam-6204	85	2	→	→	SYM
ejpam-6204	85	3	tm	tm	PROPN
ejpam-6204	85	4	.	.	PUNCT
ejpam-6204	86	1	a	a	DET
ejpam-6204	86	2	regular	regular	ADJ
ejpam-6204	86	3	curve	curve	NOUN
ejpam-6204	86	4	γ	γ	NOUN
ejpam-6204	86	5	on	on	ADP
ejpam-6204	86	6	m	m	PROPN
ejpam-6204	86	7	is	be	AUX
ejpam-6204	86	8	a	a	DET
ejpam-6204	86	9	geodesic	geodesic	NOUN
ejpam-6204	86	10	of	of	ADP
ejpam-6204	86	11	a	a	DET
ejpam-6204	86	12	spray	spray	NOUN
ejpam-6204	86	13	s	s	VERB
ejpam-6204	86	14	if	if	SCONJ
ejpam-6204	86	15	it	it	PRON
ejpam-6204	86	16	satisfies	satisfy	VERB
ejpam-6204	86	17	the	the	DET
ejpam-6204	86	18	condition	condition	NOUN
ejpam-6204	86	19	s	s	PART
ejpam-6204	86	20	◦	◦	NOUN
ejpam-6204	86	21	γ′	γ′	PUNCT
ejpam-6204	87	1	=	=	PUNCT
ejpam-6204	87	2	γ′′.	γ′′.	PROPN
ejpam-6204	88	1	locally	locally	ADV
ejpam-6204	88	2	,	,	PUNCT
ejpam-6204	88	3	if	if	SCONJ
ejpam-6204	88	4	γ(t	γ(t	NOUN
ejpam-6204	88	5	)	)	PUNCT
ejpam-6204	88	6	=	=	SYM
ejpam-6204	88	7	(	(	PUNCT
ejpam-6204	88	8	xi(t	xi(t	NOUN
ejpam-6204	88	9	)	)	PUNCT
ejpam-6204	88	10	)	)	PUNCT
ejpam-6204	88	11	,	,	PUNCT
ejpam-6204	88	12	then	then	ADV
ejpam-6204	88	13	the	the	DET
ejpam-6204	88	14	geodesic	geodesic	ADJ
ejpam-6204	88	15	equation	equation	NOUN
ejpam-6204	88	16	is	be	AUX
ejpam-6204	88	17	given	give	VERB
ejpam-6204	88	18	by	by	ADP
ejpam-6204	88	19	:	:	PUNCT
ejpam-6204	88	20	d2xi	d2xi	PROPN
ejpam-6204	88	21	dt2	dt2	PROPN
ejpam-6204	88	22	+	+	CCONJ
ejpam-6204	88	23	2gi	2gi	ADJ
ejpam-6204	88	24	(	(	PUNCT
ejpam-6204	88	25	x	x	X
ejpam-6204	88	26	,	,	PUNCT
ejpam-6204	88	27	dx	dx	PROPN
ejpam-6204	88	28	dt	dt	NOUN
ejpam-6204	88	29	)	)	PUNCT
ejpam-6204	89	1	=	=	PUNCT
ejpam-6204	89	2	0	0	X
ejpam-6204	89	3	.	.	PUNCT
ejpam-6204	90	1	(	(	PUNCT
ejpam-6204	90	2	15	15	NUM
ejpam-6204	90	3	)	)	PUNCT
ejpam-6204	90	4	in	in	ADP
ejpam-6204	90	5	other	other	ADJ
ejpam-6204	90	6	words	word	NOUN
ejpam-6204	90	7	,	,	PUNCT
ejpam-6204	90	8	the	the	DET
ejpam-6204	90	9	curve	curve	NOUN
ejpam-6204	90	10	γ(t	γ(t	NOUN
ejpam-6204	90	11	)	)	PUNCT
ejpam-6204	90	12	is	be	AUX
ejpam-6204	90	13	a	a	DET
ejpam-6204	90	14	geodesic	geodesic	NOUN
ejpam-6204	90	15	of	of	ADP
ejpam-6204	90	16	s	s	PRON
ejpam-6204	90	17	if	if	SCONJ
ejpam-6204	90	18	its	its	PRON
ejpam-6204	90	19	velocity	velocity	NOUN
ejpam-6204	90	20	yi	yi	NOUN
ejpam-6204	90	21	=	=	SYM
ejpam-6204	90	22	dxi	dxi	NOUN
ejpam-6204	90	23	dt	dt	PROPN
ejpam-6204	90	24	satisfies	satisfy	VERB
ejpam-6204	90	25	the	the	DET
ejpam-6204	90	26	above	above	ADJ
ejpam-6204	90	27	equation	equation	NOUN
ejpam-6204	90	28	.	.	PUNCT
ejpam-6204	91	1	two	two	NUM
ejpam-6204	91	2	sprays	spray	NOUN
ejpam-6204	91	3	,	,	PUNCT
ejpam-6204	91	4	s	s	X
ejpam-6204	91	5	and	and	CCONJ
ejpam-6204	91	6	s	s	PROPN
ejpam-6204	91	7	,	,	PUNCT
ejpam-6204	91	8	are	be	AUX
ejpam-6204	91	9	said	say	VERB
ejpam-6204	91	10	to	to	PART
ejpam-6204	91	11	be	be	AUX
ejpam-6204	91	12	projectively	projectively	ADV
ejpam-6204	91	13	related	relate	VERB
ejpam-6204	91	14	if	if	SCONJ
ejpam-6204	91	15	their	their	PRON
ejpam-6204	91	16	geodesics	geodesic	NOUN
ejpam-6204	91	17	remain	remain	VERB
ejpam-6204	91	18	unchanged	unchanged	ADJ
ejpam-6204	91	19	,	,	PUNCT
ejpam-6204	91	20	up	up	ADP
ejpam-6204	91	21	to	to	ADP
ejpam-6204	91	22	an	an	DET
ejpam-6204	91	23	orientation	orientation	NOUN
ejpam-6204	91	24	-	-	PUNCT
ejpam-6204	91	25	preserving	preserve	VERB
ejpam-6204	91	26	reparameterization	reparameterization	NOUN
ejpam-6204	91	27	.	.	PUNCT
ejpam-6204	92	1	in	in	ADP
ejpam-6204	92	2	this	this	DET
ejpam-6204	92	3	case	case	NOUN
ejpam-6204	92	4	,	,	PUNCT
ejpam-6204	92	5	one	one	NUM
ejpam-6204	92	6	spray	spray	NOUN
ejpam-6204	92	7	can	can	AUX
ejpam-6204	92	8	be	be	AUX
ejpam-6204	92	9	regarded	regard	VERB
ejpam-6204	92	10	as	as	ADP
ejpam-6204	92	11	a	a	DET
ejpam-6204	92	12	projective	projective	ADJ
ejpam-6204	92	13	deformation	deformation	NOUN
ejpam-6204	92	14	of	of	ADP
ejpam-6204	92	15	the	the	DET
ejpam-6204	92	16	other	other	ADJ
ejpam-6204	92	17	.	.	PUNCT
ejpam-6204	93	1	locally	locally	ADV
ejpam-6204	93	2	,	,	PUNCT
ejpam-6204	93	3	(	(	PUNCT
ejpam-6204	93	4	1	1	X
ejpam-6204	93	5	)	)	PUNCT
ejpam-6204	93	6	modifies	modify	VERB
ejpam-6204	93	7	the	the	DET
ejpam-6204	93	8	spray	spray	NOUN
ejpam-6204	93	9	coefficients	coefficient	NOUN
ejpam-6204	93	10	as	as	SCONJ
ejpam-6204	93	11	follows	follow	VERB
ejpam-6204	93	12	:	:	PUNCT
ejpam-6204	93	13	g	g	PROPN
ejpam-6204	93	14	i	i	PRON
ejpam-6204	93	15	=	=	PUNCT
ejpam-6204	93	16	gi	gi	PROPN
ejpam-6204	93	17	+	+	CCONJ
ejpam-6204	93	18	pyi	pyi	PROPN
ejpam-6204	93	19	.	.	PUNCT
ejpam-6204	93	20	to	to	PART
ejpam-6204	93	21	see	see	VERB
ejpam-6204	93	22	why	why	SCONJ
ejpam-6204	93	23	the	the	DET
ejpam-6204	93	24	geodesics	geodesic	NOUN
ejpam-6204	93	25	remain	remain	VERB
ejpam-6204	93	26	unchanged	unchanged	ADJ
ejpam-6204	93	27	under	under	ADP
ejpam-6204	93	28	this	this	DET
ejpam-6204	93	29	deformation	deformation	NOUN
ejpam-6204	93	30	,	,	PUNCT
ejpam-6204	93	31	consider	consider	VERB
ejpam-6204	93	32	the	the	DET
ejpam-6204	93	33	new	new	ADJ
ejpam-6204	93	34	geodesic	geodesic	ADJ
ejpam-6204	93	35	equation	equation	NOUN
ejpam-6204	93	36	:	:	PUNCT
ejpam-6204	93	37	d2xi	d2xi	PROPN
ejpam-6204	93	38	dt2	dt2	PROPN
ejpam-6204	94	1	+	+	NOUN
ejpam-6204	94	2	2	2	NUM
ejpam-6204	94	3	g	g	NOUN
ejpam-6204	95	1	i	i	PRON
ejpam-6204	95	2	(	(	PUNCT
ejpam-6204	95	3	x	x	PROPN
ejpam-6204	95	4	,	,	PUNCT
ejpam-6204	95	5	dx	dx	PROPN
ejpam-6204	95	6	dt	dt	NOUN
ejpam-6204	95	7	)	)	PUNCT
ejpam-6204	96	1	=	=	PUNCT
ejpam-6204	96	2	0	0	X
ejpam-6204	96	3	.	.	PUNCT
ejpam-6204	96	4	expanding	expand	VERB
ejpam-6204	96	5	g	g	PROPN
ejpam-6204	96	6	i	i	PRON
ejpam-6204	96	7	,	,	PUNCT
ejpam-6204	96	8	we	we	PRON
ejpam-6204	96	9	obtain	obtain	VERB
ejpam-6204	96	10	:	:	PUNCT
ejpam-6204	96	11	d2xi	d2xi	PROPN
ejpam-6204	96	12	dt2	dt2	PROPN
ejpam-6204	96	13	+	+	CCONJ
ejpam-6204	96	14	2gi	2gi	ADJ
ejpam-6204	96	15	(	(	PUNCT
ejpam-6204	96	16	x	x	X
ejpam-6204	96	17	,	,	PUNCT
ejpam-6204	96	18	dx	dx	PROPN
ejpam-6204	96	19	dt	dt	X
ejpam-6204	96	20	)	)	PUNCT
ejpam-6204	97	1	+	+	CCONJ
ejpam-6204	97	2	2p	2p	NUM
ejpam-6204	97	3	(	(	PUNCT
ejpam-6204	97	4	x	x	NOUN
ejpam-6204	97	5	,	,	PUNCT
ejpam-6204	97	6	dx	dx	PROPN
ejpam-6204	97	7	dt	dt	NOUN
ejpam-6204	97	8	)	)	PUNCT
ejpam-6204	97	9	dxi	dxi	NOUN
ejpam-6204	97	10	dt	dt	NOUN
ejpam-6204	98	1	=	=	NOUN
ejpam-6204	98	2	0	0	PROPN
ejpam-6204	98	3	.	.	PUNCT
ejpam-6204	99	1	(	(	PUNCT
ejpam-6204	99	2	16	16	NUM
ejpam-6204	99	3	)	)	PUNCT
ejpam-6204	99	4	now	now	ADV
ejpam-6204	99	5	,	,	PUNCT
ejpam-6204	99	6	consider	consider	VERB
ejpam-6204	99	7	a	a	DET
ejpam-6204	99	8	reparameterization	reparameterization	NOUN
ejpam-6204	99	9	t̃	t̃	PROPN
ejpam-6204	99	10	=	=	SYM
ejpam-6204	99	11	t̃(t	t̃(t	PROPN
ejpam-6204	99	12	)	)	PUNCT
ejpam-6204	99	13	with	with	ADP
ejpam-6204	99	14	dt̃	dt̃	PROPN
ejpam-6204	99	15	dt	dt	X
ejpam-6204	99	16	>	>	X
ejpam-6204	99	17	0	0	PROPN
ejpam-6204	99	18	,	,	PUNCT
ejpam-6204	99	19	then	then	ADV
ejpam-6204	99	20	(	(	PUNCT
ejpam-6204	99	21	15	15	X
ejpam-6204	99	22	)	)	PUNCT
ejpam-6204	99	23	takes	take	VERB
ejpam-6204	99	24	the	the	DET
ejpam-6204	99	25	form	form	NOUN
ejpam-6204	99	26	d2xi	d2xi	NOUN
ejpam-6204	99	27	dt̃2	dt̃2	NOUN
ejpam-6204	99	28	+	+	CCONJ
ejpam-6204	100	1	2gi	2gi	ADJ
ejpam-6204	100	2	(	(	PUNCT
ejpam-6204	100	3	x	x	X
ejpam-6204	100	4	,	,	PUNCT
ejpam-6204	100	5	dx	dx	PROPN
ejpam-6204	100	6	dt̃	dt̃	PROPN
ejpam-6204	100	7	)	)	PUNCT
ejpam-6204	101	1	+	+	CCONJ
ejpam-6204	101	2	d2	d2	PROPN
ejpam-6204	101	3	t̃	t̃	PROPN
ejpam-6204	101	4	dt2	dt2	PROPN
ejpam-6204	101	5	(	(	PUNCT
ejpam-6204	101	6	dt̃	dt̃	PROPN
ejpam-6204	101	7	dt	dt	NOUN
ejpam-6204	101	8	)	)	PUNCT
ejpam-6204	101	9	2	2	NUM
ejpam-6204	101	10	dxi	dxi	NOUN
ejpam-6204	101	11	dt̃	dt̃	NOUN
ejpam-6204	101	12	=	=	NOUN
ejpam-6204	101	13	0	0	NUM
ejpam-6204	101	14	.	.	PUNCT
ejpam-6204	101	15	(	(	PUNCT
ejpam-6204	101	16	17	17	NUM
ejpam-6204	101	17	)	)	PUNCT
ejpam-6204	101	18	this	this	DET
ejpam-6204	101	19	equation	equation	NOUN
ejpam-6204	101	20	suggests	suggest	VERB
ejpam-6204	101	21	that	that	SCONJ
ejpam-6204	101	22	the	the	DET
ejpam-6204	101	23	new	new	ADJ
ejpam-6204	101	24	geodesic	geodesic	NOUN
ejpam-6204	101	25	parameter	parameter	NOUN
ejpam-6204	101	26	t̃	t̃	PROPN
ejpam-6204	101	27	is	be	AUX
ejpam-6204	101	28	related	relate	VERB
ejpam-6204	101	29	to	to	ADP
ejpam-6204	101	30	the	the	DET
ejpam-6204	101	31	original	original	ADJ
ejpam-6204	101	32	parameter	parameter	NOUN
ejpam-6204	101	33	t	t	PROPN
ejpam-6204	101	34	by	by	ADP
ejpam-6204	101	35	a	a	DET
ejpam-6204	101	36	reparameterization	reparameterization	NOUN
ejpam-6204	101	37	.	.	PUNCT
ejpam-6204	102	1	specifically	specifically	ADV
ejpam-6204	102	2	,	,	PUNCT
ejpam-6204	102	3	the	the	DET
ejpam-6204	102	4	function	function	NOUN
ejpam-6204	102	5	p	p	X
ejpam-6204	102	6	(	(	PUNCT
ejpam-6204	102	7	x	x	NOUN
ejpam-6204	102	8	,	,	PUNCT
ejpam-6204	102	9	dxdt	dxdt	NOUN
ejpam-6204	102	10	)	)	PUNCT
ejpam-6204	102	11	induces	induce	VERB
ejpam-6204	102	12	a	a	DET
ejpam-6204	102	13	reparameterization	reparameterization	NOUN
ejpam-6204	102	14	of	of	ADP
ejpam-6204	102	15	the	the	DET
ejpam-6204	102	16	geodesic	geodesic	ADJ
ejpam-6204	102	17	equation	equation	NOUN
ejpam-6204	102	18	,	,	PUNCT
ejpam-6204	102	19	but	but	CCONJ
ejpam-6204	102	20	the	the	DET
ejpam-6204	102	21	actual	actual	ADJ
ejpam-6204	102	22	path	path	NOUN
ejpam-6204	102	23	traced	trace	VERB
ejpam-6204	102	24	by	by	ADP
ejpam-6204	102	25	the	the	DET
ejpam-6204	102	26	geodesics	geodesic	NOUN
ejpam-6204	102	27	remains	remain	VERB
ejpam-6204	102	28	unchanged	unchanged	ADJ
ejpam-6204	102	29	.	.	PUNCT
ejpam-6204	103	1	to	to	PART
ejpam-6204	103	2	see	see	VERB
ejpam-6204	103	3	this	this	PRON
ejpam-6204	103	4	explicitly	explicitly	ADV
ejpam-6204	103	5	,	,	PUNCT
ejpam-6204	103	6	comparing	compare	VERB
ejpam-6204	103	7	(	(	PUNCT
ejpam-6204	103	8	16	16	NUM
ejpam-6204	103	9	)	)	PUNCT
ejpam-6204	103	10	and	and	CCONJ
ejpam-6204	103	11	(	(	PUNCT
ejpam-6204	103	12	17	17	NUM
ejpam-6204	103	13	)	)	PUNCT
ejpam-6204	103	14	,	,	PUNCT
ejpam-6204	103	15	then	then	ADV
ejpam-6204	103	16	the	the	DET
ejpam-6204	103	17	reparameterization	reparameterization	NOUN
ejpam-6204	103	18	t̃	t̃	PROPN
ejpam-6204	103	19	=	=	SYM
ejpam-6204	103	20	t̃(t	t̃(t	PROPN
ejpam-6204	103	21	)	)	PUNCT
ejpam-6204	103	22	satisfies	satisfie	NOUN
ejpam-6204	103	23	d2t̃	d2t̃	PROPN
ejpam-6204	103	24	dt2	dt2	PROPN
ejpam-6204	103	25	=	=	PROPN
ejpam-6204	103	26	2p	2p	NUM
ejpam-6204	103	27	(	(	PUNCT
ejpam-6204	103	28	x	x	NOUN
ejpam-6204	103	29	,	,	PUNCT
ejpam-6204	103	30	dx	dx	PROPN
ejpam-6204	103	31	dt	dt	NOUN
ejpam-6204	103	32	)	)	PUNCT
ejpam-6204	103	33	dt̃	dt̃	PROPN
ejpam-6204	103	34	dt	dt	NOUN
ejpam-6204	103	35	.	.	PUNCT
ejpam-6204	104	1	s.	s.	PROPN
ejpam-6204	104	2	g.	g.	PROPN
ejpam-6204	104	3	elgendi	elgendi	PROPN
ejpam-6204	104	4	,	,	PUNCT
ejpam-6204	104	5	a.	a.	NOUN
ejpam-6204	104	6	soleiman	soleiman	PROPN
ejpam-6204	104	7	/	/	SYM
ejpam-6204	104	8	eur	eur	PROPN
ejpam-6204	104	9	.	.	PUNCT
ejpam-6204	105	1	j.	j.	PROPN
ejpam-6204	105	2	pure	pure	PROPN
ejpam-6204	105	3	appl	appl	PROPN
ejpam-6204	105	4	.	.	PROPN
ejpam-6204	105	5	math	math	PROPN
ejpam-6204	105	6	,	,	PUNCT
ejpam-6204	105	7	18	18	NUM
ejpam-6204	105	8	(	(	PUNCT
ejpam-6204	105	9	3	3	NUM
ejpam-6204	105	10	)	)	PUNCT
ejpam-6204	105	11	(	(	PUNCT
ejpam-6204	105	12	2025	2025	NUM
ejpam-6204	105	13	)	)	PUNCT
ejpam-6204	105	14	,	,	PUNCT
ejpam-6204	105	15	6204	6204	NUM
ejpam-6204	105	16	6	6	NUM
ejpam-6204	105	17	of	of	ADP
ejpam-6204	105	18	18	18	NUM
ejpam-6204	105	19	the	the	DET
ejpam-6204	105	20	key	key	ADJ
ejpam-6204	105	21	observation	observation	NOUN
ejpam-6204	105	22	is	be	AUX
ejpam-6204	105	23	that	that	SCONJ
ejpam-6204	105	24	a	a	DET
ejpam-6204	105	25	projective	projective	ADJ
ejpam-6204	105	26	deformation	deformation	NOUN
ejpam-6204	105	27	modifies	modify	VERB
ejpam-6204	105	28	the	the	DET
ejpam-6204	105	29	acceleration	acceleration	NOUN
ejpam-6204	105	30	along	along	ADP
ejpam-6204	105	31	the	the	DET
ejpam-6204	105	32	geodesics	geodesic	NOUN
ejpam-6204	105	33	but	but	CCONJ
ejpam-6204	105	34	does	do	AUX
ejpam-6204	105	35	not	not	PART
ejpam-6204	105	36	alter	alter	VERB
ejpam-6204	105	37	their	their	PRON
ejpam-6204	105	38	direction	direction	NOUN
ejpam-6204	105	39	.	.	PUNCT
ejpam-6204	106	1	the	the	DET
ejpam-6204	106	2	new	new	ADJ
ejpam-6204	106	3	spray	spray	NOUN
ejpam-6204	106	4	s	s	VERB
ejpam-6204	106	5	still	still	ADV
ejpam-6204	106	6	determines	determine	VERB
ejpam-6204	106	7	the	the	DET
ejpam-6204	106	8	same	same	ADJ
ejpam-6204	106	9	set	set	NOUN
ejpam-6204	106	10	of	of	ADP
ejpam-6204	106	11	geodesics	geodesic	NOUN
ejpam-6204	106	12	in	in	ADP
ejpam-6204	106	13	terms	term	NOUN
ejpam-6204	106	14	of	of	ADP
ejpam-6204	106	15	their	their	PRON
ejpam-6204	106	16	geometric	geometric	ADJ
ejpam-6204	106	17	trajectories	trajectory	NOUN
ejpam-6204	106	18	,	,	PUNCT
ejpam-6204	106	19	though	though	SCONJ
ejpam-6204	106	20	their	their	PRON
ejpam-6204	106	21	parameterization	parameterization	NOUN
ejpam-6204	106	22	may	may	AUX
ejpam-6204	106	23	differ	differ	VERB
ejpam-6204	106	24	.	.	PUNCT
ejpam-6204	107	1	3	3	X
ejpam-6204	107	2	.	.	X
ejpam-6204	107	3	general	general	ADJ
ejpam-6204	107	4	deformations	deformation	NOUN
ejpam-6204	107	5	of	of	ADP
ejpam-6204	107	6	sprays	spray	NOUN
ejpam-6204	107	7	for	for	ADP
ejpam-6204	107	8	any	any	DET
ejpam-6204	107	9	two	two	NUM
ejpam-6204	107	10	sprays	spray	NOUN
ejpam-6204	107	11	s1	s1	NOUN
ejpam-6204	107	12	and	and	CCONJ
ejpam-6204	107	13	s2	s2	NOUN
ejpam-6204	107	14	on	on	ADP
ejpam-6204	107	15	a	a	DET
ejpam-6204	107	16	manifold	manifold	ADJ
ejpam-6204	107	17	m	m	NOUN
ejpam-6204	107	18	,	,	PUNCT
ejpam-6204	107	19	one	one	PRON
ejpam-6204	107	20	can	can	AUX
ejpam-6204	107	21	see	see	VERB
ejpam-6204	107	22	that	that	SCONJ
ejpam-6204	107	23	the	the	DET
ejpam-6204	107	24	difference	difference	NOUN
ejpam-6204	107	25	s1−s2	s1−s2	NOUN
ejpam-6204	107	26	is	be	AUX
ejpam-6204	107	27	always	always	ADV
ejpam-6204	107	28	vertical	vertical	ADJ
ejpam-6204	107	29	.	.	PUNCT
ejpam-6204	108	1	indeed	indeed	ADV
ejpam-6204	108	2	,	,	PUNCT
ejpam-6204	108	3	j(s1	j(s1	ADJ
ejpam-6204	108	4	−	−	PROPN
ejpam-6204	108	5	s2	s2	PROPN
ejpam-6204	108	6	)	)	PUNCT
ejpam-6204	108	7	=	=	SYM
ejpam-6204	108	8	js1	js1	NOUN
ejpam-6204	108	9	−	−	NOUN
ejpam-6204	108	10	js2	js2	PROPN
ejpam-6204	109	1	=	=	PUNCT
ejpam-6204	109	2	c	c	PROPN
ejpam-6204	110	1	−	−	NOUN
ejpam-6204	110	2	c	c	NOUN
ejpam-6204	110	3	=	=	SYM
ejpam-6204	110	4	0	0	X
ejpam-6204	110	5	.	.	PUNCT
ejpam-6204	111	1	using	use	VERB
ejpam-6204	111	2	the	the	DET
ejpam-6204	111	3	fact	fact	NOUN
ejpam-6204	111	4	that	that	SCONJ
ejpam-6204	111	5	a	a	DET
ejpam-6204	111	6	vector	vector	NOUN
ejpam-6204	111	7	field	field	NOUN
ejpam-6204	111	8	x	x	PUNCT
ejpam-6204	111	9	on	on	ADP
ejpam-6204	111	10	tm	tm	PROPN
ejpam-6204	111	11	is	be	AUX
ejpam-6204	111	12	vertical	vertical	ADJ
ejpam-6204	111	13	if	if	SCONJ
ejpam-6204	111	14	and	and	CCONJ
ejpam-6204	111	15	only	only	ADV
ejpam-6204	111	16	if	if	SCONJ
ejpam-6204	111	17	jx	jx	PROPN
ejpam-6204	111	18	=	=	SYM
ejpam-6204	111	19	0	0	PROPN
ejpam-6204	111	20	,	,	PUNCT
ejpam-6204	111	21	we	we	PRON
ejpam-6204	111	22	conclude	conclude	VERB
ejpam-6204	111	23	that	that	SCONJ
ejpam-6204	111	24	s1	s1	PROPN
ejpam-6204	111	25	−	−	PROPN
ejpam-6204	111	26	s2	s2	PROPN
ejpam-6204	111	27	is	be	AUX
ejpam-6204	111	28	vertical	vertical	ADJ
ejpam-6204	111	29	.	.	PUNCT
ejpam-6204	112	1	now	now	ADV
ejpam-6204	112	2	,	,	PUNCT
ejpam-6204	112	3	using	use	VERB
ejpam-6204	112	4	the	the	DET
ejpam-6204	112	5	fact	fact	NOUN
ejpam-6204	112	6	that	that	SCONJ
ejpam-6204	112	7	the	the	DET
ejpam-6204	112	8	difference	difference	NOUN
ejpam-6204	112	9	of	of	ADP
ejpam-6204	112	10	two	two	NUM
ejpam-6204	112	11	sprays	spray	NOUN
ejpam-6204	112	12	is	be	AUX
ejpam-6204	112	13	vertical	vertical	ADJ
ejpam-6204	112	14	,	,	PUNCT
ejpam-6204	112	15	we	we	PRON
ejpam-6204	112	16	can	can	AUX
ejpam-6204	112	17	define	define	VERB
ejpam-6204	112	18	the	the	DET
ejpam-6204	112	19	general	general	ADJ
ejpam-6204	112	20	deformation	deformation	NOUN
ejpam-6204	112	21	of	of	ADP
ejpam-6204	112	22	a	a	DET
ejpam-6204	112	23	spray	spray	NOUN
ejpam-6204	112	24	s	s	PRON
ejpam-6204	112	25	as	as	SCONJ
ejpam-6204	112	26	follows	follow	VERB
ejpam-6204	112	27	.	.	PUNCT
ejpam-6204	113	1	definition	definition	NOUN
ejpam-6204	113	2	2	2	NUM
ejpam-6204	113	3	.	.	PUNCT
ejpam-6204	114	1	let	let	VERB
ejpam-6204	114	2	s	s	PRON
ejpam-6204	114	3	be	be	AUX
ejpam-6204	114	4	a	a	DET
ejpam-6204	114	5	spray	spray	NOUN
ejpam-6204	114	6	on	on	ADP
ejpam-6204	114	7	a	a	DET
ejpam-6204	114	8	manifold	manifold	ADJ
ejpam-6204	114	9	m	m	NOUN
ejpam-6204	114	10	,	,	PUNCT
ejpam-6204	114	11	and	and	CCONJ
ejpam-6204	114	12	ζ	ζ	NOUN
ejpam-6204	114	13	be	be	AUX
ejpam-6204	114	14	a	a	DET
ejpam-6204	114	15	vertical	vertical	ADJ
ejpam-6204	114	16	vector	vector	NOUN
ejpam-6204	114	17	field	field	NOUN
ejpam-6204	114	18	ζ	ζ	NOUN
ejpam-6204	114	19	∈	∈	PROPN
ejpam-6204	114	20	xv(tm	xv(tm	PROPN
ejpam-6204	114	21	)	)	PUNCT
ejpam-6204	114	22	.	.	PUNCT
ejpam-6204	115	1	the	the	DET
ejpam-6204	115	2	general	general	ADJ
ejpam-6204	115	3	deformation	deformation	NOUN
ejpam-6204	115	4	of	of	ADP
ejpam-6204	115	5	s	s	PRON
ejpam-6204	115	6	is	be	AUX
ejpam-6204	115	7	given	give	VERB
ejpam-6204	115	8	by	by	ADP
ejpam-6204	115	9	s̃	s̃	PROPN
ejpam-6204	115	10	=	=	SYM
ejpam-6204	115	11	s	s	PART
ejpam-6204	115	12	−	−	NOUN
ejpam-6204	115	13	2ζ	2ζ	NUM
ejpam-6204	115	14	.	.	PUNCT
ejpam-6204	116	1	(	(	PUNCT
ejpam-6204	116	2	18	18	NUM
ejpam-6204	116	3	)	)	PUNCT
ejpam-6204	116	4	moreover	moreover	ADV
ejpam-6204	116	5	,	,	PUNCT
ejpam-6204	116	6	the	the	DET
ejpam-6204	116	7	coefficients	coefficient	NOUN
ejpam-6204	116	8	of	of	ADP
ejpam-6204	116	9	the	the	DET
ejpam-6204	116	10	two	two	NUM
ejpam-6204	116	11	sprays	spray	NOUN
ejpam-6204	116	12	are	be	AUX
ejpam-6204	116	13	related	relate	VERB
ejpam-6204	116	14	by	by	ADP
ejpam-6204	116	15	g̃i	g̃i	NOUN
ejpam-6204	116	16	=	=	NOUN
ejpam-6204	116	17	gi	gi	X
ejpam-6204	117	1	+	+	CCONJ
ejpam-6204	117	2	ζi	ζi	PROPN
ejpam-6204	117	3	.	.	PROPN
ejpam-6204	117	4	(	(	PUNCT
ejpam-6204	117	5	19	19	NUM
ejpam-6204	117	6	)	)	PUNCT
ejpam-6204	117	7	by	by	ADP
ejpam-6204	117	8	making	make	VERB
ejpam-6204	117	9	use	use	NOUN
ejpam-6204	117	10	of	of	ADP
ejpam-6204	117	11	(	(	PUNCT
ejpam-6204	117	12	16	16	NUM
ejpam-6204	117	13	)	)	PUNCT
ejpam-6204	117	14	and	and	CCONJ
ejpam-6204	117	15	(	(	PUNCT
ejpam-6204	117	16	19	19	NUM
ejpam-6204	117	17	)	)	PUNCT
ejpam-6204	117	18	,	,	PUNCT
ejpam-6204	117	19	we	we	PRON
ejpam-6204	117	20	have	have	VERB
ejpam-6204	117	21	the	the	DET
ejpam-6204	117	22	following	follow	VERB
ejpam-6204	117	23	property	property	NOUN
ejpam-6204	117	24	:	:	PUNCT
ejpam-6204	117	25	the	the	DET
ejpam-6204	117	26	general	general	ADJ
ejpam-6204	117	27	deformation	deformation	NOUN
ejpam-6204	117	28	(	(	PUNCT
ejpam-6204	117	29	18	18	NUM
ejpam-6204	117	30	)	)	PUNCT
ejpam-6204	117	31	of	of	ADP
ejpam-6204	117	32	s	s	PROPN
ejpam-6204	117	33	is	be	AUX
ejpam-6204	117	34	projective	projective	ADJ
ejpam-6204	117	35	,	,	PUNCT
ejpam-6204	117	36	i.e.	i.e.	X
ejpam-6204	117	37	,	,	PUNCT
ejpam-6204	117	38	preserves	preserve	VERB
ejpam-6204	117	39	geodesics	geodesic	NOUN
ejpam-6204	117	40	,	,	PUNCT
ejpam-6204	117	41	if	if	SCONJ
ejpam-6204	117	42	and	and	CCONJ
ejpam-6204	117	43	only	only	ADV
ejpam-6204	117	44	if	if	SCONJ
ejpam-6204	117	45	the	the	DET
ejpam-6204	117	46	vertical	vertical	ADJ
ejpam-6204	117	47	vector	vector	NOUN
ejpam-6204	117	48	ζ	ζ	NOUN
ejpam-6204	117	49	is	be	AUX
ejpam-6204	117	50	proportional	proportional	ADJ
ejpam-6204	117	51	to	to	ADP
ejpam-6204	117	52	the	the	DET
ejpam-6204	117	53	liouville	liouville	NOUN
ejpam-6204	117	54	vector	vector	NOUN
ejpam-6204	117	55	field	field	NOUN
ejpam-6204	117	56	c	c	NOUN
ejpam-6204	117	57	(	(	PUNCT
ejpam-6204	117	58	or	or	CCONJ
ejpam-6204	117	59	equivalently	equivalently	ADV
ejpam-6204	117	60	,	,	PUNCT
ejpam-6204	117	61	ζi	ζi	PROPN
ejpam-6204	117	62	is	be	AUX
ejpam-6204	117	63	proportional	proportional	ADJ
ejpam-6204	117	64	to	to	ADP
ejpam-6204	117	65	yi	yi	NUM
ejpam-6204	117	66	)	)	PUNCT
ejpam-6204	117	67	.	.	PUNCT
ejpam-6204	118	1	for	for	ADP
ejpam-6204	118	2	a	a	DET
ejpam-6204	118	3	given	give	VERB
ejpam-6204	118	4	finsler	finsler	NOUN
ejpam-6204	118	5	manifold	manifold	NOUN
ejpam-6204	118	6	(	(	PUNCT
ejpam-6204	118	7	m	m	PROPN
ejpam-6204	118	8	,	,	PUNCT
ejpam-6204	118	9	f	f	PROPN
ejpam-6204	118	10	)	)	PUNCT
ejpam-6204	118	11	,	,	PUNCT
ejpam-6204	118	12	any	any	DET
ejpam-6204	118	13	deforamtion	deforamtion	NOUN
ejpam-6204	118	14	of	of	ADP
ejpam-6204	118	15	f	f	PROPN
ejpam-6204	118	16	implies	imply	VERB
ejpam-6204	118	17	a	a	DET
ejpam-6204	118	18	deformation	deformation	NOUN
ejpam-6204	118	19	of	of	ADP
ejpam-6204	118	20	the	the	DET
ejpam-6204	118	21	geodesic	geodesic	ADJ
ejpam-6204	118	22	spray	spray	NOUN
ejpam-6204	118	23	.	.	PUNCT
ejpam-6204	119	1	as	as	ADP
ejpam-6204	119	2	an	an	DET
ejpam-6204	119	3	example	example	NOUN
ejpam-6204	119	4	,	,	PUNCT
ejpam-6204	119	5	let	let	VERB
ejpam-6204	119	6	’s	’s	NOUN
ejpam-6204	119	7	consider	consider	VERB
ejpam-6204	119	8	the	the	DET
ejpam-6204	119	9	deformation	deformation	NOUN
ejpam-6204	119	10	of	of	ADP
ejpam-6204	119	11	a	a	DET
ejpam-6204	119	12	a	a	DET
ejpam-6204	119	13	geodesic	geodesic	ADJ
ejpam-6204	119	14	spray	spray	NOUN
ejpam-6204	119	15	of	of	ADP
ejpam-6204	119	16	a	a	DET
ejpam-6204	119	17	finsler	finsler	NOUN
ejpam-6204	119	18	manifold	manifold	NOUN
ejpam-6204	119	19	(	(	PUNCT
ejpam-6204	119	20	m	m	PROPN
ejpam-6204	119	21	,	,	PUNCT
ejpam-6204	119	22	f	f	PROPN
ejpam-6204	119	23	)	)	PUNCT
ejpam-6204	119	24	due	due	ADP
ejpam-6204	119	25	to	to	ADP
ejpam-6204	119	26	a	a	DET
ejpam-6204	119	27	conformal	conformal	ADJ
ejpam-6204	119	28	change	change	NOUN
ejpam-6204	119	29	of	of	ADP
ejpam-6204	119	30	the	the	DET
ejpam-6204	119	31	finsler	finsler	NOUN
ejpam-6204	119	32	metric	metric	PROPN
ejpam-6204	119	33	f	f	PROPN
ejpam-6204	119	34	.	.	PUNCT
ejpam-6204	120	1	example	example	NOUN
ejpam-6204	121	1	1	1	NUM
ejpam-6204	121	2	.	.	X
ejpam-6204	121	3	consider	consider	VERB
ejpam-6204	121	4	the	the	DET
ejpam-6204	121	5	conformal	conformal	ADJ
ejpam-6204	121	6	transformation	transformation	NOUN
ejpam-6204	121	7	of	of	ADP
ejpam-6204	121	8	a	a	DET
ejpam-6204	121	9	finsler	finsler	NOUN
ejpam-6204	121	10	manifold	manifold	NOUN
ejpam-6204	121	11	(	(	PUNCT
ejpam-6204	121	12	m	m	PROPN
ejpam-6204	121	13	,	,	PUNCT
ejpam-6204	121	14	f	f	PROPN
ejpam-6204	121	15	)	)	PUNCT
ejpam-6204	121	16	with	with	ADP
ejpam-6204	121	17	the	the	DET
ejpam-6204	121	18	geodesic	geodesic	ADJ
ejpam-6204	121	19	spray	spray	NOUN
ejpam-6204	121	20	s	s	PART
ejpam-6204	121	21	f̃	f̃	PROPN
ejpam-6204	121	22	=	=	SYM
ejpam-6204	121	23	eσ(x)f	eσ(x)f	PROPN
ejpam-6204	121	24	.	.	PUNCT
ejpam-6204	122	1	so	so	ADV
ejpam-6204	122	2	the	the	DET
ejpam-6204	122	3	geodesic	geodesic	ADJ
ejpam-6204	122	4	spray	spray	NOUN
ejpam-6204	122	5	s	s	VERB
ejpam-6204	122	6	is	be	AUX
ejpam-6204	122	7	deformed	deform	VERB
ejpam-6204	122	8	as	as	SCONJ
ejpam-6204	122	9	follows	follow	VERB
ejpam-6204	122	10	:	:	PUNCT
ejpam-6204	122	11	s̃	s̃	PROPN
ejpam-6204	122	12	=	=	SYM
ejpam-6204	122	13	s	s	PART
ejpam-6204	122	14	−	−	NOUN
ejpam-6204	122	15	2ζ	2ζ	NUM
ejpam-6204	122	16	.	.	PUNCT
ejpam-6204	123	1	by	by	ADP
ejpam-6204	123	2	[	[	X
ejpam-6204	123	3	18	18	NUM
ejpam-6204	123	4	]	]	PUNCT
ejpam-6204	123	5	,	,	PUNCT
ejpam-6204	123	6	the	the	DET
ejpam-6204	123	7	spray	spray	NOUN
ejpam-6204	123	8	coefficients	coefficient	NOUN
ejpam-6204	123	9	are	be	AUX
ejpam-6204	123	10	related	relate	VERB
ejpam-6204	123	11	by	by	ADP
ejpam-6204	123	12	g̃i	g̃i	NOUN
ejpam-6204	124	1	=	=	NOUN
ejpam-6204	124	2	gi	gi	X
ejpam-6204	125	1	+	+	CCONJ
ejpam-6204	125	2	ζi	ζi	PROPN
ejpam-6204	125	3	=	=	ADJ
ejpam-6204	125	4	gi	gi	NOUN
ejpam-6204	126	1	+	+	NOUN
ejpam-6204	126	2	1	1	NUM
ejpam-6204	126	3	2	2	NUM
ejpam-6204	126	4	f	f	NOUN
ejpam-6204	126	5	2σi	2σi	NOUN
ejpam-6204	126	6	−	−	PROPN
ejpam-6204	127	1	σ0y	σ0y	PROPN
ejpam-6204	127	2	i	i	PRON
ejpam-6204	127	3	,	,	PUNCT
ejpam-6204	127	4	where	where	SCONJ
ejpam-6204	127	5	σr	σr	ADV
ejpam-6204	127	6	:	:	PUNCT
ejpam-6204	127	7	=	=	SYM
ejpam-6204	127	8	∂rσ	∂rσ	PROPN
ejpam-6204	127	9	,	,	PUNCT
ejpam-6204	127	10	and	and	CCONJ
ejpam-6204	127	11	σ0	σ0	NOUN
ejpam-6204	127	12	:	:	PUNCT
ejpam-6204	127	13	=	=	PUNCT
ejpam-6204	127	14	σry	σry	PROPN
ejpam-6204	127	15	r.	r.	PROPN
ejpam-6204	127	16	s.	s.	PROPN
ejpam-6204	127	17	g.	g.	PROPN
ejpam-6204	127	18	elgendi	elgendi	PROPN
ejpam-6204	127	19	,	,	PUNCT
ejpam-6204	127	20	a.	a.	NOUN
ejpam-6204	127	21	soleiman	soleiman	PROPN
ejpam-6204	127	22	/	/	SYM
ejpam-6204	127	23	eur	eur	PROPN
ejpam-6204	127	24	.	.	PUNCT
ejpam-6204	128	1	j.	j.	PROPN
ejpam-6204	128	2	pure	pure	PROPN
ejpam-6204	128	3	appl	appl	PROPN
ejpam-6204	128	4	.	.	PROPN
ejpam-6204	128	5	math	math	PROPN
ejpam-6204	128	6	,	,	PUNCT
ejpam-6204	128	7	18	18	NUM
ejpam-6204	128	8	(	(	PUNCT
ejpam-6204	128	9	3	3	NUM
ejpam-6204	128	10	)	)	PUNCT
ejpam-6204	128	11	(	(	PUNCT
ejpam-6204	128	12	2025	2025	NUM
ejpam-6204	128	13	)	)	PUNCT
ejpam-6204	128	14	,	,	PUNCT
ejpam-6204	128	15	6204	6204	NUM
ejpam-6204	128	16	7	7	NUM
ejpam-6204	128	17	of	of	ADP
ejpam-6204	128	18	18	18	NUM
ejpam-6204	128	19	now	now	ADV
ejpam-6204	128	20	,	,	PUNCT
ejpam-6204	128	21	using	use	VERB
ejpam-6204	128	22	the	the	DET
ejpam-6204	128	23	facts	fact	NOUN
ejpam-6204	128	24	that	that	SCONJ
ejpam-6204	128	25	c	c	NOUN
ejpam-6204	128	26	=	=	SYM
ejpam-6204	128	27	yi∂̇i	yi∂̇i	PROPN
ejpam-6204	128	28	and	and	CCONJ
ejpam-6204	128	29	ℓi	ℓi	NOUN
ejpam-6204	128	30	=	=	PROPN
ejpam-6204	128	31	yi	yi	PROPN
ejpam-6204	128	32	f	f	NOUN
ejpam-6204	128	33	,	,	PUNCT
ejpam-6204	128	34	we	we	PRON
ejpam-6204	128	35	have	have	AUX
ejpam-6204	128	36	ζ	ζ	NOUN
ejpam-6204	128	37	=	=	SYM
ejpam-6204	128	38	ζi∂̇i	ζi∂̇i	NOUN
ejpam-6204	128	39	=	=	SYM
ejpam-6204	128	40	f	f	PROPN
ejpam-6204	128	41	2	2	NUM
ejpam-6204	128	42	2	2	NUM
ejpam-6204	128	43	(	(	PUNCT
ejpam-6204	128	44	gir	gir	VERB
ejpam-6204	128	45	−	−	PROPN
ejpam-6204	128	46	2ℓiℓr	2ℓiℓr	NUM
ejpam-6204	128	47	)	)	PUNCT
ejpam-6204	129	1	σr(x)∂̇i	σr(x)∂̇i	PRON
ejpam-6204	129	2	=	=	SYM
ejpam-6204	129	3	f	f	PROPN
ejpam-6204	129	4	2	2	NUM
ejpam-6204	129	5	2	2	NUM
ejpam-6204	129	6	girσr(x)∂̇i	girσr(x)∂̇i	NOUN
ejpam-6204	129	7	−	−	PROPN
ejpam-6204	129	8	σ0(x)c	σ0(x)c	X
ejpam-6204	129	9	=	=	SYM
ejpam-6204	129	10	1	1	NUM
ejpam-6204	129	11	2	2	NUM
ejpam-6204	129	12	f	f	NOUN
ejpam-6204	129	13	2σi∂̇i	2σi∂̇i	NUM
ejpam-6204	129	14	−	−	ADP
ejpam-6204	129	15	σ0c	σ0c	PROPN
ejpam-6204	129	16	,	,	PUNCT
ejpam-6204	129	17	where	where	SCONJ
ejpam-6204	129	18	ζi	ζi	PROPN
ejpam-6204	129	19	=	=	SYM
ejpam-6204	129	20	f	f	PROPN
ejpam-6204	129	21	2	2	NUM
ejpam-6204	129	22	2	2	NUM
ejpam-6204	129	23	(	(	PUNCT
ejpam-6204	129	24	gir	gir	VERB
ejpam-6204	129	25	−	−	PROPN
ejpam-6204	129	26	2ℓiℓr	2ℓiℓr	NUM
ejpam-6204	129	27	)	)	PUNCT
ejpam-6204	129	28	σr(x	σr(x	X
ejpam-6204	129	29	)	)	PUNCT
ejpam-6204	129	30	=	=	SYM
ejpam-6204	130	1	1	1	NUM
ejpam-6204	130	2	2	2	NUM
ejpam-6204	130	3	f	f	NOUN
ejpam-6204	130	4	2σi	2σi	NOUN
ejpam-6204	130	5	−	−	PROPN
ejpam-6204	131	1	σ0y	σ0y	PROPN
ejpam-6204	131	2	i.	i.	NOUN
ejpam-6204	131	3	moreover	moreover	ADV
ejpam-6204	131	4	,	,	PUNCT
ejpam-6204	131	5	the	the	DET
ejpam-6204	131	6	conformal	conformal	NOUN
ejpam-6204	131	7	change	change	NOUN
ejpam-6204	131	8	is	be	AUX
ejpam-6204	131	9	projective	projective	ADJ
ejpam-6204	131	10	,	,	PUNCT
ejpam-6204	131	11	i.e.	i.e.	X
ejpam-6204	131	12	,	,	PUNCT
ejpam-6204	131	13	preserves	preserve	VERB
ejpam-6204	131	14	the	the	DET
ejpam-6204	131	15	geodesics	geodesic	NOUN
ejpam-6204	131	16	of	of	ADP
ejpam-6204	131	17	s	s	PROPN
ejpam-6204	131	18	,	,	PUNCT
ejpam-6204	131	19	if	if	SCONJ
ejpam-6204	131	20	and	and	CCONJ
ejpam-6204	131	21	only	only	ADV
ejpam-6204	131	22	if	if	SCONJ
ejpam-6204	131	23	ζ	ζ	NOUN
ejpam-6204	131	24	=	=	SYM
ejpam-6204	131	25	c.	c.	NOUN
ejpam-6204	131	26	this	this	PRON
ejpam-6204	131	27	occurs	occur	VERB
ejpam-6204	131	28	if	if	SCONJ
ejpam-6204	131	29	and	and	CCONJ
ejpam-6204	131	30	only	only	ADV
ejpam-6204	131	31	if	if	SCONJ
ejpam-6204	131	32	σi(x	σi(x	NUM
ejpam-6204	131	33	)	)	PUNCT
ejpam-6204	131	34	=	=	SYM
ejpam-6204	132	1	0	0	X
ejpam-6204	132	2	.	.	PUNCT
ejpam-6204	133	1	that	that	PRON
ejpam-6204	133	2	is	is	ADV
ejpam-6204	133	3	,	,	PUNCT
ejpam-6204	133	4	σ	σ	PROPN
ejpam-6204	133	5	is	be	AUX
ejpam-6204	133	6	constant	constant	ADJ
ejpam-6204	133	7	.	.	PUNCT
ejpam-6204	134	1	3.1	3.1	NUM
ejpam-6204	134	2	.	.	X
ejpam-6204	134	3	projective	projective	ADJ
ejpam-6204	134	4	-	-	PUNCT
ejpam-6204	134	5	like	like	ADJ
ejpam-6204	134	6	deformation	deformation	NOUN
ejpam-6204	134	7	one	one	NUM
ejpam-6204	134	8	the	the	DET
ejpam-6204	134	9	special	special	ADJ
ejpam-6204	134	10	and	and	CCONJ
ejpam-6204	134	11	important	important	ADJ
ejpam-6204	134	12	deformation	deformation	NOUN
ejpam-6204	134	13	of	of	ADP
ejpam-6204	134	14	a	a	DET
ejpam-6204	134	15	spray	spray	NOUN
ejpam-6204	134	16	is	be	AUX
ejpam-6204	134	17	the	the	DET
ejpam-6204	134	18	projective	projective	ADJ
ejpam-6204	134	19	deformation	deformation	NOUN
ejpam-6204	134	20	,	,	PUNCT
ejpam-6204	134	21	that	that	ADV
ejpam-6204	134	22	is	be	AUX
ejpam-6204	134	23	,	,	PUNCT
ejpam-6204	134	24	s	s	PART
ejpam-6204	134	25	=	=	SYM
ejpam-6204	134	26	s	s	PART
ejpam-6204	134	27	−	−	PROPN
ejpam-6204	134	28	2p(x	2p(x	PROPN
ejpam-6204	134	29	,	,	PUNCT
ejpam-6204	134	30	y)c	y)c	NOUN
ejpam-6204	134	31	.	.	PUNCT
ejpam-6204	135	1	under	under	ADP
ejpam-6204	135	2	the	the	DET
ejpam-6204	135	3	projective	projective	ADJ
ejpam-6204	135	4	deformation	deformation	NOUN
ejpam-6204	135	5	,	,	PUNCT
ejpam-6204	135	6	the	the	DET
ejpam-6204	135	7	geodesics	geodesic	NOUN
ejpam-6204	135	8	of	of	ADP
ejpam-6204	135	9	a	a	DET
ejpam-6204	135	10	spray	spray	NOUN
ejpam-6204	135	11	are	be	AUX
ejpam-6204	135	12	preserved	preserve	VERB
ejpam-6204	135	13	.	.	PUNCT
ejpam-6204	136	1	so	so	ADV
ejpam-6204	136	2	,	,	PUNCT
ejpam-6204	136	3	in	in	ADP
ejpam-6204	136	4	this	this	DET
ejpam-6204	136	5	subsection	subsection	NOUN
ejpam-6204	136	6	we	we	PRON
ejpam-6204	136	7	consider	consider	VERB
ejpam-6204	136	8	another	another	DET
ejpam-6204	136	9	point	point	NOUN
ejpam-6204	136	10	of	of	ADP
ejpam-6204	136	11	view	view	NOUN
ejpam-6204	136	12	of	of	ADP
ejpam-6204	136	13	a	a	DET
ejpam-6204	136	14	more	more	ADV
ejpam-6204	136	15	general	general	ADJ
ejpam-6204	136	16	deformation	deformation	NOUN
ejpam-6204	136	17	than	than	ADP
ejpam-6204	136	18	the	the	DET
ejpam-6204	136	19	projective	projective	ADJ
ejpam-6204	136	20	deformation	deformation	NOUN
ejpam-6204	136	21	but	but	CCONJ
ejpam-6204	136	22	still	still	ADV
ejpam-6204	136	23	a	a	DET
ejpam-6204	136	24	special	special	ADJ
ejpam-6204	136	25	case	case	NOUN
ejpam-6204	136	26	of	of	ADP
ejpam-6204	136	27	the	the	DET
ejpam-6204	136	28	general	general	ADJ
ejpam-6204	136	29	deformation	deformation	NOUN
ejpam-6204	136	30	of	of	ADP
ejpam-6204	136	31	a	a	DET
ejpam-6204	136	32	spray	spray	NOUN
ejpam-6204	136	33	s.	s.	PROPN
ejpam-6204	136	34	in	in	ADP
ejpam-6204	136	35	this	this	DET
ejpam-6204	136	36	section	section	NOUN
ejpam-6204	136	37	,	,	PUNCT
ejpam-6204	136	38	we	we	PRON
ejpam-6204	136	39	introduce	introduce	VERB
ejpam-6204	136	40	the	the	DET
ejpam-6204	136	41	porjective	porjective	ADJ
ejpam-6204	136	42	-	-	PUNCT
ejpam-6204	136	43	like	like	ADJ
ejpam-6204	136	44	deformation	deformation	NOUN
ejpam-6204	136	45	as	as	SCONJ
ejpam-6204	136	46	follows	follow	VERB
ejpam-6204	136	47	:	:	PUNCT
ejpam-6204	136	48	definition	definition	NOUN
ejpam-6204	136	49	3	3	NUM
ejpam-6204	136	50	.	.	PUNCT
ejpam-6204	137	1	let	let	VERB
ejpam-6204	137	2	s	s	PRON
ejpam-6204	137	3	be	be	AUX
ejpam-6204	137	4	a	a	DET
ejpam-6204	137	5	spray	spray	NOUN
ejpam-6204	137	6	on	on	ADP
ejpam-6204	137	7	a	a	DET
ejpam-6204	137	8	manifold	manifold	ADJ
ejpam-6204	137	9	m	m	NOUN
ejpam-6204	137	10	,	,	PUNCT
ejpam-6204	137	11	and	and	CCONJ
ejpam-6204	137	12	consider	consider	VERB
ejpam-6204	137	13	any	any	DET
ejpam-6204	137	14	vertical	vertical	ADJ
ejpam-6204	137	15	vector	vector	NOUN
ejpam-6204	137	16	field	field	NOUN
ejpam-6204	137	17	ξ	ξ	PROPN
ejpam-6204	137	18	∈	∈	PROPN
ejpam-6204	137	19	xv(tm	xv(tm	PROPN
ejpam-6204	137	20	)	)	PUNCT
ejpam-6204	137	21	.	.	PUNCT
ejpam-6204	138	1	the	the	DET
ejpam-6204	138	2	projective	projective	NOUN
ejpam-6204	138	3	-	-	PUNCT
ejpam-6204	138	4	like	like	ADJ
ejpam-6204	138	5	deformation	deformation	NOUN
ejpam-6204	138	6	of	of	ADP
ejpam-6204	138	7	s	s	PRON
ejpam-6204	138	8	is	be	AUX
ejpam-6204	138	9	given	give	VERB
ejpam-6204	138	10	by	by	ADP
ejpam-6204	138	11	s̃	s̃	PROPN
ejpam-6204	138	12	=	=	SYM
ejpam-6204	138	13	s	s	PART
ejpam-6204	138	14	−	−	PROPN
ejpam-6204	138	15	2p(x	2p(x	PROPN
ejpam-6204	138	16	,	,	PUNCT
ejpam-6204	138	17	y)ξ	y)ξ	PUNCT
ejpam-6204	138	18	.	.	PUNCT
ejpam-6204	139	1	(	(	PUNCT
ejpam-6204	139	2	20	20	NUM
ejpam-6204	139	3	)	)	PUNCT
ejpam-6204	139	4	where	where	SCONJ
ejpam-6204	139	5	p(x	p(x	PROPN
ejpam-6204	139	6	,	,	PUNCT
ejpam-6204	139	7	y	y	NOUN
ejpam-6204	139	8	)	)	PUNCT
ejpam-6204	139	9	∈	∈	PROPN
ejpam-6204	139	10	c∞(t	c∞(t	PROPN
ejpam-6204	139	11	m	m	NOUN
ejpam-6204	139	12	)	)	PUNCT
ejpam-6204	139	13	is	be	AUX
ejpam-6204	139	14	a	a	DET
ejpam-6204	139	15	smooth	smooth	ADJ
ejpam-6204	139	16	,	,	PUNCT
ejpam-6204	139	17	and	and	CCONJ
ejpam-6204	139	18	positively	positively	ADV
ejpam-6204	139	19	homogeneous	homogeneous	ADJ
ejpam-6204	139	20	function	function	NOUN
ejpam-6204	139	21	of	of	ADP
ejpam-6204	139	22	degree	degree	NOUN
ejpam-6204	139	23	1	1	NUM
ejpam-6204	139	24	in	in	ADP
ejpam-6204	139	25	y	y	PROPN
ejpam-6204	139	26	,	,	PUNCT
ejpam-6204	139	27	and	and	CCONJ
ejpam-6204	139	28	called	call	VERB
ejpam-6204	139	29	the	the	DET
ejpam-6204	139	30	deformation	deformation	NOUN
ejpam-6204	139	31	factor	factor	NOUN
ejpam-6204	139	32	.	.	PUNCT
ejpam-6204	140	1	moreover	moreover	ADV
ejpam-6204	140	2	,	,	PUNCT
ejpam-6204	140	3	the	the	DET
ejpam-6204	140	4	coefficients	coefficient	NOUN
ejpam-6204	140	5	of	of	ADP
ejpam-6204	140	6	the	the	DET
ejpam-6204	140	7	two	two	NUM
ejpam-6204	140	8	sprays	spray	NOUN
ejpam-6204	140	9	are	be	AUX
ejpam-6204	140	10	related	relate	VERB
ejpam-6204	140	11	by	by	ADP
ejpam-6204	140	12	g̃i	g̃i	NOUN
ejpam-6204	141	1	=	=	NOUN
ejpam-6204	141	2	gi	gi	X
ejpam-6204	142	1	+	+	NUM
ejpam-6204	143	1	pξi	pξi	NOUN
ejpam-6204	143	2	.	.	PUNCT
ejpam-6204	144	1	(	(	PUNCT
ejpam-6204	144	2	21	21	NUM
ejpam-6204	144	3	)	)	PUNCT
ejpam-6204	144	4	in	in	ADP
ejpam-6204	144	5	a	a	DET
ejpam-6204	144	6	similar	similar	ADJ
ejpam-6204	144	7	manner	manner	NOUN
ejpam-6204	144	8	to	to	ADP
ejpam-6204	144	9	what	what	PRON
ejpam-6204	144	10	we	we	PRON
ejpam-6204	144	11	discuss	discuss	VERB
ejpam-6204	144	12	in	in	ADP
ejpam-6204	144	13	property	property	NOUN
ejpam-6204	144	14	3	3	NUM
ejpam-6204	144	15	,	,	PUNCT
ejpam-6204	144	16	if	if	SCONJ
ejpam-6204	144	17	ξ	ξ	PRON
ejpam-6204	144	18	:	:	PUNCT
ejpam-6204	144	19	=	=	SYM
ejpam-6204	144	20	c	c	X
ejpam-6204	144	21	,	,	PUNCT
ejpam-6204	144	22	then	then	ADV
ejpam-6204	144	23	the	the	DET
ejpam-6204	144	24	porjectivelike	porjectivelike	NOUN
ejpam-6204	144	25	spray	spray	VERB
ejpam-6204	144	26	deformation	deformation	NOUN
ejpam-6204	144	27	(	(	PUNCT
ejpam-6204	144	28	20	20	NUM
ejpam-6204	144	29	)	)	PUNCT
ejpam-6204	144	30	reduces	reduce	VERB
ejpam-6204	144	31	to	to	ADP
ejpam-6204	144	32	the	the	DET
ejpam-6204	144	33	projective	projective	ADJ
ejpam-6204	144	34	deformation	deformation	NOUN
ejpam-6204	144	35	,	,	PUNCT
ejpam-6204	144	36	and	and	CCONJ
ejpam-6204	144	37	p(x	p(x	PROPN
ejpam-6204	144	38	,	,	PUNCT
ejpam-6204	144	39	y	y	NOUN
ejpam-6204	144	40	)	)	PUNCT
ejpam-6204	144	41	is	be	AUX
ejpam-6204	144	42	called	call	VERB
ejpam-6204	144	43	projective	projective	ADJ
ejpam-6204	144	44	factor	factor	NOUN
ejpam-6204	144	45	.	.	PUNCT
ejpam-6204	145	1	it	it	PRON
ejpam-6204	145	2	is	be	AUX
ejpam-6204	145	3	clear	clear	ADJ
ejpam-6204	145	4	that	that	SCONJ
ejpam-6204	145	5	,	,	PUNCT
ejpam-6204	145	6	as	as	SCONJ
ejpam-6204	145	7	s̃	s̃	PROPN
ejpam-6204	145	8	is	be	AUX
ejpam-6204	145	9	a	a	DET
ejpam-6204	145	10	spray	spray	NOUN
ejpam-6204	145	11	,	,	PUNCT
ejpam-6204	145	12	then	then	ADV
ejpam-6204	145	13	ξ	ξ	PROPN
ejpam-6204	145	14	is	be	AUX
ejpam-6204	145	15	homogenous	homogenous	ADJ
ejpam-6204	145	16	of	of	ADP
ejpam-6204	145	17	degree	degree	NOUN
ejpam-6204	145	18	one	one	NUM
ejpam-6204	145	19	,	,	PUNCT
ejpam-6204	145	20	that	that	PRON
ejpam-6204	145	21	is	be	AUX
ejpam-6204	145	22	[	[	X
ejpam-6204	145	23	c	c	X
ejpam-6204	145	24	,	,	PUNCT
ejpam-6204	145	25	ξ	ξ	X
ejpam-6204	145	26	]	]	X
ejpam-6204	145	27	=	=	SYM
ejpam-6204	145	28	0	0	X
ejpam-6204	145	29	.	.	PUNCT
ejpam-6204	146	1	(	(	PUNCT
ejpam-6204	146	2	22	22	X
ejpam-6204	146	3	)	)	PUNCT
ejpam-6204	146	4	taking	take	VERB
ejpam-6204	146	5	the	the	DET
ejpam-6204	146	6	following	follow	VERB
ejpam-6204	146	7	vector	vector	NOUN
ejpam-6204	146	8	one	one	NUM
ejpam-6204	146	9	form	form	NOUN
ejpam-6204	146	10	µ	µ	X
ejpam-6204	146	11	:	:	PUNCT
ejpam-6204	146	12	=	=	SYM
ejpam-6204	147	1	[	[	X
ejpam-6204	147	2	j	j	X
ejpam-6204	147	3	,	,	PUNCT
ejpam-6204	147	4	ξ	ξ	PROPN
ejpam-6204	147	5	]	]	PUNCT
ejpam-6204	147	6	,	,	PUNCT
ejpam-6204	147	7	we	we	PRON
ejpam-6204	147	8	have	have	VERB
ejpam-6204	147	9	:	:	PUNCT
ejpam-6204	147	10	lemma	lemma	PROPN
ejpam-6204	147	11	1	1	NUM
ejpam-6204	147	12	.	.	PUNCT
ejpam-6204	148	1	the	the	DET
ejpam-6204	148	2	endomorphism	endomorphism	PROPN
ejpam-6204	148	3	µ	µ	PROPN
ejpam-6204	148	4	has	have	VERB
ejpam-6204	148	5	the	the	DET
ejpam-6204	148	6	following	follow	VERB
ejpam-6204	148	7	properties	property	NOUN
ejpam-6204	148	8	µj	µj	ADP
ejpam-6204	148	9	=	=	SYM
ejpam-6204	148	10	0	0	PROPN
ejpam-6204	148	11	,	,	PUNCT
ejpam-6204	148	12	jµ	jµ	PROPN
ejpam-6204	148	13	=	=	NOUN
ejpam-6204	148	14	0	0	NUM
ejpam-6204	148	15	,	,	PUNCT
ejpam-6204	148	16	µ2	µ2	PROPN
ejpam-6204	148	17	=	=	SYM
ejpam-6204	148	18	0	0	NUM
ejpam-6204	148	19	,	,	PUNCT
ejpam-6204	148	20	γµ+	γµ+	VERB
ejpam-6204	148	21	µγ	µγ	PROPN
ejpam-6204	149	1	=	=	NOUN
ejpam-6204	149	2	0	0	X
ejpam-6204	149	3	.	.	PUNCT
ejpam-6204	149	4	proof	proof	NOUN
ejpam-6204	149	5	.	.	PUNCT
ejpam-6204	150	1	since	since	SCONJ
ejpam-6204	150	2	j	j	PROPN
ejpam-6204	150	3	γ̃	γ̃	PROPN
ejpam-6204	150	4	=	=	SYM
ejpam-6204	150	5	jγ	jγ	PROPN
ejpam-6204	150	6	=	=	SYM
ejpam-6204	150	7	j	j	PROPN
ejpam-6204	150	8	,	,	PUNCT
ejpam-6204	150	9	then	then	ADV
ejpam-6204	150	10	γ̃	γ̃	PROPN
ejpam-6204	150	11	=	=	SYM
ejpam-6204	150	12	j(γ	j(γ	PROPN
ejpam-6204	150	13	+	+	NUM
ejpam-6204	150	14	µ	µ	X
ejpam-6204	150	15	)	)	PUNCT
ejpam-6204	150	16	=	=	SYM
ejpam-6204	150	17	j	j	PROPN
ejpam-6204	151	1	+	+	CCONJ
ejpam-6204	151	2	jµ	jµ	PROPN
ejpam-6204	151	3	=	=	PUNCT
ejpam-6204	151	4	j	j	NOUN
ejpam-6204	152	1	=	=	NOUN
ejpam-6204	152	2	⇒	⇒	VERB
ejpam-6204	152	3	jµ	jµ	X
ejpam-6204	152	4	=	=	NOUN
ejpam-6204	152	5	0	0	X
ejpam-6204	152	6	.	.	PUNCT
ejpam-6204	152	7	similarly	similarly	ADV
ejpam-6204	152	8	,	,	PUNCT
ejpam-6204	152	9	using	use	VERB
ejpam-6204	152	10	the	the	DET
ejpam-6204	152	11	fact	fact	NOUN
ejpam-6204	152	12	that	that	SCONJ
ejpam-6204	152	13	γ̃j	γ̃j	PROPN
ejpam-6204	152	14	=	=	PUNCT
ejpam-6204	152	15	γj	γj	PROPN
ejpam-6204	152	16	=	=	PUNCT
ejpam-6204	152	17	−j	−j	NOUN
ejpam-6204	152	18	,	,	PUNCT
ejpam-6204	152	19	we	we	PRON
ejpam-6204	152	20	get	get	VERB
ejpam-6204	152	21	µj	µj	PROPN
ejpam-6204	152	22	=	=	ADJ
ejpam-6204	152	23	0	0	PROPN
ejpam-6204	152	24	.	.	PUNCT
ejpam-6204	153	1	therefore	therefore	ADV
ejpam-6204	153	2	,	,	PUNCT
ejpam-6204	153	3	we	we	PRON
ejpam-6204	153	4	conclude	conclude	VERB
ejpam-6204	153	5	that	that	PRON
ejpam-6204	153	6	µ2	µ2	PROPN
ejpam-6204	153	7	=	=	NOUN
ejpam-6204	153	8	0	0	PROPN
ejpam-6204	153	9	.	.	PUNCT
ejpam-6204	154	1	since	since	SCONJ
ejpam-6204	154	2	γ̃2	γ̃2	PROPN
ejpam-6204	154	3	=	=	PROPN
ejpam-6204	154	4	i	i	PROPN
ejpam-6204	154	5	and	and	CCONJ
ejpam-6204	154	6	γ2	γ2	PROPN
ejpam-6204	154	7	=	=	SYM
ejpam-6204	154	8	i	i	PROPN
ejpam-6204	154	9	,	,	PUNCT
ejpam-6204	154	10	then	then	ADV
ejpam-6204	154	11	we	we	PRON
ejpam-6204	154	12	obtain	obtain	VERB
ejpam-6204	154	13	that	that	DET
ejpam-6204	154	14	γµ+	γµ+	NOUN
ejpam-6204	154	15	µγ	µγ	PROPN
ejpam-6204	155	1	=	=	NOUN
ejpam-6204	155	2	0	0	PROPN
ejpam-6204	155	3	.	.	PUNCT
ejpam-6204	155	4	s.	s.	PROPN
ejpam-6204	155	5	g.	g.	PROPN
ejpam-6204	155	6	elgendi	elgendi	PROPN
ejpam-6204	155	7	,	,	PUNCT
ejpam-6204	155	8	a.	a.	NOUN
ejpam-6204	155	9	soleiman	soleiman	PROPN
ejpam-6204	155	10	/	/	SYM
ejpam-6204	155	11	eur	eur	PROPN
ejpam-6204	155	12	.	.	PUNCT
ejpam-6204	156	1	j.	j.	PROPN
ejpam-6204	156	2	pure	pure	PROPN
ejpam-6204	156	3	appl	appl	PROPN
ejpam-6204	156	4	.	.	PROPN
ejpam-6204	156	5	math	math	PROPN
ejpam-6204	156	6	,	,	PUNCT
ejpam-6204	156	7	18	18	NUM
ejpam-6204	156	8	(	(	PUNCT
ejpam-6204	156	9	3	3	NUM
ejpam-6204	156	10	)	)	PUNCT
ejpam-6204	156	11	(	(	PUNCT
ejpam-6204	156	12	2025	2025	NUM
ejpam-6204	156	13	)	)	PUNCT
ejpam-6204	156	14	,	,	PUNCT
ejpam-6204	156	15	6204	6204	NUM
ejpam-6204	156	16	8	8	NUM
ejpam-6204	156	17	of	of	ADP
ejpam-6204	156	18	18	18	NUM
ejpam-6204	156	19	proposition	proposition	NOUN
ejpam-6204	156	20	1	1	NUM
ejpam-6204	156	21	.	.	PUNCT
ejpam-6204	157	1	under	under	ADP
ejpam-6204	157	2	the	the	DET
ejpam-6204	157	3	projective	projective	ADJ
ejpam-6204	157	4	-	-	PUNCT
ejpam-6204	157	5	like	like	ADJ
ejpam-6204	157	6	deformation	deformation	NOUN
ejpam-6204	157	7	(	(	PUNCT
ejpam-6204	157	8	20	20	NUM
ejpam-6204	157	9	)	)	PUNCT
ejpam-6204	157	10	of	of	ADP
ejpam-6204	157	11	a	a	DET
ejpam-6204	157	12	spray	spray	NOUN
ejpam-6204	157	13	s	s	VERB
ejpam-6204	157	14	with	with	ADP
ejpam-6204	157	15	deformation	deformation	NOUN
ejpam-6204	157	16	factor	factor	NOUN
ejpam-6204	157	17	p(x	p(x	PROPN
ejpam-6204	157	18	,	,	PUNCT
ejpam-6204	157	19	y	y	PROPN
ejpam-6204	157	20	)	)	PUNCT
ejpam-6204	157	21	,	,	PUNCT
ejpam-6204	157	22	the	the	DET
ejpam-6204	157	23	barthel	barthel	PROPN
ejpam-6204	157	24	connection	connection	PROPN
ejpam-6204	157	25	γ̃	γ̃	PROPN
ejpam-6204	157	26	has	have	VERB
ejpam-6204	157	27	the	the	DET
ejpam-6204	157	28	form	form	NOUN
ejpam-6204	157	29	γ̃	γ̃	PROPN
ejpam-6204	157	30	=	=	PUNCT
ejpam-6204	157	31	γ−	γ−	PROPN
ejpam-6204	157	32	2(pµ+	2(pµ+	NUM
ejpam-6204	157	33	djp	djp	PROPN
ejpam-6204	157	34	⊗	⊗	PROPN
ejpam-6204	157	35	ξ	ξ	PROPN
ejpam-6204	157	36	)	)	PUNCT
ejpam-6204	157	37	.	.	PUNCT
ejpam-6204	158	1	(	(	PUNCT
ejpam-6204	158	2	23	23	NUM
ejpam-6204	158	3	)	)	PUNCT
ejpam-6204	158	4	consequently	consequently	ADV
ejpam-6204	158	5	,	,	PUNCT
ejpam-6204	158	6	the	the	DET
ejpam-6204	158	7	horizontal	horizontal	ADJ
ejpam-6204	158	8	and	and	CCONJ
ejpam-6204	158	9	vertical	vertical	ADJ
ejpam-6204	158	10	projections	projection	NOUN
ejpam-6204	158	11	h̃	h̃	PROPN
ejpam-6204	158	12	and	and	CCONJ
ejpam-6204	158	13	ṽ	ṽ	PROPN
ejpam-6204	158	14	becomes	become	VERB
ejpam-6204	158	15	h̃	h̃	PROPN
ejpam-6204	158	16	=	=	SYM
ejpam-6204	158	17	h−	h−	PROPN
ejpam-6204	158	18	l	l	NOUN
ejpam-6204	158	19	,	,	PUNCT
ejpam-6204	158	20	ṽ	ṽ	PROPN
ejpam-6204	158	21	=	=	SYM
ejpam-6204	158	22	v	v	PROPN
ejpam-6204	158	23	+	+	CCONJ
ejpam-6204	158	24	l	l	NOUN
ejpam-6204	158	25	,	,	PUNCT
ejpam-6204	158	26	where	where	SCONJ
ejpam-6204	158	27	,	,	PUNCT
ejpam-6204	158	28	l	l	NOUN
ejpam-6204	158	29	is	be	AUX
ejpam-6204	158	30	the	the	DET
ejpam-6204	158	31	vector	vector	ADJ
ejpam-6204	158	32	1	1	NUM
ejpam-6204	158	33	-	-	PUNCT
ejpam-6204	158	34	form	form	NOUN
ejpam-6204	158	35	defined	define	VERB
ejpam-6204	158	36	by	by	ADP
ejpam-6204	158	37	l	l	NOUN
ejpam-6204	158	38	:	:	PUNCT
ejpam-6204	159	1	=	=	SYM
ejpam-6204	159	2	pµ+	pµ+	ADV
ejpam-6204	159	3	djp	djp	PROPN
ejpam-6204	159	4	⊗	⊗	PROPN
ejpam-6204	159	5	ξ	ξ	PROPN
ejpam-6204	159	6	.	.	PUNCT
ejpam-6204	160	1	(	(	PUNCT
ejpam-6204	160	2	24	24	NUM
ejpam-6204	160	3	)	)	PUNCT
ejpam-6204	160	4	proof	proof	NOUN
ejpam-6204	160	5	.	.	PUNCT
ejpam-6204	161	1	using	use	VERB
ejpam-6204	161	2	the	the	DET
ejpam-6204	161	3	formula	formula	NOUN
ejpam-6204	161	4	[	[	X
ejpam-6204	161	5	17	17	NUM
ejpam-6204	161	6	]	]	PUNCT
ejpam-6204	161	7	[	[	X
ejpam-6204	161	8	j	j	X
ejpam-6204	161	9	,	,	PUNCT
ejpam-6204	161	10	fx	fx	PROPN
ejpam-6204	161	11	]	]	PUNCT
ejpam-6204	161	12	=	=	SYM
ejpam-6204	161	13	f	f	X
ejpam-6204	162	1	[	[	X
ejpam-6204	162	2	j	j	X
ejpam-6204	162	3	,	,	PUNCT
ejpam-6204	162	4	x	x	X
ejpam-6204	162	5	]	]	X
ejpam-6204	162	6	+	+	CCONJ
ejpam-6204	162	7	djf	djf	ADJ
ejpam-6204	162	8	⊗x	⊗x	NOUN
ejpam-6204	162	9	−	−	PROPN
ejpam-6204	162	10	df	df	PROPN
ejpam-6204	162	11	⊗	⊗	PROPN
ejpam-6204	162	12	jx	jx	PROPN
ejpam-6204	162	13	,	,	PUNCT
ejpam-6204	162	14	and	and	CCONJ
ejpam-6204	162	15	the	the	DET
ejpam-6204	162	16	fact	fact	NOUN
ejpam-6204	162	17	that	that	SCONJ
ejpam-6204	162	18	ξ	ξ	PROPN
ejpam-6204	162	19	is	be	AUX
ejpam-6204	162	20	a	a	DET
ejpam-6204	162	21	vertical	vertical	ADJ
ejpam-6204	162	22	vector	vector	NOUN
ejpam-6204	162	23	field	field	NOUN
ejpam-6204	162	24	,	,	PUNCT
ejpam-6204	162	25	we	we	PRON
ejpam-6204	162	26	obtain	obtain	VERB
ejpam-6204	162	27	γ̃	γ̃	PROPN
ejpam-6204	162	28	=	=	PUNCT
ejpam-6204	163	1	[	[	X
ejpam-6204	163	2	j	j	PROPN
ejpam-6204	163	3	,	,	PUNCT
ejpam-6204	163	4	s̃	s̃	PROPN
ejpam-6204	163	5	]	]	X
ejpam-6204	163	6	=	=	PUNCT
ejpam-6204	164	1	[	[	X
ejpam-6204	164	2	j	j	X
ejpam-6204	164	3	,	,	PUNCT
ejpam-6204	164	4	s	s	PART
ejpam-6204	164	5	−	−	PROPN
ejpam-6204	164	6	2pξ	2pξ	NOUN
ejpam-6204	164	7	]	]	PUNCT
ejpam-6204	165	1	=	=	PUNCT
ejpam-6204	166	1	[	[	X
ejpam-6204	166	2	j	j	X
ejpam-6204	166	3	,	,	PUNCT
ejpam-6204	166	4	s]−	s]−	PROPN
ejpam-6204	166	5	2[j	2[j	NUM
ejpam-6204	166	6	,	,	PUNCT
ejpam-6204	166	7	pξ	pξ	ADP
ejpam-6204	166	8	]	]	PUNCT
ejpam-6204	166	9	=	=	SYM
ejpam-6204	166	10	γ−	γ−	PROPN
ejpam-6204	166	11	2(pµ+	2(pµ+	NUM
ejpam-6204	166	12	djp	djp	PROPN
ejpam-6204	166	13	⊗	⊗	PROPN
ejpam-6204	166	14	ξ	ξ	PROPN
ejpam-6204	166	15	)	)	PUNCT
ejpam-6204	166	16	.	.	PUNCT
ejpam-6204	167	1	hence	hence	ADV
ejpam-6204	167	2	,	,	PUNCT
ejpam-6204	167	3	using	use	VERB
ejpam-6204	167	4	the	the	DET
ejpam-6204	167	5	facts	fact	NOUN
ejpam-6204	167	6	h̃	h̃	PROPN
ejpam-6204	167	7	=	=	NOUN
ejpam-6204	167	8	1	1	NUM
ejpam-6204	167	9	2(i	2(i	NUM
ejpam-6204	167	10	+	+	PUNCT
ejpam-6204	167	11	γ̃	γ̃	PROPN
ejpam-6204	167	12	)	)	PUNCT
ejpam-6204	167	13	,	,	PUNCT
ejpam-6204	167	14	and	and	CCONJ
ejpam-6204	167	15	ṽ	ṽ	PROPN
ejpam-6204	167	16	=	=	SYM
ejpam-6204	167	17	1	1	NUM
ejpam-6204	167	18	2(i	2(i	NUM
ejpam-6204	167	19	−	−	PROPN
ejpam-6204	167	20	γ̃	γ̃	PROPN
ejpam-6204	167	21	)	)	PUNCT
ejpam-6204	167	22	,	,	PUNCT
ejpam-6204	167	23	the	the	DET
ejpam-6204	167	24	proof	proof	NOUN
ejpam-6204	167	25	completes	complete	VERB
ejpam-6204	167	26	.	.	PUNCT
ejpam-6204	168	1	proposition	proposition	NOUN
ejpam-6204	168	2	2	2	NUM
ejpam-6204	168	3	.	.	PUNCT
ejpam-6204	169	1	under	under	ADP
ejpam-6204	169	2	the	the	DET
ejpam-6204	169	3	projective	projective	ADJ
ejpam-6204	169	4	-	-	PUNCT
ejpam-6204	169	5	like	like	ADJ
ejpam-6204	169	6	deformation	deformation	NOUN
ejpam-6204	169	7	(	(	PUNCT
ejpam-6204	169	8	20	20	NUM
ejpam-6204	169	9	)	)	PUNCT
ejpam-6204	169	10	of	of	ADP
ejpam-6204	169	11	a	a	DET
ejpam-6204	169	12	spray	spray	NOUN
ejpam-6204	169	13	s	s	VERB
ejpam-6204	169	14	with	with	ADP
ejpam-6204	169	15	deformation	deformation	NOUN
ejpam-6204	169	16	factor	factor	NOUN
ejpam-6204	169	17	p(x	p(x	PROPN
ejpam-6204	169	18	,	,	PUNCT
ejpam-6204	169	19	y	y	PROPN
ejpam-6204	169	20	)	)	PUNCT
ejpam-6204	169	21	.	.	PUNCT
ejpam-6204	170	1	the	the	DET
ejpam-6204	170	2	jacobi	jacobi	PROPN
ejpam-6204	170	3	endomorphism	endomorphism	PROPN
ejpam-6204	170	4	φ̃	φ̃	PROPN
ejpam-6204	170	5	is	be	AUX
ejpam-6204	170	6	given	give	VERB
ejpam-6204	170	7	by	by	ADP
ejpam-6204	170	8	φ̃	φ̃	PROPN
ejpam-6204	170	9	=	=	SYM
ejpam-6204	170	10	φ−	φ−	PROPN
ejpam-6204	170	11	(	(	PUNCT
ejpam-6204	170	12	p2µ[s	p2µ[s	NOUN
ejpam-6204	170	13	,	,	PUNCT
ejpam-6204	170	14	µ	µ	X
ejpam-6204	170	15	]	]	X
ejpam-6204	170	16	+	+	CCONJ
ejpam-6204	170	17	s(p)µ	s(p)µ	NOUN
ejpam-6204	170	18	)	)	PUNCT
ejpam-6204	170	19	+	+	CCONJ
ejpam-6204	170	20	(	(	PUNCT
ejpam-6204	170	21	2dhp−pdµp−∇djp)⊗	2dhp−pdµp−∇djp)⊗	NUM
ejpam-6204	170	22	ξ	ξ	X
ejpam-6204	170	23	−p	−p	NOUN
ejpam-6204	170	24	v[s	v[s	NOUN
ejpam-6204	170	25	,	,	PUNCT
ejpam-6204	170	26	µ]−	µ]−	ADV
ejpam-6204	170	27	djp	djp	VERB
ejpam-6204	170	28	⊗	⊗	PROPN
ejpam-6204	170	29	v[s	v[s	PROPN
ejpam-6204	170	30	,	,	PUNCT
ejpam-6204	170	31	ξ]−	ξ]−	PROPN
ejpam-6204	170	32	pdµp	pdµp	VERB
ejpam-6204	170	33	⊗	⊗	PROPN
ejpam-6204	170	34	ξ	ξ	PROPN
ejpam-6204	170	35	−	−	PROPN
ejpam-6204	170	36	2dξp	2dξp	NUM
ejpam-6204	170	37	djp	djp	PROPN
ejpam-6204	170	38	⊗	⊗	PROPN
ejpam-6204	170	39	ξ	ξ	X
ejpam-6204	170	40	−2p(v[ξ	−2p(v[ξ	PROPN
ejpam-6204	170	41	,	,	PUNCT
ejpam-6204	170	42	h]−	h]−	PROPN
ejpam-6204	170	43	v[ξ	v[ξ	NOUN
ejpam-6204	170	44	,	,	PUNCT
ejpam-6204	170	45	l	l	NOUN
ejpam-6204	170	46	]	]	X
ejpam-6204	170	47	)	)	PUNCT
ejpam-6204	171	1	+	+	CCONJ
ejpam-6204	171	2	p{µ[s	p{µ[s	ADJ
ejpam-6204	171	3	,	,	PUNCT
ejpam-6204	171	4	h]−	h]−	X
ejpam-6204	171	5	djp	djp	VERB
ejpam-6204	171	6	⊗	⊗	PROPN
ejpam-6204	171	7	µ[s	µ[s	NOUN
ejpam-6204	171	8	,	,	PUNCT
ejpam-6204	171	9	ξ]−	ξ]−	PROPN
ejpam-6204	171	10	2pµ[ξ	2pµ[ξ	NUM
ejpam-6204	171	11	,	,	PUNCT
ejpam-6204	171	12	h	h	NOUN
ejpam-6204	171	13	]	]	X
ejpam-6204	171	14	}	}	PUNCT
ejpam-6204	171	15	−{pdj	−{pdj	NOUN
ejpam-6204	172	1	[	[	X
ejpam-6204	172	2	s,µ]p	s,µ]p	VERB
ejpam-6204	172	3	+	+	X
ejpam-6204	172	4	djpdj	djpdj	VERB
ejpam-6204	173	1	[	[	X
ejpam-6204	173	2	s	s	X
ejpam-6204	173	3	,	,	PUNCT
ejpam-6204	173	4	ξ]p	ξ]p	NOUN
ejpam-6204	173	5	+	+	X
ejpam-6204	173	6	2pdj	2pdj	NUM
ejpam-6204	174	1	[	[	X
ejpam-6204	174	2	ξ	ξ	X
ejpam-6204	174	3	,	,	PUNCT
ejpam-6204	174	4	h]p	h]p	PROPN
ejpam-6204	174	5	}	}	PUNCT
ejpam-6204	174	6	⊗	⊗	PROPN
ejpam-6204	174	7	ξ	ξ	PROPN
ejpam-6204	174	8	.	.	PUNCT
ejpam-6204	175	1	proof	proof	NOUN
ejpam-6204	175	2	.	.	PUNCT
ejpam-6204	176	1	under	under	ADP
ejpam-6204	176	2	the	the	DET
ejpam-6204	176	3	spray	spray	NOUN
ejpam-6204	176	4	deformation	deformation	NOUN
ejpam-6204	176	5	(	(	PUNCT
ejpam-6204	176	6	20	20	NUM
ejpam-6204	176	7	)	)	PUNCT
ejpam-6204	176	8	,	,	PUNCT
ejpam-6204	176	9	with	with	ADP
ejpam-6204	176	10	deformation	deformation	NOUN
ejpam-6204	176	11	factor	factor	NOUN
ejpam-6204	176	12	p(x	p(x	PROPN
ejpam-6204	176	13	,	,	PUNCT
ejpam-6204	176	14	y	y	PROPN
ejpam-6204	176	15	)	)	PUNCT
ejpam-6204	176	16	,	,	PUNCT
ejpam-6204	176	17	taking	take	VERB
ejpam-6204	176	18	into	into	ADP
ejpam-6204	176	19	account	account	NOUN
ejpam-6204	176	20	proposition	proposition	NOUN
ejpam-6204	176	21	1	1	NUM
ejpam-6204	176	22	,	,	PUNCT
ejpam-6204	176	23	one	one	PRON
ejpam-6204	176	24	can	can	AUX
ejpam-6204	176	25	show	show	VERB
ejpam-6204	176	26	that	that	SCONJ
ejpam-6204	177	1	[	[	X
ejpam-6204	177	2	s̃	s̃	PROPN
ejpam-6204	177	3	,	,	PUNCT
ejpam-6204	177	4	h̃	h̃	PROPN
ejpam-6204	177	5	]	]	PUNCT
ejpam-6204	177	6	=	=	PUNCT
ejpam-6204	178	1	[	[	X
ejpam-6204	178	2	s	s	X
ejpam-6204	178	3	−	−	PROPN
ejpam-6204	178	4	2pξ	2pξ	NOUN
ejpam-6204	178	5	,	,	PUNCT
ejpam-6204	178	6	h−	h−	PROPN
ejpam-6204	178	7	l	l	NOUN
ejpam-6204	178	8	]	]	X
ejpam-6204	178	9	=	=	PUNCT
ejpam-6204	179	1	[	[	X
ejpam-6204	179	2	s	s	X
ejpam-6204	179	3	,	,	PUNCT
ejpam-6204	179	4	h]−	h]−	PUNCT
ejpam-6204	180	1	[	[	X
ejpam-6204	180	2	s	s	X
ejpam-6204	180	3	,	,	PUNCT
ejpam-6204	180	4	l]−	l]−	VERB
ejpam-6204	180	5	2[pξ	2[pξ	NUM
ejpam-6204	180	6	,	,	PUNCT
ejpam-6204	180	7	h	h	NOUN
ejpam-6204	180	8	]	]	X
ejpam-6204	180	9	+	+	CCONJ
ejpam-6204	180	10	2[pξ	2[pξ	NUM
ejpam-6204	180	11	,	,	PUNCT
ejpam-6204	180	12	l	l	NOUN
ejpam-6204	180	13	]	]	X
ejpam-6204	180	14	.	.	PUNCT
ejpam-6204	181	1	(	(	PUNCT
ejpam-6204	181	2	25	25	NUM
ejpam-6204	181	3	)	)	PUNCT
ejpam-6204	181	4	on	on	ADP
ejpam-6204	181	5	the	the	DET
ejpam-6204	181	6	other	other	ADJ
ejpam-6204	181	7	hand	hand	NOUN
ejpam-6204	181	8	,	,	PUNCT
ejpam-6204	181	9	taking	take	VERB
ejpam-6204	181	10	into	into	ADP
ejpam-6204	181	11	account	account	NOUN
ejpam-6204	181	12	the	the	DET
ejpam-6204	181	13	expression	expression	NOUN
ejpam-6204	181	14	of	of	ADP
ejpam-6204	181	15	l	l	NOUN
ejpam-6204	181	16	given	give	VERB
ejpam-6204	181	17	by	by	ADP
ejpam-6204	181	18	(	(	PUNCT
ejpam-6204	181	19	24	24	NUM
ejpam-6204	181	20	)	)	PUNCT
ejpam-6204	181	21	,	,	PUNCT
ejpam-6204	181	22	and	and	CCONJ
ejpam-6204	181	23	using	use	VERB
ejpam-6204	181	24	the	the	DET
ejpam-6204	181	25	following	follow	VERB
ejpam-6204	181	26	relations	relation	NOUN
ejpam-6204	181	27	:	:	PUNCT
ejpam-6204	181	28	ξ	ξ	PROPN
ejpam-6204	181	29	∈	∈	PROPN
ejpam-6204	181	30	xv(t	xv(t	X
ejpam-6204	181	31	m	m	NOUN
ejpam-6204	181	32	)	)	PUNCT
ejpam-6204	181	33	,	,	PUNCT
ejpam-6204	181	34	hξ	hξ	X
ejpam-6204	181	35	=	=	NOUN
ejpam-6204	181	36	lξ	lξ	NOUN
ejpam-6204	181	37	=	=	SYM
ejpam-6204	181	38	0	0	NUM
ejpam-6204	181	39	,	,	PUNCT
ejpam-6204	181	40	together	together	ADV
ejpam-6204	181	41	with	with	ADP
ejpam-6204	181	42	the	the	DET
ejpam-6204	181	43	facts	fact	NOUN
ejpam-6204	182	1	that	that	SCONJ
ejpam-6204	182	2	,	,	PUNCT
ejpam-6204	182	3	for	for	ADP
ejpam-6204	182	4	f	f	PROPN
ejpam-6204	182	5	,	,	PUNCT
ejpam-6204	182	6	g	g	PROPN
ejpam-6204	182	7	∈	∈	PROPN
ejpam-6204	182	8	c∞(t	c∞(t	NOUN
ejpam-6204	182	9	m),k	m),k	PROPN
ejpam-6204	182	10	∈	∈	PROPN
ejpam-6204	182	11	ψ1(t	ψ1(t	X
ejpam-6204	182	12	m	m	PROPN
ejpam-6204	182	13	)	)	PUNCT
ejpam-6204	182	14	,	,	PUNCT
ejpam-6204	182	15	ω	ω	PROPN
ejpam-6204	182	16	∈	∈	PROPN
ejpam-6204	182	17	λ1(t	λ1(t	X
ejpam-6204	182	18	m	m	VERB
ejpam-6204	182	19	):	):	PUNCT
ejpam-6204	183	1	[	[	X
ejpam-6204	183	2	x	x	X
ejpam-6204	183	3	,	,	PUNCT
ejpam-6204	183	4	fk	fk	INTJ
ejpam-6204	183	5	]	]	X
ejpam-6204	183	6	=	=	SYM
ejpam-6204	183	7	(	(	PUNCT
ejpam-6204	183	8	dxf)k	dxf)k	NOUN
ejpam-6204	183	9	+	+	CCONJ
ejpam-6204	183	10	f	f	X
ejpam-6204	184	1	[	[	X
ejpam-6204	184	2	x	x	X
ejpam-6204	184	3	,	,	PUNCT
ejpam-6204	184	4	k	k	X
ejpam-6204	184	5	]	]	X
ejpam-6204	184	6	,	,	PUNCT
ejpam-6204	184	7	[	[	X
ejpam-6204	184	8	x	x	X
ejpam-6204	184	9	,	,	PUNCT
ejpam-6204	184	10	ω	ω	PROPN
ejpam-6204	184	11	⊗	⊗	PROPN
ejpam-6204	184	12	y	y	PROPN
ejpam-6204	184	13	]	]	PUNCT
ejpam-6204	185	1	=	=	PUNCT
ejpam-6204	186	1	[	[	X
ejpam-6204	186	2	x	x	X
ejpam-6204	186	3	,	,	PUNCT
ejpam-6204	186	4	ω]⊗	ω]⊗	X
ejpam-6204	186	5	y	y	PROPN
ejpam-6204	186	6	+	+	PROPN
ejpam-6204	186	7	ω	ω	PROPN
ejpam-6204	186	8	⊗	⊗	PROPN
ejpam-6204	187	1	[	[	X
ejpam-6204	187	2	x	x	X
ejpam-6204	187	3	,	,	PUNCT
ejpam-6204	187	4	y	y	PROPN
ejpam-6204	187	5	]	]	PUNCT
ejpam-6204	187	6	,	,	PUNCT
ejpam-6204	187	7	s.	s.	PROPN
ejpam-6204	187	8	g.	g.	PROPN
ejpam-6204	187	9	elgendi	elgendi	PROPN
ejpam-6204	187	10	,	,	PUNCT
ejpam-6204	187	11	a.	a.	NOUN
ejpam-6204	187	12	soleiman	soleiman	PROPN
ejpam-6204	187	13	/	/	SYM
ejpam-6204	187	14	eur	eur	PROPN
ejpam-6204	187	15	.	.	PUNCT
ejpam-6204	188	1	j.	j.	PROPN
ejpam-6204	188	2	pure	pure	PROPN
ejpam-6204	188	3	appl	appl	PROPN
ejpam-6204	188	4	.	.	PROPN
ejpam-6204	188	5	math	math	PROPN
ejpam-6204	188	6	,	,	PUNCT
ejpam-6204	188	7	18	18	NUM
ejpam-6204	188	8	(	(	PUNCT
ejpam-6204	188	9	3	3	NUM
ejpam-6204	188	10	)	)	PUNCT
ejpam-6204	188	11	(	(	PUNCT
ejpam-6204	188	12	2025	2025	NUM
ejpam-6204	188	13	)	)	PUNCT
ejpam-6204	188	14	,	,	PUNCT
ejpam-6204	188	15	6204	6204	NUM
ejpam-6204	188	16	9	9	NUM
ejpam-6204	188	17	of	of	ADP
ejpam-6204	188	18	18	18	NUM
ejpam-6204	188	19	dfk+ω⊗y	dfk+ω⊗y	NOUN
ejpam-6204	188	20	g	g	NOUN
ejpam-6204	188	21	=	=	PROPN
ejpam-6204	188	22	fdkg	fdkg	PROPN
ejpam-6204	188	23	+	+	CCONJ
ejpam-6204	188	24	ω	ω	NOUN
ejpam-6204	188	25	⊗	⊗	PROPN
ejpam-6204	188	26	dy	dy	NOUN
ejpam-6204	188	27	g.	g.	PROPN
ejpam-6204	189	1	it	it	PRON
ejpam-6204	189	2	follows	follow	VERB
ejpam-6204	189	3	that	that	SCONJ
ejpam-6204	189	4	[	[	X
ejpam-6204	189	5	s	s	X
ejpam-6204	189	6	,	,	PUNCT
ejpam-6204	189	7	l	l	NOUN
ejpam-6204	189	8	]	]	X
ejpam-6204	189	9	=	=	PUNCT
ejpam-6204	190	1	[	[	X
ejpam-6204	190	2	s	s	ADP
ejpam-6204	190	3	,	,	PUNCT
ejpam-6204	190	4	pµ+	pµ+	ADV
ejpam-6204	190	5	djp	djp	PROPN
ejpam-6204	190	6	⊗	⊗	PROPN
ejpam-6204	190	7	ξ	ξ	X
ejpam-6204	190	8	]	]	X
ejpam-6204	190	9	=	=	PUNCT
ejpam-6204	191	1	[	[	X
ejpam-6204	191	2	s	s	X
ejpam-6204	191	3	,	,	PUNCT
ejpam-6204	191	4	pµ	pµ	X
ejpam-6204	191	5	]	]	PUNCT
ejpam-6204	191	6	+	+	CCONJ
ejpam-6204	192	1	[	[	X
ejpam-6204	192	2	s	s	X
ejpam-6204	192	3	,	,	PUNCT
ejpam-6204	192	4	djp	djp	VERB
ejpam-6204	192	5	⊗	⊗	PROPN
ejpam-6204	192	6	ξ	ξ	X
ejpam-6204	192	7	]	]	X
ejpam-6204	192	8	=	=	SYM
ejpam-6204	192	9	s(p)µ+	s(p)µ+	NOUN
ejpam-6204	192	10	p[s	p[s	PROPN
ejpam-6204	192	11	,	,	PUNCT
ejpam-6204	192	12	µ	µ	X
ejpam-6204	192	13	]	]	X
ejpam-6204	193	1	+	+	CCONJ
ejpam-6204	193	2	[	[	X
ejpam-6204	193	3	s	s	X
ejpam-6204	193	4	,	,	PUNCT
ejpam-6204	193	5	djp]⊗	djp]⊗	NOUN
ejpam-6204	193	6	ξ	ξ	X
ejpam-6204	194	1	+	+	CCONJ
ejpam-6204	194	2	djp	djp	ADJ
ejpam-6204	194	3	⊗	⊗	PROPN
ejpam-6204	195	1	[	[	X
ejpam-6204	195	2	s	s	X
ejpam-6204	195	3	,	,	PUNCT
ejpam-6204	195	4	ξ	ξ	X
ejpam-6204	195	5	]	]	X
ejpam-6204	195	6	=	=	SYM
ejpam-6204	195	7	s(p)µ+	s(p)µ+	NOUN
ejpam-6204	195	8	p[s	p[s	PROPN
ejpam-6204	195	9	,	,	PUNCT
ejpam-6204	195	10	µ	µ	X
ejpam-6204	195	11	]	]	X
ejpam-6204	195	12	+	+	CCONJ
ejpam-6204	195	13	lsdjp	lsdjp	ADJ
ejpam-6204	195	14	⊗	⊗	PROPN
ejpam-6204	195	15	ξ	ξ	PROPN
ejpam-6204	196	1	+	+	CCONJ
ejpam-6204	196	2	djp	djp	ADJ
ejpam-6204	196	3	⊗	⊗	PROPN
ejpam-6204	197	1	[	[	X
ejpam-6204	197	2	s	s	X
ejpam-6204	197	3	,	,	PUNCT
ejpam-6204	197	4	ξ	ξ	NOUN
ejpam-6204	197	5	]	]	PUNCT
ejpam-6204	197	6	.	.	PUNCT
ejpam-6204	198	1	[	[	X
ejpam-6204	198	2	pξ	pξ	NOUN
ejpam-6204	198	3	,	,	PUNCT
ejpam-6204	198	4	h	h	NOUN
ejpam-6204	198	5	]	]	X
ejpam-6204	198	6	=	=	PUNCT
ejpam-6204	198	7	dp	dp	NOUN
ejpam-6204	199	1	⊗	⊗	NOUN
ejpam-6204	199	2	hξ	hξ	INTJ
ejpam-6204	199	3	−	−	PROPN
ejpam-6204	199	4	dhp	dhp	PROPN
ejpam-6204	199	5	⊗	⊗	PROPN
ejpam-6204	199	6	ξ	ξ	PROPN
ejpam-6204	200	1	+	+	PUNCT
ejpam-6204	200	2	p[ξ	p[ξ	ADJ
ejpam-6204	200	3	,	,	PUNCT
ejpam-6204	200	4	h	h	NOUN
ejpam-6204	200	5	]	]	X
ejpam-6204	200	6	=	=	SYM
ejpam-6204	200	7	p[ξ	p[ξ	NOUN
ejpam-6204	200	8	,	,	PUNCT
ejpam-6204	200	9	h]−	h]−	PROPN
ejpam-6204	200	10	dhp	dhp	PROPN
ejpam-6204	200	11	⊗	⊗	PROPN
ejpam-6204	200	12	ξ	ξ	PROPN
ejpam-6204	200	13	.	.	PUNCT
ejpam-6204	201	1	[	[	X
ejpam-6204	201	2	pξ	pξ	NOUN
ejpam-6204	201	3	,	,	PUNCT
ejpam-6204	201	4	l	l	NOUN
ejpam-6204	201	5	]	]	X
ejpam-6204	201	6	=	=	PUNCT
ejpam-6204	201	7	dp	dp	NOUN
ejpam-6204	201	8	⊗	⊗	NOUN
ejpam-6204	201	9	lξ	lξ	NOUN
ejpam-6204	201	10	−	−	PROPN
ejpam-6204	201	11	dlp	dlp	NOUN
ejpam-6204	201	12	⊗	⊗	PROPN
ejpam-6204	201	13	ξ	ξ	PROPN
ejpam-6204	201	14	+	+	PUNCT
ejpam-6204	201	15	p[ξ	p[ξ	ADJ
ejpam-6204	201	16	,	,	PUNCT
ejpam-6204	201	17	l	l	NOUN
ejpam-6204	201	18	]	]	X
ejpam-6204	201	19	=	=	SYM
ejpam-6204	201	20	p[ξ	p[ξ	NOUN
ejpam-6204	201	21	,	,	PUNCT
ejpam-6204	201	22	l]−	l]−	NOUN
ejpam-6204	201	23	dlp	dlp	NOUN
ejpam-6204	201	24	⊗	⊗	PROPN
ejpam-6204	201	25	ξ	ξ	PROPN
ejpam-6204	202	1	=	=	SYM
ejpam-6204	202	2	p[ξ	p[ξ	NOUN
ejpam-6204	202	3	,	,	PUNCT
ejpam-6204	202	4	l]−	l]−	PRON
ejpam-6204	202	5	pdµp	pdµp	NOUN
ejpam-6204	203	1	⊗	⊗	PROPN
ejpam-6204	203	2	ξ	ξ	PROPN
ejpam-6204	203	3	−	−	PROPN
ejpam-6204	203	4	dξp	dξp	PROPN
ejpam-6204	203	5	djp	djp	PROPN
ejpam-6204	203	6	⊗	⊗	PROPN
ejpam-6204	203	7	ξ	ξ	PROPN
ejpam-6204	203	8	.	.	PUNCT
ejpam-6204	204	1	in	in	ADP
ejpam-6204	204	2	view	view	NOUN
ejpam-6204	204	3	of	of	ADP
ejpam-6204	204	4	the	the	DET
ejpam-6204	204	5	above	above	ADJ
ejpam-6204	204	6	relations	relation	NOUN
ejpam-6204	204	7	,	,	PUNCT
ejpam-6204	204	8	equation	equation	NOUN
ejpam-6204	204	9	(	(	PUNCT
ejpam-6204	204	10	25	25	NUM
ejpam-6204	204	11	)	)	PUNCT
ejpam-6204	204	12	becomes	become	VERB
ejpam-6204	204	13	[	[	X
ejpam-6204	204	14	s̃	s̃	PROPN
ejpam-6204	204	15	,	,	PUNCT
ejpam-6204	204	16	h̃	h̃	PROPN
ejpam-6204	204	17	]	]	PUNCT
ejpam-6204	204	18	=	=	PUNCT
ejpam-6204	205	1	[	[	X
ejpam-6204	205	2	s	s	X
ejpam-6204	205	3	,	,	PUNCT
ejpam-6204	205	4	h]−	h]−	PROPN
ejpam-6204	205	5	s(p)µ−	s(p)µ−	NOUN
ejpam-6204	205	6	p[s	p[s	PROPN
ejpam-6204	205	7	,	,	PUNCT
ejpam-6204	205	8	µ]−	µ]−	PRON
ejpam-6204	205	9	lsdjp	lsdjp	VERB
ejpam-6204	205	10	⊗	⊗	PROPN
ejpam-6204	205	11	ξ	ξ	PROPN
ejpam-6204	206	1	−	−	PROPN
ejpam-6204	206	2	djp	djp	X
ejpam-6204	206	3	⊗	⊗	PROPN
ejpam-6204	207	1	[	[	X
ejpam-6204	207	2	s	s	X
ejpam-6204	207	3	,	,	PUNCT
ejpam-6204	207	4	ξ	ξ	X
ejpam-6204	207	5	]	]	X
ejpam-6204	207	6	+	+	CCONJ
ejpam-6204	207	7	2dhp	2dhp	PROPN
ejpam-6204	207	8	⊗	⊗	PROPN
ejpam-6204	207	9	ξ	ξ	PROPN
ejpam-6204	208	1	−	−	PROPN
ejpam-6204	208	2	2pdµp	2pdµp	NUM
ejpam-6204	208	3	⊗	⊗	PROPN
ejpam-6204	208	4	ξ	ξ	PROPN
ejpam-6204	208	5	−	−	PROPN
ejpam-6204	208	6	2dξp	2dξp	NUM
ejpam-6204	208	7	djp	djp	PROPN
ejpam-6204	208	8	⊗	⊗	PROPN
ejpam-6204	208	9	ξ	ξ	PROPN
ejpam-6204	209	1	−	−	PROPN
ejpam-6204	209	2	2p([ξ	2p([ξ	NUM
ejpam-6204	209	3	,	,	PUNCT
ejpam-6204	209	4	h]−	h]−	X
ejpam-6204	210	1	[	[	X
ejpam-6204	210	2	ξ	ξ	X
ejpam-6204	210	3	,	,	PUNCT
ejpam-6204	210	4	l	l	NOUN
ejpam-6204	210	5	]	]	X
ejpam-6204	210	6	)	)	PUNCT
ejpam-6204	210	7	.	.	PUNCT
ejpam-6204	211	1	now	now	ADV
ejpam-6204	211	2	,	,	PUNCT
ejpam-6204	211	3	using	use	VERB
ejpam-6204	211	4	the	the	DET
ejpam-6204	211	5	definition	definition	NOUN
ejpam-6204	211	6	of	of	ADP
ejpam-6204	211	7	the	the	DET
ejpam-6204	211	8	jacobi	jacobi	PROPN
ejpam-6204	211	9	endomorphism	endomorphism	PROPN
ejpam-6204	211	10	φ̃	φ̃	PROPN
ejpam-6204	211	11	:	:	PUNCT
ejpam-6204	211	12	=	=	SYM
ejpam-6204	211	13	ṽ	ṽ	PROPN
ejpam-6204	211	14	◦	◦	NOUN
ejpam-6204	212	1	[	[	X
ejpam-6204	212	2	s̃	s̃	PROPN
ejpam-6204	212	3	,	,	PUNCT
ejpam-6204	212	4	h̃	h̃	PROPN
ejpam-6204	212	5	]	]	PUNCT
ejpam-6204	212	6	and	and	CCONJ
ejpam-6204	212	7	we	we	PRON
ejpam-6204	212	8	compose	compose	VERB
ejpam-6204	212	9	to	to	ADP
ejpam-6204	212	10	the	the	DET
ejpam-6204	212	11	left	left	ADJ
ejpam-6204	212	12	both	both	DET
ejpam-6204	212	13	terms	term	NOUN
ejpam-6204	212	14	in	in	ADP
ejpam-6204	212	15	the	the	DET
ejpam-6204	212	16	above	above	ADJ
ejpam-6204	212	17	formula	formula	NOUN
ejpam-6204	212	18	by	by	ADP
ejpam-6204	212	19	ṽ	ṽ	PROPN
ejpam-6204	212	20	,	,	PUNCT
ejpam-6204	212	21	taking	take	VERB
ejpam-6204	212	22	into	into	ADP
ejpam-6204	212	23	account	account	NOUN
ejpam-6204	212	24	proposition	proposition	NOUN
ejpam-6204	212	25	1	1	NUM
ejpam-6204	212	26	,	,	PUNCT
ejpam-6204	212	27	one	one	PRON
ejpam-6204	212	28	can	can	AUX
ejpam-6204	212	29	show	show	VERB
ejpam-6204	212	30	that	that	SCONJ
ejpam-6204	212	31	:	:	PUNCT
ejpam-6204	212	32	φ̃	φ̃	PROPN
ejpam-6204	212	33	:	:	PUNCT
ejpam-6204	212	34	=	=	SYM
ejpam-6204	212	35	ṽ	ṽ	PROPN
ejpam-6204	212	36	◦	◦	NOUN
ejpam-6204	213	1	[	[	X
ejpam-6204	213	2	s̃	s̃	PROPN
ejpam-6204	213	3	,	,	PUNCT
ejpam-6204	213	4	h̃	h̃	PROPN
ejpam-6204	213	5	]	]	X
ejpam-6204	213	6	=	=	SYM
ejpam-6204	213	7	(	(	PUNCT
ejpam-6204	213	8	v	v	NOUN
ejpam-6204	213	9	+	+	X
ejpam-6204	213	10	l)[s̃	l)[s̃	PROPN
ejpam-6204	213	11	,	,	PUNCT
ejpam-6204	213	12	h̃	h̃	PROPN
ejpam-6204	213	13	]	]	PUNCT
ejpam-6204	213	14	=	=	SYM
ejpam-6204	213	15	v[s̃	v[s̃	NOUN
ejpam-6204	213	16	,	,	PUNCT
ejpam-6204	213	17	h̃	h̃	PROPN
ejpam-6204	213	18	]	]	PUNCT
ejpam-6204	213	19	+	+	NUM
ejpam-6204	213	20	l[s̃	l[s̃	NOUN
ejpam-6204	213	21	,	,	PUNCT
ejpam-6204	213	22	h̃	h̃	PROPN
ejpam-6204	213	23	]	]	PUNCT
ejpam-6204	213	24	.	.	PUNCT
ejpam-6204	214	1	(	(	PUNCT
ejpam-6204	214	2	26	26	NUM
ejpam-6204	214	3	)	)	PUNCT
ejpam-6204	214	4	on	on	ADP
ejpam-6204	214	5	the	the	DET
ejpam-6204	214	6	other	other	ADJ
ejpam-6204	214	7	hand	hand	NOUN
ejpam-6204	214	8	,	,	PUNCT
ejpam-6204	214	9	using	use	VERB
ejpam-6204	214	10	the	the	DET
ejpam-6204	214	11	facts	fact	NOUN
ejpam-6204	214	12	that	that	SCONJ
ejpam-6204	214	13	v	v	X
ejpam-6204	214	14	◦	◦	NOUN
ejpam-6204	214	15	µ	µ	X
ejpam-6204	214	16	=	=	SYM
ejpam-6204	214	17	vµ	vµ	PROPN
ejpam-6204	214	18	=	=	SYM
ejpam-6204	214	19	µ	µ	X
ejpam-6204	214	20	,	,	PUNCT
ejpam-6204	214	21	vξ	vξ	PROPN
ejpam-6204	214	22	=	=	SYM
ejpam-6204	214	23	ξ	ξ	PROPN
ejpam-6204	214	24	,	,	PUNCT
ejpam-6204	214	25	µ	µ	X
ejpam-6204	214	26	◦	◦	NOUN
ejpam-6204	214	27	µ	µ	X
ejpam-6204	214	28	=	=	PUNCT
ejpam-6204	214	29	jµ	jµ	PROPN
ejpam-6204	214	30	=	=	SYM
ejpam-6204	214	31	0	0	NUM
ejpam-6204	214	32	,	,	PUNCT
ejpam-6204	214	33	µξ	µξ	ADP
ejpam-6204	214	34	=	=	NOUN
ejpam-6204	214	35	0	0	NUM
ejpam-6204	214	36	,	,	PUNCT
ejpam-6204	214	37	lξ	lξ	NOUN
ejpam-6204	214	38	=	=	PUNCT
ejpam-6204	214	39	jξ	jξ	NOUN
ejpam-6204	214	40	=	=	SYM
ejpam-6204	214	41	0	0	NUM
ejpam-6204	214	42	,	,	PUNCT
ejpam-6204	214	43	v	v	NOUN
ejpam-6204	214	44	=	=	SYM
ejpam-6204	215	1	j	j	PROPN
ejpam-6204	216	1	[	[	X
ejpam-6204	216	2	s	s	X
ejpam-6204	216	3	,	,	PUNCT
ejpam-6204	216	4	h	h	NOUN
ejpam-6204	216	5	]	]	X
ejpam-6204	216	6	,	,	PUNCT
ejpam-6204	216	7	we	we	PRON
ejpam-6204	216	8	get	get	VERB
ejpam-6204	216	9	v[s̃	v[s̃	NOUN
ejpam-6204	216	10	,	,	PUNCT
ejpam-6204	216	11	h̃	h̃	PROPN
ejpam-6204	216	12	]	]	PUNCT
ejpam-6204	216	13	=	=	SYM
ejpam-6204	216	14	φ−	φ−	PROPN
ejpam-6204	216	15	s(p)µ−	s(p)µ−	NOUN
ejpam-6204	216	16	p	p	PROPN
ejpam-6204	216	17	v[s	v[s	PROPN
ejpam-6204	216	18	,	,	PUNCT
ejpam-6204	216	19	µ]−	µ]−	ADV
ejpam-6204	216	20	lsdjp	lsdjp	VERB
ejpam-6204	216	21	⊗	⊗	PROPN
ejpam-6204	216	22	ξ	ξ	PROPN
ejpam-6204	217	1	−	−	PROPN
ejpam-6204	217	2	djp	djp	PROPN
ejpam-6204	217	3	⊗	⊗	PROPN
ejpam-6204	217	4	v[s	v[s	PROPN
ejpam-6204	217	5	,	,	PUNCT
ejpam-6204	217	6	ξ	ξ	X
ejpam-6204	217	7	]	]	X
ejpam-6204	217	8	+2dhp	+2dhp	PROPN
ejpam-6204	217	9	⊗	⊗	PROPN
ejpam-6204	217	10	ξ	ξ	PROPN
ejpam-6204	218	1	−	−	PROPN
ejpam-6204	218	2	2pdµp	2pdµp	NUM
ejpam-6204	218	3	⊗	⊗	PROPN
ejpam-6204	218	4	ξ	ξ	PROPN
ejpam-6204	218	5	−	−	PROPN
ejpam-6204	218	6	2dξp	2dξp	NUM
ejpam-6204	218	7	djp	djp	PROPN
ejpam-6204	218	8	⊗	⊗	PROPN
ejpam-6204	218	9	ξ	ξ	PROPN
ejpam-6204	218	10	−	−	PROPN
ejpam-6204	218	11	2p(v[ξ	2p(v[ξ	NUM
ejpam-6204	218	12	,	,	PUNCT
ejpam-6204	218	13	h]−	h]−	PROPN
ejpam-6204	218	14	v[ξ	v[ξ	NOUN
ejpam-6204	218	15	,	,	PUNCT
ejpam-6204	218	16	l	l	NOUN
ejpam-6204	218	17	]	]	X
ejpam-6204	218	18	)	)	PUNCT
ejpam-6204	218	19	.	.	PUNCT
ejpam-6204	219	1	l[s̃	l[s̃	PROPN
ejpam-6204	219	2	,	,	PUNCT
ejpam-6204	219	3	h̃	h̃	PROPN
ejpam-6204	219	4	]	]	X
ejpam-6204	219	5	=	=	SYM
ejpam-6204	219	6	pµ[s̃	pµ[s̃	PROPN
ejpam-6204	219	7	,	,	PUNCT
ejpam-6204	219	8	h̃	h̃	PROPN
ejpam-6204	219	9	]	]	PUNCT
ejpam-6204	219	10	+	+	CCONJ
ejpam-6204	219	11	djp([s̃	djp([s̃	PROPN
ejpam-6204	219	12	,	,	PUNCT
ejpam-6204	219	13	h̃])⊗	h̃])⊗	NOUN
ejpam-6204	219	14	ξ	ξ	X
ejpam-6204	219	15	=	=	SYM
ejpam-6204	219	16	p{µ[s	p{µ[s	PROPN
ejpam-6204	219	17	,	,	PUNCT
ejpam-6204	219	18	h]−	h]−	PROPN
ejpam-6204	219	19	pµ[s	pµ[s	PROPN
ejpam-6204	219	20	,	,	PUNCT
ejpam-6204	219	21	µ	µ	X
ejpam-6204	219	22	]	]	X
ejpam-6204	219	23	+	+	CCONJ
ejpam-6204	219	24	djp	djp	ADJ
ejpam-6204	219	25	⊗	⊗	PROPN
ejpam-6204	219	26	µ[s	µ[s	NOUN
ejpam-6204	219	27	,	,	PUNCT
ejpam-6204	219	28	ξ	ξ	X
ejpam-6204	219	29	]	]	X
ejpam-6204	220	1	+	+	CCONJ
ejpam-6204	220	2	2pµ[ξ	2pµ[ξ	NUM
ejpam-6204	220	3	,	,	PUNCT
ejpam-6204	220	4	h	h	NOUN
ejpam-6204	220	5	]	]	X
ejpam-6204	220	6	}	}	PUNCT
ejpam-6204	220	7	+	+	ADJ
ejpam-6204	220	8	{	{	PUNCT
ejpam-6204	220	9	d(j	d(j	PROPN
ejpam-6204	220	10	[	[	X
ejpam-6204	220	11	s	s	X
ejpam-6204	220	12	,	,	PUNCT
ejpam-6204	220	13	h]−pj	h]−pj	X
ejpam-6204	221	1	[	[	X
ejpam-6204	221	2	s,µ]−djp⊗j	s,µ]−djp⊗j	NOUN
ejpam-6204	221	3	[	[	X
ejpam-6204	221	4	s	s	X
ejpam-6204	221	5	,	,	PUNCT
ejpam-6204	221	6	ξ]−2pj	ξ]−2pj	PUNCT
ejpam-6204	221	7	[	[	X
ejpam-6204	221	8	ξ	ξ	X
ejpam-6204	221	9	,	,	PUNCT
ejpam-6204	221	10	h])p	h])p	NOUN
ejpam-6204	221	11	}	}	PUNCT
ejpam-6204	221	12	⊗	⊗	PROPN
ejpam-6204	221	13	ξ	ξ	X
ejpam-6204	221	14	=	=	SYM
ejpam-6204	221	15	p{µ[s	p{µ[s	ADJ
ejpam-6204	221	16	,	,	PUNCT
ejpam-6204	221	17	h	h	NOUN
ejpam-6204	221	18	]	]	X
ejpam-6204	222	1	+	+	CCONJ
ejpam-6204	222	2	pµ[s	pµ[s	PROPN
ejpam-6204	222	3	,	,	PUNCT
ejpam-6204	222	4	µ	µ	X
ejpam-6204	222	5	]	]	X
ejpam-6204	222	6	+	+	CCONJ
ejpam-6204	222	7	djp	djp	ADJ
ejpam-6204	222	8	⊗	⊗	PROPN
ejpam-6204	222	9	µ[s	µ[s	NOUN
ejpam-6204	222	10	,	,	PUNCT
ejpam-6204	222	11	ξ	ξ	X
ejpam-6204	222	12	]	]	X
ejpam-6204	222	13	+	+	CCONJ
ejpam-6204	222	14	2pµ[ξ	2pµ[ξ	NUM
ejpam-6204	222	15	,	,	PUNCT
ejpam-6204	222	16	h	h	NOUN
ejpam-6204	222	17	]	]	X
ejpam-6204	222	18	}	}	PUNCT
ejpam-6204	222	19	+	+	PROPN
ejpam-6204	222	20	{	{	PUNCT
ejpam-6204	222	21	dvp	dvp	PROPN
ejpam-6204	222	22	−	−	PROPN
ejpam-6204	222	23	pdj	pdj	PROPN
ejpam-6204	222	24	[	[	X
ejpam-6204	222	25	s,µ]p	s,µ]p	NOUN
ejpam-6204	222	26	−	−	PROPN
ejpam-6204	222	27	djpdj	djpdj	NOUN
ejpam-6204	223	1	[	[	X
ejpam-6204	223	2	s	s	X
ejpam-6204	223	3	,	,	PUNCT
ejpam-6204	223	4	ξ]p	ξ]p	NOUN
ejpam-6204	223	5	−	−	PROPN
ejpam-6204	223	6	2pdj	2pdj	PROPN
ejpam-6204	224	1	[	[	X
ejpam-6204	224	2	ξ	ξ	X
ejpam-6204	224	3	,	,	PUNCT
ejpam-6204	224	4	h]p	h]p	PROPN
ejpam-6204	224	5	}	}	PUNCT
ejpam-6204	224	6	⊗	⊗	PROPN
ejpam-6204	224	7	ξ	ξ	PROPN
ejpam-6204	224	8	in	in	ADP
ejpam-6204	224	9	view	view	NOUN
ejpam-6204	224	10	of	of	ADP
ejpam-6204	224	11	,	,	PUNCT
ejpam-6204	224	12	the	the	DET
ejpam-6204	224	13	action	action	NOUN
ejpam-6204	224	14	of	of	ADP
ejpam-6204	224	15	the	the	DET
ejpam-6204	224	16	dynamical	dynamical	ADJ
ejpam-6204	224	17	covariant	covariant	ADJ
ejpam-6204	224	18	derivative	derivative	ADJ
ejpam-6204	224	19	∇	∇	NOUN
ejpam-6204	224	20	on	on	ADP
ejpam-6204	224	21	the	the	DET
ejpam-6204	224	22	semi	semi	ADJ
ejpam-6204	224	23	-	-	ADJ
ejpam-6204	224	24	basic	basic	ADJ
ejpam-6204	224	25	1	1	NUM
ejpam-6204	224	26	-	-	PUNCT
ejpam-6204	224	27	form	form	NOUN
ejpam-6204	224	28	djp	djp	NOUN
ejpam-6204	224	29	is	be	AUX
ejpam-6204	224	30	given	give	VERB
ejpam-6204	224	31	by	by	ADP
ejpam-6204	224	32	∇djp	∇djp	PROPN
ejpam-6204	224	33	=	=	SYM
ejpam-6204	224	34	lsdjp	lsdjp	NOUN
ejpam-6204	224	35	−	−	PROPN
ejpam-6204	224	36	dvp	dvp	PROPN
ejpam-6204	224	37	.	.	PUNCT
ejpam-6204	225	1	now	now	ADV
ejpam-6204	225	2	,	,	PUNCT
ejpam-6204	225	3	by	by	ADP
ejpam-6204	225	4	substituting	substitute	VERB
ejpam-6204	225	5	(	(	PUNCT
ejpam-6204	225	6	26	26	NUM
ejpam-6204	225	7	)	)	PUNCT
ejpam-6204	225	8	,	,	PUNCT
ejpam-6204	225	9	the	the	DET
ejpam-6204	225	10	required	require	VERB
ejpam-6204	225	11	formula	formula	NOUN
ejpam-6204	225	12	of	of	ADP
ejpam-6204	225	13	the	the	DET
ejpam-6204	225	14	jacobi	jacobi	PROPN
ejpam-6204	225	15	endomorphism	endomorphism	PROPN
ejpam-6204	225	16	φ̃	φ̃	PROPN
ejpam-6204	225	17	is	be	AUX
ejpam-6204	225	18	obtained	obtain	VERB
ejpam-6204	225	19	,	,	PUNCT
ejpam-6204	225	20	and	and	CCONJ
ejpam-6204	225	21	this	this	PRON
ejpam-6204	225	22	completes	complete	VERB
ejpam-6204	225	23	the	the	DET
ejpam-6204	225	24	proof	proof	NOUN
ejpam-6204	225	25	.	.	PUNCT
ejpam-6204	226	1	s.	s.	PROPN
ejpam-6204	226	2	g.	g.	PROPN
ejpam-6204	226	3	elgendi	elgendi	PROPN
ejpam-6204	226	4	,	,	PUNCT
ejpam-6204	226	5	a.	a.	NOUN
ejpam-6204	226	6	soleiman	soleiman	PROPN
ejpam-6204	226	7	/	/	SYM
ejpam-6204	226	8	eur	eur	PROPN
ejpam-6204	226	9	.	.	PUNCT
ejpam-6204	227	1	j.	j.	PROPN
ejpam-6204	227	2	pure	pure	PROPN
ejpam-6204	227	3	appl	appl	PROPN
ejpam-6204	227	4	.	.	PROPN
ejpam-6204	227	5	math	math	PROPN
ejpam-6204	227	6	,	,	PUNCT
ejpam-6204	227	7	18	18	NUM
ejpam-6204	227	8	(	(	PUNCT
ejpam-6204	227	9	3	3	NUM
ejpam-6204	227	10	)	)	PUNCT
ejpam-6204	227	11	(	(	PUNCT
ejpam-6204	227	12	2025	2025	NUM
ejpam-6204	227	13	)	)	PUNCT
ejpam-6204	227	14	,	,	PUNCT
ejpam-6204	227	15	6204	6204	NUM
ejpam-6204	227	16	10	10	NUM
ejpam-6204	227	17	of	of	ADP
ejpam-6204	227	18	18	18	NUM
ejpam-6204	227	19	theorem	theorem	NOUN
ejpam-6204	227	20	1	1	NUM
ejpam-6204	227	21	.	.	PUNCT
ejpam-6204	228	1	the	the	DET
ejpam-6204	228	2	barthel	barthel	PROPN
ejpam-6204	228	3	curvature	curvature	PROPN
ejpam-6204	228	4	tensor	tensor	NOUN
ejpam-6204	228	5	r̃	r̃	NOUN
ejpam-6204	228	6	associated	associate	VERB
ejpam-6204	228	7	with	with	ADP
ejpam-6204	228	8	the	the	DET
ejpam-6204	228	9	spray	spray	NOUN
ejpam-6204	228	10	deformation	deformation	NOUN
ejpam-6204	228	11	(	(	PUNCT
ejpam-6204	228	12	20	20	NUM
ejpam-6204	228	13	)	)	PUNCT
ejpam-6204	228	14	,	,	PUNCT
ejpam-6204	228	15	with	with	ADP
ejpam-6204	228	16	deformation	deformation	NOUN
ejpam-6204	228	17	factor	factor	NOUN
ejpam-6204	228	18	p(x	p(x	PROPN
ejpam-6204	228	19	,	,	PUNCT
ejpam-6204	228	20	y	y	PROPN
ejpam-6204	228	21	)	)	PUNCT
ejpam-6204	228	22	,	,	PUNCT
ejpam-6204	228	23	is	be	AUX
ejpam-6204	228	24	determined	determine	VERB
ejpam-6204	228	25	by	by	ADP
ejpam-6204	228	26	r̃	r̃	NOUN
ejpam-6204	228	27	=	=	SYM
ejpam-6204	228	28	r+	r+	NOUN
ejpam-6204	229	1	[	[	X
ejpam-6204	229	2	h	h	NOUN
ejpam-6204	229	3	,	,	PUNCT
ejpam-6204	229	4	l]−nl	l]−nl	PROPN
ejpam-6204	229	5	,	,	PUNCT
ejpam-6204	230	1	where	where	SCONJ
ejpam-6204	230	2	l	l	NOUN
ejpam-6204	230	3	defined	define	VERB
ejpam-6204	230	4	by	by	ADP
ejpam-6204	230	5	(	(	PUNCT
ejpam-6204	230	6	24	24	NUM
ejpam-6204	230	7	)	)	PUNCT
ejpam-6204	230	8	,	,	PUNCT
ejpam-6204	230	9	and	and	CCONJ
ejpam-6204	230	10	nl	nl	NOUN
ejpam-6204	230	11	:	:	PUNCT
ejpam-6204	230	12	=	=	SYM
ejpam-6204	230	13	1	1	NUM
ejpam-6204	230	14	2	2	NUM
ejpam-6204	230	15	[	[	X
ejpam-6204	230	16	l	l	NOUN
ejpam-6204	230	17	,	,	PUNCT
ejpam-6204	230	18	l	l	NOUN
ejpam-6204	230	19	]	]	X
ejpam-6204	230	20	is	be	AUX
ejpam-6204	230	21	the	the	DET
ejpam-6204	230	22	nijenhuis	nijenhuis	PROPN
ejpam-6204	230	23	torsion	torsion	NOUN
ejpam-6204	230	24	of	of	ADP
ejpam-6204	230	25	l.	l.	PROPN
ejpam-6204	230	26	proof	proof	PROPN
ejpam-6204	230	27	.	.	PUNCT
ejpam-6204	231	1	the	the	DET
ejpam-6204	231	2	proof	proof	NOUN
ejpam-6204	231	3	follows	follow	VERB
ejpam-6204	231	4	from	from	ADP
ejpam-6204	231	5	proposition	proposition	NOUN
ejpam-6204	231	6	23	23	NUM
ejpam-6204	231	7	,	,	PUNCT
ejpam-6204	231	8	together	together	ADV
ejpam-6204	231	9	with	with	ADP
ejpam-6204	231	10	the	the	DET
ejpam-6204	231	11	fact	fact	NOUN
ejpam-6204	231	12	that	that	SCONJ
ejpam-6204	231	13	r̃	r̃	NOUN
ejpam-6204	231	14	=	=	SYM
ejpam-6204	231	15	−1	−1	NOUN
ejpam-6204	231	16	2	2	NUM
ejpam-6204	231	17	[	[	X
ejpam-6204	231	18	h̃	h̃	PROPN
ejpam-6204	231	19	,	,	PUNCT
ejpam-6204	231	20	h̃	h̃	PROPN
ejpam-6204	231	21	]	]	PUNCT
ejpam-6204	231	22	,	,	PUNCT
ejpam-6204	231	23	and	and	CCONJ
ejpam-6204	231	24	taking	take	VERB
ejpam-6204	231	25	into	into	ADP
ejpam-6204	231	26	account	account	NOUN
ejpam-6204	231	27	the	the	DET
ejpam-6204	231	28	properties	property	NOUN
ejpam-6204	231	29	of	of	ADP
ejpam-6204	231	30	the	the	DET
ejpam-6204	231	31	frölicher	frölicher	ADJ
ejpam-6204	231	32	-	-	PUNCT
ejpam-6204	231	33	nijenhuis	nijenhuis	NOUN
ejpam-6204	231	34	bracket	bracket	NOUN
ejpam-6204	231	35	[	[	X
ejpam-6204	231	36	17	17	NUM
ejpam-6204	231	37	]	]	PUNCT
ejpam-6204	231	38	.	.	PUNCT
ejpam-6204	232	1	corollary	corollary	ADJ
ejpam-6204	232	2	1	1	NUM
ejpam-6204	232	3	.	.	PUNCT
ejpam-6204	233	1	the	the	DET
ejpam-6204	233	2	berwald	berwald	PROPN
ejpam-6204	233	3	connection	connection	NOUN
ejpam-6204	233	4	d̃	d̃	PROPN
ejpam-6204	233	5	◦	◦	NOUN
ejpam-6204	233	6	associated	associate	VERB
ejpam-6204	233	7	with	with	ADP
ejpam-6204	233	8	the	the	DET
ejpam-6204	233	9	spray	spray	NOUN
ejpam-6204	233	10	deformation	deformation	NOUN
ejpam-6204	233	11	(	(	PUNCT
ejpam-6204	233	12	20	20	NUM
ejpam-6204	233	13	)	)	PUNCT
ejpam-6204	233	14	,	,	PUNCT
ejpam-6204	233	15	with	with	ADP
ejpam-6204	233	16	deformation	deformation	NOUN
ejpam-6204	233	17	factor	factor	NOUN
ejpam-6204	233	18	p(x	p(x	PROPN
ejpam-6204	233	19	,	,	PUNCT
ejpam-6204	233	20	y	y	PROPN
ejpam-6204	233	21	)	)	PUNCT
ejpam-6204	233	22	,	,	PUNCT
ejpam-6204	233	23	is	be	AUX
ejpam-6204	233	24	determined	determine	VERB
ejpam-6204	233	25	by	by	ADP
ejpam-6204	233	26	d̃	d̃	PROPN
ejpam-6204	233	27	◦	◦	NOUN
ejpam-6204	233	28	jxjy	jxjy	NOUN
ejpam-6204	233	29	=	=	PUNCT
ejpam-6204	234	1	d	d	PUNCT
ejpam-6204	234	2	◦	◦	NOUN
ejpam-6204	234	3	jxjy	jxjy	PROPN
ejpam-6204	234	4	d̃	d̃	PROPN
ejpam-6204	234	5	◦	◦	PROPN
ejpam-6204	234	6	h̃x	h̃x	VERB
ejpam-6204	234	7	jy	jy	PROPN
ejpam-6204	235	1	=	=	SYM
ejpam-6204	235	2	d	d	PROPN
ejpam-6204	235	3	◦	◦	NOUN
ejpam-6204	235	4	hxjy	hxjy	NOUN
ejpam-6204	235	5	−	−	NOUN
ejpam-6204	236	1	[	[	X
ejpam-6204	236	2	lx	lx	NOUN
ejpam-6204	236	3	,	,	PUNCT
ejpam-6204	236	4	jy	jy	PROPN
ejpam-6204	236	5	]	]	PUNCT
ejpam-6204	237	1	+	+	CCONJ
ejpam-6204	237	2	l[hx	l[hx	PROPN
ejpam-6204	237	3	,	,	PUNCT
ejpam-6204	237	4	jy	jy	X
ejpam-6204	237	5	]	]	PUNCT
ejpam-6204	237	6	.	.	PUNCT
ejpam-6204	238	1	proof	proof	NOUN
ejpam-6204	238	2	.	.	PUNCT
ejpam-6204	239	1	the	the	DET
ejpam-6204	239	2	proof	proof	NOUN
ejpam-6204	239	3	follows	follow	VERB
ejpam-6204	239	4	from	from	ADP
ejpam-6204	239	5	proposition	proposition	NOUN
ejpam-6204	239	6	23	23	NUM
ejpam-6204	239	7	,	,	PUNCT
ejpam-6204	239	8	together	together	ADV
ejpam-6204	239	9	with	with	ADP
ejpam-6204	239	10	the	the	DET
ejpam-6204	239	11	facts	fact	NOUN
ejpam-6204	239	12	that	that	SCONJ
ejpam-6204	239	13	(	(	PUNCT
ejpam-6204	239	14	for	for	ADP
ejpam-6204	239	15	example	example	NOUN
ejpam-6204	239	16	,	,	PUNCT
ejpam-6204	239	17	see	see	VERB
ejpam-6204	239	18	[	[	X
ejpam-6204	239	19	19	19	NUM
ejpam-6204	239	20	]	]	SYM
ejpam-6204	239	21	)	)	PUNCT
ejpam-6204	240	1	d	d	PUNCT
ejpam-6204	240	2	◦	◦	NOUN
ejpam-6204	240	3	jxjy	jxjy	NOUN
ejpam-6204	240	4	=	=	PUNCT
ejpam-6204	241	1	j	j	PROPN
ejpam-6204	242	1	[	[	X
ejpam-6204	242	2	jx	jx	PROPN
ejpam-6204	242	3	,	,	PUNCT
ejpam-6204	242	4	y	y	PROPN
ejpam-6204	242	5	]	]	PUNCT
ejpam-6204	242	6	,	,	PUNCT
ejpam-6204	242	7	d	d	X
ejpam-6204	242	8	◦	◦	NOUN
ejpam-6204	242	9	hxjy	hxjy	NOUN
ejpam-6204	242	10	=	=	SYM
ejpam-6204	242	11	v[hx	v[hx	PROPN
ejpam-6204	242	12	,	,	PUNCT
ejpam-6204	242	13	jy	jy	X
ejpam-6204	242	14	]	]	PUNCT
ejpam-6204	242	15	.	.	PUNCT
ejpam-6204	243	1	this	this	PRON
ejpam-6204	243	2	completes	complete	VERB
ejpam-6204	243	3	the	the	DET
ejpam-6204	243	4	proof	proof	NOUN
ejpam-6204	243	5	.	.	PUNCT
ejpam-6204	244	1	now	now	ADV
ejpam-6204	244	2	,	,	PUNCT
ejpam-6204	244	3	we	we	PRON
ejpam-6204	244	4	retrieve	retrieve	VERB
ejpam-6204	244	5	some	some	DET
ejpam-6204	244	6	important	important	ADJ
ejpam-6204	244	7	results	result	NOUN
ejpam-6204	244	8	of	of	ADP
ejpam-6204	244	9	projective	projective	ADJ
ejpam-6204	244	10	deformation	deformation	NOUN
ejpam-6204	244	11	.	.	PUNCT
ejpam-6204	245	1	in	in	ADP
ejpam-6204	245	2	the	the	DET
ejpam-6204	245	3	deformation	deformation	NOUN
ejpam-6204	245	4	(	(	PUNCT
ejpam-6204	245	5	20	20	NUM
ejpam-6204	245	6	)	)	PUNCT
ejpam-6204	245	7	,	,	PUNCT
ejpam-6204	245	8	if	if	SCONJ
ejpam-6204	245	9	ξ	ξ	X
ejpam-6204	245	10	=	=	SYM
ejpam-6204	245	11	c	c	NOUN
ejpam-6204	245	12	,	,	PUNCT
ejpam-6204	245	13	then	then	ADV
ejpam-6204	245	14	the	the	DET
ejpam-6204	245	15	deformation	deformation	NOUN
ejpam-6204	245	16	reduces	reduce	VERB
ejpam-6204	245	17	to	to	ADP
ejpam-6204	245	18	the	the	DET
ejpam-6204	245	19	projective	projective	ADJ
ejpam-6204	245	20	deformation	deformation	NOUN
ejpam-6204	245	21	s	s	PART
ejpam-6204	245	22	=	=	SYM
ejpam-6204	245	23	s	s	PART
ejpam-6204	245	24	−	−	PROPN
ejpam-6204	245	25	2p(x	2p(x	PROPN
ejpam-6204	245	26	,	,	PUNCT
ejpam-6204	245	27	y	y	PROPN
ejpam-6204	245	28	)	)	PUNCT
ejpam-6204	245	29	c	c	NOUN
ejpam-6204	245	30	(	(	PUNCT
ejpam-6204	245	31	27	27	NUM
ejpam-6204	245	32	)	)	PUNCT
ejpam-6204	245	33	corollary	corollary	ADJ
ejpam-6204	245	34	2	2	NUM
ejpam-6204	245	35	.	.	PUNCT
ejpam-6204	246	1	[	[	X
ejpam-6204	246	2	3	3	X
ejpam-6204	246	3	]	]	PUNCT
ejpam-6204	246	4	under	under	ADP
ejpam-6204	246	5	the	the	DET
ejpam-6204	246	6	projective	projective	ADJ
ejpam-6204	246	7	deformation	deformation	NOUN
ejpam-6204	246	8	s	s	PART
ejpam-6204	246	9	=	=	SYM
ejpam-6204	246	10	s	s	PART
ejpam-6204	246	11	−	−	PROPN
ejpam-6204	246	12	2p(x	2p(x	PROPN
ejpam-6204	246	13	,	,	PUNCT
ejpam-6204	246	14	y	y	PROPN
ejpam-6204	246	15	)	)	PUNCT
ejpam-6204	246	16	c	c	X
ejpam-6204	246	17	,	,	PUNCT
ejpam-6204	246	18	we	we	PRON
ejpam-6204	246	19	have	have	VERB
ejpam-6204	246	20	γ	γ	NOUN
ejpam-6204	246	21	=	=	SYM
ejpam-6204	246	22	γ−	γ−	PROPN
ejpam-6204	247	1	2(pj	2(pj	NUM
ejpam-6204	247	2	+	+	CCONJ
ejpam-6204	247	3	djp	djp	VERB
ejpam-6204	247	4	⊗	⊗	PROPN
ejpam-6204	247	5	c	c	NOUN
ejpam-6204	247	6	)	)	PUNCT
ejpam-6204	248	1	,	,	PUNCT
ejpam-6204	248	2	h	h	NOUN
ejpam-6204	248	3	=	=	PRON
ejpam-6204	249	1	h−	h−	PROPN
ejpam-6204	249	2	pj	pj	PROPN
ejpam-6204	250	1	−	−	PROPN
ejpam-6204	250	2	djp	djp	PROPN
ejpam-6204	250	3	⊗	⊗	PROPN
ejpam-6204	250	4	c	c	NOUN
ejpam-6204	250	5	,	,	PUNCT
ejpam-6204	250	6	v	v	NOUN
ejpam-6204	250	7	=	=	SYM
ejpam-6204	250	8	v	v	PROPN
ejpam-6204	250	9	+	+	CCONJ
ejpam-6204	250	10	pj	pj	PROPN
ejpam-6204	250	11	+	+	CCONJ
ejpam-6204	250	12	djp	djp	PROPN
ejpam-6204	250	13	⊗	⊗	PROPN
ejpam-6204	250	14	c	c	PROPN
ejpam-6204	250	15	,	,	PUNCT
ejpam-6204	250	16	φ	φ	PROPN
ejpam-6204	250	17	=	=	SYM
ejpam-6204	250	18	φ+	φ+	X
ejpam-6204	250	19	(	(	PUNCT
ejpam-6204	250	20	p2−lsp)j	p2−lsp)j	PROPN
ejpam-6204	250	21	+	+	CCONJ
ejpam-6204	250	22	(	(	PUNCT
ejpam-6204	250	23	2dhp−pdjp−∇djp)⊗	2dhp−pdjp−∇djp)⊗	NUM
ejpam-6204	250	24	c	c	NOUN
ejpam-6204	250	25	,	,	PUNCT
ejpam-6204	250	26	r	r	NOUN
ejpam-6204	250	27	=	=	PUNCT
ejpam-6204	250	28	r+	r+	NOUN
ejpam-6204	250	29	djdhp	djdhp	PROPN
ejpam-6204	250	30	⊗	⊗	PROPN
ejpam-6204	250	31	c	c	PROPN
ejpam-6204	250	32	+	+	CCONJ
ejpam-6204	250	33	(	(	PUNCT
ejpam-6204	250	34	pdjp	pdjp	ADJ
ejpam-6204	250	35	−	−	PROPN
ejpam-6204	250	36	dhp	dhp	PROPN
ejpam-6204	250	37	)	)	PUNCT
ejpam-6204	250	38	∧	∧	PROPN
ejpam-6204	250	39	j	j	PROPN
ejpam-6204	250	40	,	,	PUNCT
ejpam-6204	250	41	proof	proof	NOUN
ejpam-6204	250	42	.	.	PUNCT
ejpam-6204	251	1	the	the	DET
ejpam-6204	251	2	proof	proof	NOUN
ejpam-6204	251	3	follows	follow	VERB
ejpam-6204	251	4	from	from	ADP
ejpam-6204	251	5	the	the	DET
ejpam-6204	251	6	above	above	ADJ
ejpam-6204	251	7	results	result	NOUN
ejpam-6204	251	8	,	,	PUNCT
ejpam-6204	251	9	taking	take	VERB
ejpam-6204	251	10	into	into	ADP
ejpam-6204	251	11	account	account	NOUN
ejpam-6204	251	12	the	the	DET
ejpam-6204	251	13	fact	fact	NOUN
ejpam-6204	251	14	that	that	SCONJ
ejpam-6204	251	15	,	,	PUNCT
ejpam-6204	251	16	under	under	ADP
ejpam-6204	251	17	projective	projective	ADJ
ejpam-6204	251	18	deformation	deformation	NOUN
ejpam-6204	251	19	,	,	PUNCT
ejpam-6204	251	20	the	the	DET
ejpam-6204	251	21	vertical	vertical	ADJ
ejpam-6204	251	22	vector	vector	NOUN
ejpam-6204	251	23	field	field	NOUN
ejpam-6204	251	24	ξ	ξ	X
ejpam-6204	251	25	=	=	SYM
ejpam-6204	251	26	c	c	PROPN
ejpam-6204	251	27	,	,	PUNCT
ejpam-6204	251	28	the	the	DET
ejpam-6204	251	29	vector	vector	NOUN
ejpam-6204	251	30	form	form	NOUN
ejpam-6204	251	31	µ	µ	X
ejpam-6204	251	32	=	=	PUNCT
ejpam-6204	252	1	[	[	X
ejpam-6204	252	2	j	j	X
ejpam-6204	252	3	,	,	PUNCT
ejpam-6204	252	4	c	c	X
ejpam-6204	252	5	]	]	X
ejpam-6204	252	6	=	=	SYM
ejpam-6204	252	7	j	j	PROPN
ejpam-6204	252	8	,	,	PUNCT
ejpam-6204	252	9	and	and	CCONJ
ejpam-6204	252	10	hence	hence	ADV
ejpam-6204	252	11	the	the	DET
ejpam-6204	252	12	vector	vector	ADJ
ejpam-6204	252	13	1	1	NUM
ejpam-6204	252	14	-	-	PUNCT
ejpam-6204	252	15	form	form	NOUN
ejpam-6204	252	16	l	l	NOUN
ejpam-6204	252	17	=	=	PUNCT
ejpam-6204	253	1	p	p	X
ejpam-6204	253	2	j	j	PROPN
ejpam-6204	253	3	+	+	CCONJ
ejpam-6204	253	4	djp	djp	PROPN
ejpam-6204	253	5	⊗	⊗	PROPN
ejpam-6204	253	6	c	c	NOUN
ejpam-6204	253	7	,	,	PUNCT
ejpam-6204	253	8	together	together	ADV
ejpam-6204	253	9	with	with	ADP
ejpam-6204	253	10	the	the	DET
ejpam-6204	253	11	following	follow	VERB
ejpam-6204	253	12	relations	relation	NOUN
ejpam-6204	253	13	:	:	PUNCT
ejpam-6204	253	14	c(p	c(p	NOUN
ejpam-6204	253	15	)	)	PUNCT
ejpam-6204	253	16	=	=	SYM
ejpam-6204	254	1	p	p	X
ejpam-6204	254	2	,	,	PUNCT
ejpam-6204	254	3	[	[	X
ejpam-6204	254	4	c	c	X
ejpam-6204	254	5	,	,	PUNCT
ejpam-6204	254	6	s	s	X
ejpam-6204	254	7	]	]	X
ejpam-6204	254	8	=	=	SYM
ejpam-6204	254	9	s	s	X
ejpam-6204	254	10	,	,	PUNCT
ejpam-6204	254	11	[	[	X
ejpam-6204	254	12	c	c	X
ejpam-6204	254	13	,	,	PUNCT
ejpam-6204	254	14	h	h	NOUN
ejpam-6204	254	15	]	]	X
ejpam-6204	254	16	=	=	SYM
ejpam-6204	254	17	0	0	NUM
ejpam-6204	254	18	,	,	PUNCT
ejpam-6204	254	19	[	[	X
ejpam-6204	254	20	c	c	X
ejpam-6204	254	21	,	,	PUNCT
ejpam-6204	254	22	j	j	NOUN
ejpam-6204	254	23	]	]	X
ejpam-6204	254	24	=	=	PUNCT
ejpam-6204	254	25	−j	−j	NOUN
ejpam-6204	254	26	,	,	PUNCT
ejpam-6204	254	27	[	[	X
ejpam-6204	254	28	c	c	X
ejpam-6204	254	29	,	,	PUNCT
ejpam-6204	254	30	l	l	NOUN
ejpam-6204	254	31	]	]	X
ejpam-6204	254	32	=	=	SYM
ejpam-6204	254	33	0	0	NUM
ejpam-6204	254	34	,	,	PUNCT
ejpam-6204	254	35	hc	hc	PROPN
ejpam-6204	254	36	=	=	SYM
ejpam-6204	254	37	lc	lc	PROPN
ejpam-6204	254	38	=	=	SYM
ejpam-6204	254	39	0	0	PROPN
ejpam-6204	254	40	,	,	PUNCT
ejpam-6204	254	41	[	[	X
ejpam-6204	254	42	s	s	X
ejpam-6204	254	43	,	,	PUNCT
ejpam-6204	254	44	j	j	PROPN
ejpam-6204	254	45	]	]	X
ejpam-6204	254	46	=	=	SYM
ejpam-6204	255	1	−γ	−γ	NOUN
ejpam-6204	255	2	,	,	PUNCT
ejpam-6204	255	3	vc	vc	PROPN
ejpam-6204	255	4	=	=	SYM
ejpam-6204	255	5	c	c	PROPN
ejpam-6204	255	6	,	,	PUNCT
ejpam-6204	255	7	vs	vs	ADP
ejpam-6204	255	8	=	=	NOUN
ejpam-6204	255	9	0	0	NUM
ejpam-6204	255	10	,	,	PUNCT
ejpam-6204	255	11	vγ	vγ	NOUN
ejpam-6204	255	12	=	=	NOUN
ejpam-6204	255	13	−v	−v	NOUN
ejpam-6204	255	14	.	.	PUNCT
ejpam-6204	256	1	s.	s.	PROPN
ejpam-6204	256	2	g.	g.	PROPN
ejpam-6204	256	3	elgendi	elgendi	PROPN
ejpam-6204	256	4	,	,	PUNCT
ejpam-6204	256	5	a.	a.	NOUN
ejpam-6204	256	6	soleiman	soleiman	PROPN
ejpam-6204	256	7	/	/	SYM
ejpam-6204	256	8	eur	eur	PROPN
ejpam-6204	256	9	.	.	PUNCT
ejpam-6204	257	1	j.	j.	PROPN
ejpam-6204	257	2	pure	pure	PROPN
ejpam-6204	257	3	appl	appl	PROPN
ejpam-6204	257	4	.	.	PROPN
ejpam-6204	257	5	math	math	PROPN
ejpam-6204	257	6	,	,	PUNCT
ejpam-6204	257	7	18	18	NUM
ejpam-6204	257	8	(	(	PUNCT
ejpam-6204	257	9	3	3	NUM
ejpam-6204	257	10	)	)	PUNCT
ejpam-6204	257	11	(	(	PUNCT
ejpam-6204	257	12	2025	2025	NUM
ejpam-6204	257	13	)	)	PUNCT
ejpam-6204	257	14	,	,	PUNCT
ejpam-6204	257	15	6204	6204	NUM
ejpam-6204	257	16	11	11	NUM
ejpam-6204	257	17	of	of	ADP
ejpam-6204	257	18	18	18	NUM
ejpam-6204	257	19	4	4	NUM
ejpam-6204	257	20	.	.	PUNCT
ejpam-6204	258	1	some	some	DET
ejpam-6204	258	2	special	special	ADJ
ejpam-6204	258	3	cases	case	NOUN
ejpam-6204	258	4	many	many	ADJ
ejpam-6204	258	5	of	of	ADP
ejpam-6204	258	6	the	the	DET
ejpam-6204	258	7	known	know	VERB
ejpam-6204	258	8	special	special	ADJ
ejpam-6204	258	9	finsler	finsler	NOUN
ejpam-6204	258	10	metrics	metric	NOUN
ejpam-6204	258	11	yield	yield	VERB
ejpam-6204	258	12	a	a	DET
ejpam-6204	258	13	deformation	deformation	NOUN
ejpam-6204	258	14	for	for	ADP
ejpam-6204	258	15	the	the	DET
ejpam-6204	258	16	background	background	NOUN
ejpam-6204	258	17	geodesic	geodesic	NOUN
ejpam-6204	258	18	spray	spray	NOUN
ejpam-6204	258	19	.	.	PUNCT
ejpam-6204	259	1	as	as	ADP
ejpam-6204	259	2	examples	example	NOUN
ejpam-6204	259	3	,	,	PUNCT
ejpam-6204	259	4	in	in	ADP
ejpam-6204	259	5	this	this	DET
ejpam-6204	259	6	section	section	NOUN
ejpam-6204	259	7	,	,	PUNCT
ejpam-6204	259	8	we	we	PRON
ejpam-6204	259	9	consider	consider	VERB
ejpam-6204	259	10	two	two	NUM
ejpam-6204	259	11	rich	rich	ADJ
ejpam-6204	259	12	classes	class	NOUN
ejpam-6204	259	13	of	of	ADP
ejpam-6204	259	14	finsler	finsler	NOUN
ejpam-6204	259	15	metrics	metric	NOUN
ejpam-6204	259	16	.	.	PUNCT
ejpam-6204	260	1	namely	namely	ADV
ejpam-6204	260	2	,	,	PUNCT
ejpam-6204	260	3	we	we	PRON
ejpam-6204	260	4	consider	consider	VERB
ejpam-6204	260	5	the	the	DET
ejpam-6204	260	6	class	class	NOUN
ejpam-6204	260	7	of	of	ADP
ejpam-6204	260	8	(	(	PUNCT
ejpam-6204	260	9	α	α	NOUN
ejpam-6204	260	10	,	,	PUNCT
ejpam-6204	260	11	β)-metrics	β)-metrics	PUNCT
ejpam-6204	260	12	and	and	CCONJ
ejpam-6204	260	13	the	the	DET
ejpam-6204	260	14	class	class	NOUN
ejpam-6204	260	15	of	of	ADP
ejpam-6204	260	16	spherically	spherically	PROPN
ejpam-6204	260	17	symmetric	symmetric	ADJ
ejpam-6204	260	18	finsler	finsler	NOUN
ejpam-6204	260	19	metrics	metric	NOUN
ejpam-6204	260	20	.	.	PUNCT
ejpam-6204	261	1	4.1	4.1	NUM
ejpam-6204	261	2	.	.	PUNCT
ejpam-6204	262	1	(	(	PUNCT
ejpam-6204	262	2	α	α	X
ejpam-6204	262	3	,	,	PUNCT
ejpam-6204	262	4	β)-metrics	β)-metrics	PUNCT
ejpam-6204	262	5	the	the	DET
ejpam-6204	262	6	geodesic	geodesic	NOUN
ejpam-6204	262	7	spray	spray	NOUN
ejpam-6204	262	8	s̃	s̃	PROPN
ejpam-6204	262	9	of	of	ADP
ejpam-6204	262	10	an	an	DET
ejpam-6204	262	11	(	(	PUNCT
ejpam-6204	262	12	α	α	NOUN
ejpam-6204	262	13	,	,	PUNCT
ejpam-6204	262	14	β)-metric	β)-metric	PUNCT
ejpam-6204	262	15	f	f	PROPN
ejpam-6204	262	16	is	be	AUX
ejpam-6204	262	17	given	give	VERB
ejpam-6204	262	18	by	by	ADP
ejpam-6204	262	19	[	[	X
ejpam-6204	262	20	4	4	NUM
ejpam-6204	262	21	,	,	PUNCT
ejpam-6204	262	22	20	20	NUM
ejpam-6204	262	23	]	]	PUNCT
ejpam-6204	262	24	g̃i	g̃i	NOUN
ejpam-6204	262	25	=	=	PUNCT
ejpam-6204	262	26	gi	gi	X
ejpam-6204	262	27	+	+	CCONJ
ejpam-6204	262	28	αqsi0	αqsi0	NOUN
ejpam-6204	263	1	+	+	SYM
ejpam-6204	263	2	θ	θ	PROPN
ejpam-6204	263	3	{	{	PUNCT
ejpam-6204	263	4	−2αqs0	−2αqs0	PROPN
ejpam-6204	263	5	+	+	CCONJ
ejpam-6204	263	6	r00	r00	NOUN
ejpam-6204	263	7	}	}	PUNCT
ejpam-6204	263	8	{	{	PUNCT
ejpam-6204	263	9	yi	yi	NOUN
ejpam-6204	263	10	α	α	NOUN
ejpam-6204	263	11	+	+	CCONJ
ejpam-6204	263	12	q′	q′	NOUN
ejpam-6204	264	1	q−	q−	PROPN
ejpam-6204	264	2	sq′	sq′	PROPN
ejpam-6204	264	3	b	b	PROPN
ejpam-6204	264	4	i	i	PROPN
ejpam-6204	264	5	}	}	PUNCT
ejpam-6204	264	6	,	,	PUNCT
ejpam-6204	264	7	(	(	PUNCT
ejpam-6204	264	8	28	28	NUM
ejpam-6204	264	9	)	)	PUNCT
ejpam-6204	264	10	where	where	SCONJ
ejpam-6204	264	11	g̃i	g̃i	NOUN
ejpam-6204	264	12	(	(	PUNCT
ejpam-6204	264	13	resp	resp	NOUN
ejpam-6204	264	14	.	.	PUNCT
ejpam-6204	265	1	gi	gi	X
ejpam-6204	265	2	)	)	PUNCT
ejpam-6204	265	3	are	be	AUX
ejpam-6204	265	4	the	the	DET
ejpam-6204	265	5	coefficients	coefficient	NOUN
ejpam-6204	265	6	of	of	ADP
ejpam-6204	265	7	the	the	DET
ejpam-6204	265	8	geodesic	geodesic	ADJ
ejpam-6204	265	9	spray	spray	NOUN
ejpam-6204	265	10	of	of	ADP
ejpam-6204	265	11	f	f	PROPN
ejpam-6204	265	12	(	(	PUNCT
ejpam-6204	265	13	resp	resp	NOUN
ejpam-6204	265	14	.	.	PUNCT
ejpam-6204	266	1	α	α	X
ejpam-6204	266	2	)	)	PUNCT
ejpam-6204	266	3	,	,	PUNCT
ejpam-6204	266	4	and	and	CCONJ
ejpam-6204	266	5	rij	rij	X
ejpam-6204	266	6	=	=	SYM
ejpam-6204	266	7	1	1	NUM
ejpam-6204	266	8	2	2	NUM
ejpam-6204	266	9	(	(	PUNCT
ejpam-6204	266	10	bi|j	bi|j	NOUN
ejpam-6204	266	11	+	+	NOUN
ejpam-6204	266	12	bj|i	bj|i	NOUN
ejpam-6204	266	13	)	)	PUNCT
ejpam-6204	266	14	,	,	PUNCT
ejpam-6204	266	15	sij	sij	PROPN
ejpam-6204	266	16	=	=	SYM
ejpam-6204	266	17	1	1	NUM
ejpam-6204	266	18	2	2	NUM
ejpam-6204	266	19	(	(	PUNCT
ejpam-6204	266	20	bi|j	bi|j	NOUN
ejpam-6204	266	21	−	−	NOUN
ejpam-6204	266	22	bj|i	bj|i	NOUN
ejpam-6204	266	23	)	)	PUNCT
ejpam-6204	266	24	,	,	PUNCT
ejpam-6204	266	25	r00	r00	VERB
ejpam-6204	266	26	:	:	PUNCT
ejpam-6204	266	27	=	=	SYM
ejpam-6204	266	28	rijy	rijy	NOUN
ejpam-6204	266	29	iyj	iyj	VERB
ejpam-6204	266	30	,	,	PUNCT
ejpam-6204	266	31	si0	si0	PROPN
ejpam-6204	266	32	:	:	PUNCT
ejpam-6204	266	33	=	=	PUNCT
ejpam-6204	266	34	sijy	sijy	PROPN
ejpam-6204	266	35	j	j	PROPN
ejpam-6204	266	36	,	,	PUNCT
ejpam-6204	266	37	sij	sij	PROPN
ejpam-6204	266	38	:	:	PUNCT
ejpam-6204	266	39	=	=	SYM
ejpam-6204	266	40	shja	shja	VERB
ejpam-6204	266	41	ih	ih	NOUN
ejpam-6204	266	42	,	,	PUNCT
ejpam-6204	266	43	sj	sj	INTJ
ejpam-6204	266	44	:	:	PUNCT
ejpam-6204	266	45	=	=	SYM
ejpam-6204	266	46	sijb	sijb	NOUN
ejpam-6204	267	1	i	i	PRON
ejpam-6204	267	2	,	,	PUNCT
ejpam-6204	267	3	bi	bi	NOUN
ejpam-6204	267	4	:	:	PUNCT
ejpam-6204	267	5	=	=	SYM
ejpam-6204	267	6	bja	bja	PROPN
ejpam-6204	267	7	ij	ij	INTJ
ejpam-6204	267	8	q	q	PROPN
ejpam-6204	267	9	:	:	PUNCT
ejpam-6204	267	10	=	=	SYM
ejpam-6204	267	11	ϕ′	ϕ′	PUNCT
ejpam-6204	268	1	ϕ−	ϕ−	X
ejpam-6204	268	2	sϕ′	sϕ′	INTJ
ejpam-6204	268	3	,	,	PUNCT
ejpam-6204	268	4	(	(	PUNCT
ejpam-6204	268	5	29	29	NUM
ejpam-6204	268	6	)	)	PUNCT
ejpam-6204	268	7	θ	θ	NOUN
ejpam-6204	268	8	:	:	PUNCT
ejpam-6204	269	1	=	=	SYM
ejpam-6204	269	2	q−	q−	PROPN
ejpam-6204	269	3	sq′	sq′	X
ejpam-6204	269	4	2(1	2(1	NUM
ejpam-6204	269	5	+	+	CCONJ
ejpam-6204	269	6	sq+	sq+	NOUN
ejpam-6204	269	7	(	(	PUNCT
ejpam-6204	269	8	b2	b2	NOUN
ejpam-6204	269	9	−	−	PROPN
ejpam-6204	269	10	s2)q′	s2)q′	PROPN
ejpam-6204	269	11	)	)	PUNCT
ejpam-6204	269	12	,	,	PUNCT
ejpam-6204	269	13	(	(	PUNCT
ejpam-6204	269	14	30	30	X
ejpam-6204	269	15	)	)	PUNCT
ejpam-6204	269	16	the	the	DET
ejpam-6204	269	17	symbol	symbol	NOUN
ejpam-6204	269	18	|	|	ADV
ejpam-6204	269	19	refers	refer	VERB
ejpam-6204	269	20	to	to	ADP
ejpam-6204	269	21	the	the	DET
ejpam-6204	269	22	covariant	covariant	ADJ
ejpam-6204	269	23	derivative	derivative	NOUN
ejpam-6204	269	24	with	with	ADP
ejpam-6204	269	25	respect	respect	NOUN
ejpam-6204	269	26	to	to	ADP
ejpam-6204	269	27	the	the	DET
ejpam-6204	269	28	levi	levi	PROPN
ejpam-6204	269	29	-	-	PUNCT
ejpam-6204	269	30	civita	civita	PROPN
ejpam-6204	269	31	connection	connection	NOUN
ejpam-6204	269	32	of	of	ADP
ejpam-6204	269	33	α	α	NOUN
ejpam-6204	269	34	,	,	PUNCT
ejpam-6204	269	35	and	and	CCONJ
ejpam-6204	269	36	q′	q′	NOUN
ejpam-6204	269	37	(	(	PUNCT
ejpam-6204	269	38	resp	resp	NOUN
ejpam-6204	269	39	.	.	PUNCT
ejpam-6204	270	1	ϕ′	ϕ′	PUNCT
ejpam-6204	270	2	)	)	PUNCT
ejpam-6204	271	1	mean	mean	VERB
ejpam-6204	271	2	the	the	DET
ejpam-6204	271	3	derivative	derivative	NOUN
ejpam-6204	271	4	of	of	ADP
ejpam-6204	271	5	q	q	PROPN
ejpam-6204	271	6	(	(	PUNCT
ejpam-6204	271	7	resp	resp	NOUN
ejpam-6204	271	8	.	.	PUNCT
ejpam-6204	272	1	ϕ	ϕ	NOUN
ejpam-6204	272	2	)	)	PUNCT
ejpam-6204	272	3	with	with	ADP
ejpam-6204	272	4	respect	respect	NOUN
ejpam-6204	272	5	to	to	ADP
ejpam-6204	272	6	s.	s.	PROPN
ejpam-6204	272	7	the	the	DET
ejpam-6204	272	8	two	two	NUM
ejpam-6204	272	9	sprays	spray	NOUN
ejpam-6204	273	1	s̃	s̃	PROPN
ejpam-6204	273	2	(	(	PUNCT
ejpam-6204	273	3	resp	resp	NOUN
ejpam-6204	273	4	.	.	PUNCT
ejpam-6204	274	1	s	s	X
ejpam-6204	274	2	)	)	PUNCT
ejpam-6204	274	3	of	of	ADP
ejpam-6204	274	4	the	the	DET
ejpam-6204	274	5	metrics	metric	NOUN
ejpam-6204	274	6	f	f	NOUN
ejpam-6204	274	7	(	(	PUNCT
ejpam-6204	274	8	resp	resp	NOUN
ejpam-6204	274	9	.	.	PUNCT
ejpam-6204	275	1	α	α	X
ejpam-6204	275	2	)	)	PUNCT
ejpam-6204	275	3	are	be	AUX
ejpam-6204	275	4	related	relate	VERB
ejpam-6204	275	5	by	by	ADP
ejpam-6204	275	6	s̃	s̃	PROPN
ejpam-6204	275	7	=	=	SYM
ejpam-6204	275	8	s	s	PART
ejpam-6204	275	9	−	−	PROPN
ejpam-6204	275	10	2pξ	2pξ	NOUN
ejpam-6204	275	11	,	,	PUNCT
ejpam-6204	275	12	where	where	SCONJ
ejpam-6204	275	13	the	the	DET
ejpam-6204	275	14	vertical	vertical	ADJ
ejpam-6204	275	15	vector	vector	NOUN
ejpam-6204	275	16	ξ	ξ	PROPN
ejpam-6204	275	17	is	be	AUX
ejpam-6204	275	18	given	give	VERB
ejpam-6204	275	19	by	by	ADP
ejpam-6204	275	20	pξ	pξ	ADP
ejpam-6204	275	21	=	=	SYM
ejpam-6204	275	22	pξi∂̇i	pξi∂̇i	PROPN
ejpam-6204	275	23	=	=	PUNCT
ejpam-6204	275	24	(	(	PUNCT
ejpam-6204	275	25	αqsi0	αqsi0	NOUN
ejpam-6204	276	1	+	+	SYM
ejpam-6204	276	2	θ	θ	PROPN
ejpam-6204	276	3	{	{	PUNCT
ejpam-6204	276	4	−2αqs0	−2αqs0	PROPN
ejpam-6204	276	5	+	+	CCONJ
ejpam-6204	276	6	r00	r00	NOUN
ejpam-6204	276	7	}	}	PUNCT
ejpam-6204	276	8	{	{	PUNCT
ejpam-6204	276	9	yi	yi	NOUN
ejpam-6204	276	10	α	α	NOUN
ejpam-6204	276	11	+	+	CCONJ
ejpam-6204	276	12	q′	q′	NOUN
ejpam-6204	277	1	q−	q−	PROPN
ejpam-6204	277	2	sq′	sq′	X
ejpam-6204	277	3	b	b	NOUN
ejpam-6204	277	4	i	i	NOUN
ejpam-6204	277	5	}	}	PUNCT
ejpam-6204	277	6	)	)	PUNCT
ejpam-6204	278	1	∂̇i	∂̇i	PRON
ejpam-6204	278	2	let	let	VERB
ejpam-6204	278	3	’s	’s	NOUN
ejpam-6204	278	4	study	study	VERB
ejpam-6204	278	5	when	when	SCONJ
ejpam-6204	278	6	the	the	DET
ejpam-6204	278	7	two	two	NUM
ejpam-6204	278	8	sprays	spray	NOUN
ejpam-6204	278	9	are	be	AUX
ejpam-6204	278	10	protectively	protectively	ADV
ejpam-6204	278	11	related	relate	VERB
ejpam-6204	278	12	(	(	PUNCT
ejpam-6204	278	13	that	that	PRON
ejpam-6204	278	14	is	is	ADV
ejpam-6204	278	15	,	,	PUNCT
ejpam-6204	278	16	ξ	ξ	X
ejpam-6204	278	17	=	=	SYM
ejpam-6204	278	18	c	c	X
ejpam-6204	278	19	)	)	PUNCT
ejpam-6204	278	20	as	as	SCONJ
ejpam-6204	278	21	shown	show	VERB
ejpam-6204	278	22	in	in	ADP
ejpam-6204	278	23	the	the	DET
ejpam-6204	278	24	following	follow	VERB
ejpam-6204	278	25	theorem	theorem	PROPN
ejpam-6204	278	26	.	.	PUNCT
ejpam-6204	278	27	theorem	theorem	NOUN
ejpam-6204	278	28	2	2	NUM
ejpam-6204	278	29	.	.	PUNCT
ejpam-6204	279	1	let	let	VERB
ejpam-6204	279	2	f	f	PROPN
ejpam-6204	279	3	=	=	PUNCT
ejpam-6204	279	4	αϕ(s	αϕ(s	X
ejpam-6204	279	5	)	)	PUNCT
ejpam-6204	279	6	be	be	VERB
ejpam-6204	279	7	an	an	DET
ejpam-6204	279	8	(	(	PUNCT
ejpam-6204	279	9	α	α	NOUN
ejpam-6204	279	10	,	,	PUNCT
ejpam-6204	279	11	β)-metric	β)-metric	PUNCT
ejpam-6204	279	12	,	,	PUNCT
ejpam-6204	279	13	then	then	ADV
ejpam-6204	279	14	the	the	DET
ejpam-6204	279	15	associated	associated	ADJ
ejpam-6204	279	16	sprays	spray	NOUN
ejpam-6204	279	17	with	with	ADP
ejpam-6204	279	18	f	f	PROPN
ejpam-6204	279	19	and	and	CCONJ
ejpam-6204	279	20	the	the	DET
ejpam-6204	279	21	riemannian	riemannian	ADJ
ejpam-6204	279	22	metric	metric	PROPN
ejpam-6204	279	23	α	α	PROPN
ejpam-6204	279	24	are	be	AUX
ejpam-6204	279	25	projectively	projectively	ADV
ejpam-6204	279	26	related	relate	VERB
ejpam-6204	279	27	if	if	SCONJ
ejpam-6204	279	28	and	and	CCONJ
ejpam-6204	279	29	only	only	ADV
ejpam-6204	279	30	if	if	SCONJ
ejpam-6204	279	31	2αϕ′si0	2αϕ′si0	NUM
ejpam-6204	279	32	+	+	NUM
ejpam-6204	279	33	r00ϕ	r00ϕ	PROPN
ejpam-6204	279	34	′′bi	′′bi	PROPN
ejpam-6204	279	35	−	−	PROPN
ejpam-6204	279	36	r00ϕ	r00ϕ	VERB
ejpam-6204	280	1	′′	′′	PROPN
ejpam-6204	280	2	β	β	PROPN
ejpam-6204	280	3	α2	α2	PROPN
ejpam-6204	280	4	yi	yi	PROPN
ejpam-6204	280	5	=	=	PUNCT
ejpam-6204	280	6	0	0	PROPN
ejpam-6204	280	7	.	.	PUNCT
ejpam-6204	281	1	(	(	PUNCT
ejpam-6204	281	2	31	31	NUM
ejpam-6204	281	3	)	)	PUNCT
ejpam-6204	281	4	in	in	ADP
ejpam-6204	281	5	this	this	DET
ejpam-6204	281	6	case	case	NOUN
ejpam-6204	281	7	,	,	PUNCT
ejpam-6204	281	8	we	we	PRON
ejpam-6204	281	9	have	have	VERB
ejpam-6204	281	10	s	s	NOUN
ejpam-6204	281	11	=	=	PUNCT
ejpam-6204	281	12	sα	sα	ADJ
ejpam-6204	281	13	−	−	PROPN
ejpam-6204	281	14	2pc	2pc	NOUN
ejpam-6204	281	15	,	,	PUNCT
ejpam-6204	281	16	p	p	NOUN
ejpam-6204	281	17	=	=	NOUN
ejpam-6204	281	18	1	1	NUM
ejpam-6204	281	19	2	2	NUM
ejpam-6204	281	20	r00ϕ	r00ϕ	NOUN
ejpam-6204	281	21	′	′	NUM
ejpam-6204	281	22	αϕ	αϕ	NUM
ejpam-6204	281	23	.	.	PUNCT
ejpam-6204	282	1	s.	s.	PROPN
ejpam-6204	282	2	g.	g.	PROPN
ejpam-6204	282	3	elgendi	elgendi	PROPN
ejpam-6204	282	4	,	,	PUNCT
ejpam-6204	282	5	a.	a.	NOUN
ejpam-6204	282	6	soleiman	soleiman	PROPN
ejpam-6204	282	7	/	/	SYM
ejpam-6204	282	8	eur	eur	PROPN
ejpam-6204	282	9	.	.	PUNCT
ejpam-6204	283	1	j.	j.	PROPN
ejpam-6204	283	2	pure	pure	PROPN
ejpam-6204	283	3	appl	appl	PROPN
ejpam-6204	283	4	.	.	PROPN
ejpam-6204	283	5	math	math	PROPN
ejpam-6204	283	6	,	,	PUNCT
ejpam-6204	283	7	18	18	NUM
ejpam-6204	283	8	(	(	PUNCT
ejpam-6204	283	9	3	3	NUM
ejpam-6204	283	10	)	)	PUNCT
ejpam-6204	283	11	(	(	PUNCT
ejpam-6204	283	12	2025	2025	NUM
ejpam-6204	283	13	)	)	PUNCT
ejpam-6204	283	14	,	,	PUNCT
ejpam-6204	283	15	6204	6204	NUM
ejpam-6204	283	16	12	12	NUM
ejpam-6204	283	17	of	of	ADP
ejpam-6204	283	18	18	18	NUM
ejpam-6204	283	19	proof	proof	NOUN
ejpam-6204	283	20	.	.	PUNCT
ejpam-6204	284	1	in	in	ADP
ejpam-6204	284	2	[	[	X
ejpam-6204	284	3	21	21	NUM
ejpam-6204	284	4	]	]	X
ejpam-6204	284	5	,	,	PUNCT
ejpam-6204	284	6	c.	c.	PROPN
ejpam-6204	284	7	shibata	shibata	PROPN
ejpam-6204	284	8	introduced	introduce	VERB
ejpam-6204	284	9	the	the	DET
ejpam-6204	284	10	β	β	NOUN
ejpam-6204	284	11	-	-	NOUN
ejpam-6204	284	12	change	change	NOUN
ejpam-6204	284	13	of	of	ADP
ejpam-6204	284	14	a	a	DET
ejpam-6204	284	15	riemannian	riemannian	ADJ
ejpam-6204	284	16	metric	metric	ADJ
ejpam-6204	284	17	α	α	NOUN
ejpam-6204	284	18	,	,	PUNCT
ejpam-6204	284	19	that	that	ADV
ejpam-6204	284	20	is	is	ADV
ejpam-6204	284	21	,	,	PUNCT
ejpam-6204	284	22	f	f	PROPN
ejpam-6204	284	23	=	=	SYM
ejpam-6204	284	24	f(α	f(α	PROPN
ejpam-6204	284	25	,	,	PUNCT
ejpam-6204	284	26	β	β	NOUN
ejpam-6204	284	27	)	)	PUNCT
ejpam-6204	284	28	where	where	SCONJ
ejpam-6204	284	29	f	f	PROPN
ejpam-6204	284	30	is	be	AUX
ejpam-6204	284	31	homogeneous	homogeneous	ADJ
ejpam-6204	284	32	function	function	NOUN
ejpam-6204	284	33	of	of	ADP
ejpam-6204	284	34	degree	degree	NOUN
ejpam-6204	284	35	1	1	NUM
ejpam-6204	284	36	in	in	ADP
ejpam-6204	284	37	α	α	NOUN
ejpam-6204	284	38	and	and	CCONJ
ejpam-6204	284	39	β	β	X
ejpam-6204	284	40	.	.	PUNCT
ejpam-6204	285	1	he	he	PRON
ejpam-6204	285	2	characterized	characterize	VERB
ejpam-6204	285	3	when	when	SCONJ
ejpam-6204	285	4	this	this	DET
ejpam-6204	285	5	change	change	NOUN
ejpam-6204	285	6	is	be	AUX
ejpam-6204	285	7	projective	projective	ADJ
ejpam-6204	285	8	change	change	NOUN
ejpam-6204	285	9	,	,	PUNCT
ejpam-6204	285	10	that	that	ADV
ejpam-6204	285	11	is	is	ADV
ejpam-6204	285	12	,	,	PUNCT
ejpam-6204	285	13	the	the	DET
ejpam-6204	285	14	sprays	spray	NOUN
ejpam-6204	285	15	of	of	ADP
ejpam-6204	285	16	f	f	PROPN
ejpam-6204	285	17	and	and	CCONJ
ejpam-6204	285	18	α	α	PROPN
ejpam-6204	285	19	are	be	AUX
ejpam-6204	285	20	projectively	projectively	ADV
ejpam-6204	285	21	related	relate	VERB
ejpam-6204	285	22	.	.	PUNCT
ejpam-6204	286	1	namely	namely	ADV
ejpam-6204	286	2	,	,	PUNCT
ejpam-6204	286	3	the	the	DET
ejpam-6204	286	4	two	two	NUM
ejpam-6204	286	5	sprays	spray	NOUN
ejpam-6204	286	6	are	be	AUX
ejpam-6204	286	7	projectively	projectively	ADV
ejpam-6204	286	8	related	relate	VERB
ejpam-6204	286	9	if	if	SCONJ
ejpam-6204	286	10	and	and	CCONJ
ejpam-6204	286	11	only	only	ADV
ejpam-6204	286	12	if	if	SCONJ
ejpam-6204	286	13	2qsi0	2qsi0	NUM
ejpam-6204	286	14	+	+	X
ejpam-6204	286	15	q0r00	q0r00	ADJ
ejpam-6204	286	16	(	(	PUNCT
ejpam-6204	286	17	bi	bi	NOUN
ejpam-6204	286	18	−	−	PROPN
ejpam-6204	286	19	β	β	X
ejpam-6204	286	20	α2	α2	PROPN
ejpam-6204	286	21	yi	yi	PROPN
ejpam-6204	286	22	)	)	PUNCT
ejpam-6204	287	1	=	=	PUNCT
ejpam-6204	287	2	0	0	NUM
ejpam-6204	287	3	,	,	PUNCT
ejpam-6204	287	4	where	where	SCONJ
ejpam-6204	287	5	q	q	NOUN
ejpam-6204	287	6	:	:	PUNCT
ejpam-6204	287	7	=	=	SYM
ejpam-6204	287	8	f∂βf	f∂βf	PROPN
ejpam-6204	287	9	and	and	CCONJ
ejpam-6204	287	10	q0	q0	VERB
ejpam-6204	287	11	:	:	PUNCT
ejpam-6204	288	1	=	=	SYM
ejpam-6204	288	2	f∂2	f∂2	NOUN
ejpam-6204	288	3	βf	βf	INTJ
ejpam-6204	288	4	.	.	PUNCT
ejpam-6204	289	1	now	now	ADV
ejpam-6204	289	2	,	,	PUNCT
ejpam-6204	289	3	since	since	SCONJ
ejpam-6204	289	4	f	f	PROPN
ejpam-6204	289	5	is	be	AUX
ejpam-6204	289	6	homogeneous	homogeneous	ADJ
ejpam-6204	289	7	function	function	NOUN
ejpam-6204	289	8	of	of	ADP
ejpam-6204	289	9	degree	degree	NOUN
ejpam-6204	289	10	1	1	NUM
ejpam-6204	289	11	in	in	ADP
ejpam-6204	289	12	α	α	PROPN
ejpam-6204	289	13	and	and	CCONJ
ejpam-6204	289	14	β	β	NOUN
ejpam-6204	289	15	,	,	PUNCT
ejpam-6204	289	16	then	then	ADV
ejpam-6204	289	17	we	we	PRON
ejpam-6204	289	18	can	can	AUX
ejpam-6204	289	19	write	write	VERB
ejpam-6204	289	20	f	f	PROPN
ejpam-6204	290	1	=	=	PUNCT
ejpam-6204	290	2	αf	αf	X
ejpam-6204	290	3	(	(	PUNCT
ejpam-6204	290	4	1	1	NUM
ejpam-6204	290	5	,	,	PUNCT
ejpam-6204	290	6	β	β	X
ejpam-6204	290	7	α	α	NOUN
ejpam-6204	290	8	)	)	PUNCT
ejpam-6204	291	1	=	=	PUNCT
ejpam-6204	291	2	αf(1	αf(1	NOUN
ejpam-6204	291	3	,	,	PUNCT
ejpam-6204	291	4	s	s	PART
ejpam-6204	291	5	)	)	PUNCT
ejpam-6204	291	6	=	=	SYM
ejpam-6204	291	7	αϕ(s	αϕ(	NOUN
ejpam-6204	291	8	)	)	PUNCT
ejpam-6204	291	9	,	,	PUNCT
ejpam-6204	291	10	where	where	SCONJ
ejpam-6204	291	11	we	we	PRON
ejpam-6204	291	12	set	set	VERB
ejpam-6204	291	13	ϕ(s	ϕ(s	PRON
ejpam-6204	291	14	)	)	PUNCT
ejpam-6204	291	15	:	:	PUNCT
ejpam-6204	292	1	=	=	SYM
ejpam-6204	292	2	f(1	f(1	PROPN
ejpam-6204	292	3	,	,	PUNCT
ejpam-6204	292	4	s	s	NOUN
ejpam-6204	292	5	)	)	PUNCT
ejpam-6204	292	6	.	.	PUNCT
ejpam-6204	293	1	that	that	PRON
ejpam-6204	293	2	is	be	AUX
ejpam-6204	293	3	,	,	PUNCT
ejpam-6204	293	4	q	q	PUNCT
ejpam-6204	293	5	=	=	SYM
ejpam-6204	293	6	f∂βf	f∂βf	PROPN
ejpam-6204	293	7	=	=	SYM
ejpam-6204	293	8	αϕϕ′	αϕϕ′	NUM
ejpam-6204	293	9	,	,	PUNCT
ejpam-6204	293	10	q0	q0	NOUN
ejpam-6204	293	11	=	=	SYM
ejpam-6204	294	1	f∂2	f∂2	NOUN
ejpam-6204	294	2	βf	βf	NOUN
ejpam-6204	295	1	=	=	SYM
ejpam-6204	295	2	ϕϕ′′.	ϕϕ′′.	PROPN
ejpam-6204	296	1	moreover	moreover	ADV
ejpam-6204	296	2	,	,	PUNCT
ejpam-6204	296	3	contracting	contracting	NOUN
ejpam-6204	296	4	(	(	PUNCT
ejpam-6204	296	5	31	31	NUM
ejpam-6204	296	6	)	)	PUNCT
ejpam-6204	296	7	by	by	ADP
ejpam-6204	296	8	bi	bi	NOUN
ejpam-6204	296	9	,	,	PUNCT
ejpam-6204	296	10	we	we	PRON
ejpam-6204	296	11	get	get	VERB
ejpam-6204	296	12	2αϕ′s0	2αϕ′s0	NOUN
ejpam-6204	296	13	=	=	SYM
ejpam-6204	296	14	−r00ϕ	−r00ϕ	PRON
ejpam-6204	296	15	′′	′′	PROPN
ejpam-6204	296	16	(	(	PUNCT
ejpam-6204	296	17	b2	b2	PROPN
ejpam-6204	296	18	−	−	PROPN
ejpam-6204	296	19	β2	β2	NOUN
ejpam-6204	296	20	α2	α2	PROPN
ejpam-6204	296	21	)	)	PUNCT
ejpam-6204	296	22	.	.	PUNCT
ejpam-6204	297	1	by	by	ADP
ejpam-6204	297	2	substituting	substitute	VERB
ejpam-6204	297	3	from	from	ADP
ejpam-6204	297	4	the	the	DET
ejpam-6204	297	5	above	above	ADJ
ejpam-6204	297	6	equation	equation	NOUN
ejpam-6204	297	7	and	and	CCONJ
ejpam-6204	297	8	(	(	PUNCT
ejpam-6204	297	9	31	31	NUM
ejpam-6204	297	10	)	)	PUNCT
ejpam-6204	297	11	into	into	ADP
ejpam-6204	297	12	(	(	PUNCT
ejpam-6204	297	13	28	28	NUM
ejpam-6204	297	14	)	)	PUNCT
ejpam-6204	297	15	,	,	PUNCT
ejpam-6204	297	16	we	we	PRON
ejpam-6204	297	17	get	get	VERB
ejpam-6204	297	18	gi	gi	NOUN
ejpam-6204	298	1	=	=	NOUN
ejpam-6204	298	2	gi	gi	NUM
ejpam-6204	298	3	α	α	NOUN
ejpam-6204	299	1	+	+	NOUN
ejpam-6204	299	2	1	1	NUM
ejpam-6204	299	3	2	2	NUM
ejpam-6204	299	4	r00ϕ	r00ϕ	NOUN
ejpam-6204	299	5	′	′	NUM
ejpam-6204	299	6	αϕ	αϕ	NUM
ejpam-6204	299	7	yi	yi	PROPN
ejpam-6204	299	8	.	.	PUNCT
ejpam-6204	300	1	corollary	corollary	ADJ
ejpam-6204	300	2	3	3	X
ejpam-6204	300	3	.	.	PUNCT
ejpam-6204	301	1	let	let	VERB
ejpam-6204	301	2	f	f	PROPN
ejpam-6204	301	3	=	=	PUNCT
ejpam-6204	301	4	αϕ(s	αϕ(s	X
ejpam-6204	301	5	)	)	PUNCT
ejpam-6204	301	6	be	be	VERB
ejpam-6204	301	7	an	an	DET
ejpam-6204	301	8	(	(	PUNCT
ejpam-6204	301	9	α	α	NOUN
ejpam-6204	301	10	,	,	PUNCT
ejpam-6204	301	11	β)-metric	β)-metric	PUNCT
ejpam-6204	301	12	and	and	CCONJ
ejpam-6204	301	13	β	β	X
ejpam-6204	301	14	be	be	AUX
ejpam-6204	301	15	a	a	DET
ejpam-6204	301	16	closed	closed	ADJ
ejpam-6204	301	17	1	1	NUM
ejpam-6204	301	18	-	-	PUNCT
ejpam-6204	301	19	form	form	NOUN
ejpam-6204	301	20	,	,	PUNCT
ejpam-6204	301	21	then	then	ADV
ejpam-6204	301	22	the	the	DET
ejpam-6204	301	23	associated	associated	ADJ
ejpam-6204	301	24	sprays	spray	NOUN
ejpam-6204	301	25	with	with	ADP
ejpam-6204	301	26	f	f	PROPN
ejpam-6204	301	27	and	and	CCONJ
ejpam-6204	301	28	the	the	DET
ejpam-6204	301	29	riemannian	riemannian	ADJ
ejpam-6204	301	30	metric	metric	PROPN
ejpam-6204	301	31	α	α	PROPN
ejpam-6204	301	32	are	be	AUX
ejpam-6204	301	33	projectively	projectively	ADV
ejpam-6204	301	34	related	relate	VERB
ejpam-6204	301	35	if	if	SCONJ
ejpam-6204	301	36	and	and	CCONJ
ejpam-6204	301	37	only	only	ADV
ejpam-6204	301	38	if	if	SCONJ
ejpam-6204	301	39	f	f	PROPN
ejpam-6204	301	40	is	be	AUX
ejpam-6204	301	41	of	of	ADP
ejpam-6204	301	42	randers	rander	NOUN
ejpam-6204	301	43	type	type	NOUN
ejpam-6204	301	44	or	or	CCONJ
ejpam-6204	301	45	β	β	NOUN
ejpam-6204	301	46	is	be	AUX
ejpam-6204	301	47	parallel	parallel	ADJ
ejpam-6204	301	48	with	with	ADP
ejpam-6204	301	49	respect	respect	NOUN
ejpam-6204	301	50	to	to	ADP
ejpam-6204	301	51	the	the	DET
ejpam-6204	301	52	levi	levi	PROPN
ejpam-6204	301	53	-	-	PUNCT
ejpam-6204	301	54	civita	civita	PROPN
ejpam-6204	301	55	connection	connection	NOUN
ejpam-6204	301	56	of	of	ADP
ejpam-6204	301	57	α	α	PROPN
ejpam-6204	301	58	.	.	PUNCT
ejpam-6204	302	1	proof	proof	NOUN
ejpam-6204	302	2	.	.	PUNCT
ejpam-6204	303	1	assume	assume	VERB
ejpam-6204	303	2	that	that	SCONJ
ejpam-6204	303	3	f	f	PROPN
ejpam-6204	303	4	=	=	PUNCT
ejpam-6204	303	5	αϕ(s	αϕ(s	X
ejpam-6204	303	6	)	)	PUNCT
ejpam-6204	303	7	is	be	AUX
ejpam-6204	303	8	an	an	DET
ejpam-6204	303	9	(	(	PUNCT
ejpam-6204	303	10	α	α	NOUN
ejpam-6204	303	11	,	,	PUNCT
ejpam-6204	303	12	β)-metric	β)-metric	PUNCT
ejpam-6204	303	13	which	which	PRON
ejpam-6204	303	14	is	be	AUX
ejpam-6204	303	15	projectively	projectively	ADV
ejpam-6204	303	16	related	relate	VERB
ejpam-6204	303	17	to	to	ADP
ejpam-6204	303	18	the	the	DET
ejpam-6204	303	19	riemannian	riemannian	ADJ
ejpam-6204	303	20	metric	metric	NOUN
ejpam-6204	303	21	α	α	PROPN
ejpam-6204	303	22	as	as	ADV
ejpam-6204	303	23	well	well	ADV
ejpam-6204	303	24	as	as	ADP
ejpam-6204	303	25	that	that	SCONJ
ejpam-6204	303	26	β	β	PROPN
ejpam-6204	303	27	is	be	AUX
ejpam-6204	303	28	a	a	DET
ejpam-6204	303	29	closed	closed	ADJ
ejpam-6204	303	30	1	1	NUM
ejpam-6204	303	31	-	-	PUNCT
ejpam-6204	303	32	form	form	NOUN
ejpam-6204	303	33	.	.	PUNCT
ejpam-6204	304	1	then	then	ADV
ejpam-6204	304	2	sij	sij	PROPN
ejpam-6204	304	3	=	=	SYM
ejpam-6204	304	4	0	0	PUNCT
ejpam-6204	304	5	and	and	CCONJ
ejpam-6204	304	6	hence	hence	ADV
ejpam-6204	304	7	si0	si0	NOUN
ejpam-6204	304	8	=	=	SYM
ejpam-6204	304	9	0	0	X
ejpam-6204	304	10	.	.	PUNCT
ejpam-6204	305	1	that	that	ADV
ejpam-6204	305	2	is	is	ADV
ejpam-6204	305	3	(	(	PUNCT
ejpam-6204	305	4	31	31	NUM
ejpam-6204	305	5	)	)	PUNCT
ejpam-6204	305	6	reduces	reduce	VERB
ejpam-6204	305	7	to	to	PART
ejpam-6204	305	8	r00ϕ	r00ϕ	VERB
ejpam-6204	306	1	′′	′′	PROPN
ejpam-6204	306	2	(	(	PUNCT
ejpam-6204	306	3	bi	bi	NOUN
ejpam-6204	306	4	−	−	PROPN
ejpam-6204	306	5	β	β	X
ejpam-6204	306	6	α2	α2	PROPN
ejpam-6204	306	7	yi	yi	PROPN
ejpam-6204	306	8	)	)	PUNCT
ejpam-6204	307	1	=	=	PUNCT
ejpam-6204	307	2	0	0	X
ejpam-6204	307	3	.	.	X
ejpam-6204	307	4	using	use	VERB
ejpam-6204	307	5	[	[	X
ejpam-6204	307	6	22	22	NUM
ejpam-6204	307	7	,	,	PUNCT
ejpam-6204	307	8	lemma	lemma	PROPN
ejpam-6204	307	9	3.2	3.2	NUM
ejpam-6204	307	10	]	]	PUNCT
ejpam-6204	307	11	,	,	PUNCT
ejpam-6204	307	12	bi	bi	NOUN
ejpam-6204	307	13	−	−	PROPN
ejpam-6204	307	14	β	β	X
ejpam-6204	307	15	α2	α2	PROPN
ejpam-6204	307	16	y	y	PROPN
ejpam-6204	307	17	i	i	PRON
ejpam-6204	307	18	̸=	̸=	PROPN
ejpam-6204	307	19	0	0	NUM
ejpam-6204	307	20	.	.	PUNCT
ejpam-6204	308	1	then	then	ADV
ejpam-6204	308	2	,	,	PUNCT
ejpam-6204	308	3	we	we	PRON
ejpam-6204	308	4	have	have	VERB
ejpam-6204	308	5	r00	r00	NOUN
ejpam-6204	308	6	=	=	SYM
ejpam-6204	308	7	0	0	NUM
ejpam-6204	308	8	or	or	CCONJ
ejpam-6204	308	9	ϕ′′	ϕ′′	PRON
ejpam-6204	308	10	=	=	NOUN
ejpam-6204	309	1	0	0	X
ejpam-6204	309	2	.	.	PUNCT
ejpam-6204	310	1	the	the	DET
ejpam-6204	310	2	later	later	ADJ
ejpam-6204	310	3	implies	imply	VERB
ejpam-6204	310	4	that	that	SCONJ
ejpam-6204	310	5	ϕ	ϕ	NOUN
ejpam-6204	310	6	=	=	PUNCT
ejpam-6204	310	7	c1s+	c1s+	PROPN
ejpam-6204	310	8	c2	c2	PROPN
ejpam-6204	310	9	which	which	PRON
ejpam-6204	310	10	means	mean	VERB
ejpam-6204	310	11	that	that	SCONJ
ejpam-6204	310	12	f	f	PROPN
ejpam-6204	310	13	is	be	AUX
ejpam-6204	310	14	of	of	ADP
ejpam-6204	310	15	randers	rander	NOUN
ejpam-6204	310	16	type	type	NOUN
ejpam-6204	310	17	.	.	PUNCT
ejpam-6204	311	1	the	the	DET
ejpam-6204	311	2	choice	choice	NOUN
ejpam-6204	311	3	r00	r00	NOUN
ejpam-6204	311	4	=	=	SYM
ejpam-6204	311	5	0	0	NUM
ejpam-6204	311	6	implies	imply	VERB
ejpam-6204	311	7	r00	r00	NOUN
ejpam-6204	311	8	=	=	SYM
ejpam-6204	311	9	rijy	rijy	NOUN
ejpam-6204	311	10	iyj	iyj	VERB
ejpam-6204	311	11	=	=	SYM
ejpam-6204	311	12	0	0	X
ejpam-6204	311	13	.	.	PUNCT
ejpam-6204	312	1	taking	take	VERB
ejpam-6204	312	2	the	the	DET
ejpam-6204	312	3	derivative	derivative	NOUN
ejpam-6204	312	4	twice	twice	ADV
ejpam-6204	312	5	with	with	ADP
ejpam-6204	312	6	respect	respect	NOUN
ejpam-6204	312	7	to	to	ADP
ejpam-6204	312	8	yh	yh	PROPN
ejpam-6204	312	9	and	and	CCONJ
ejpam-6204	312	10	yk	yk	PROPN
ejpam-6204	312	11	respectively	respectively	ADV
ejpam-6204	312	12	together	together	ADV
ejpam-6204	312	13	with	with	ADP
ejpam-6204	312	14	using	use	VERB
ejpam-6204	312	15	the	the	DET
ejpam-6204	312	16	fact	fact	NOUN
ejpam-6204	312	17	that	that	SCONJ
ejpam-6204	312	18	β	β	NOUN
ejpam-6204	312	19	is	be	AUX
ejpam-6204	312	20	closed	closed	ADJ
ejpam-6204	312	21	,	,	PUNCT
ejpam-6204	312	22	we	we	PRON
ejpam-6204	312	23	get	get	VERB
ejpam-6204	312	24	rhk	rhk	ADJ
ejpam-6204	312	25	=	=	SYM
ejpam-6204	312	26	1	1	NUM
ejpam-6204	312	27	2	2	NUM
ejpam-6204	312	28	(	(	PUNCT
ejpam-6204	312	29	bh|k	bh|k	X
ejpam-6204	313	1	+	+	CCONJ
ejpam-6204	313	2	bk|h	bk|h	X
ejpam-6204	313	3	)	)	PUNCT
ejpam-6204	313	4	=	=	PUNCT
ejpam-6204	313	5	bh|k	bh|k	X
ejpam-6204	313	6	=	=	PUNCT
ejpam-6204	313	7	0	0	X
ejpam-6204	313	8	.	.	PUNCT
ejpam-6204	314	1	that	that	PRON
ejpam-6204	314	2	is	be	AUX
ejpam-6204	314	3	,	,	PUNCT
ejpam-6204	314	4	β	β	X
ejpam-6204	314	5	is	be	AUX
ejpam-6204	314	6	parallel	parallel	ADJ
ejpam-6204	314	7	and	and	CCONJ
ejpam-6204	314	8	this	this	PRON
ejpam-6204	314	9	complete	complete	ADJ
ejpam-6204	314	10	the	the	DET
ejpam-6204	314	11	proof	proof	NOUN
ejpam-6204	314	12	.	.	PUNCT
ejpam-6204	315	1	s.	s.	PROPN
ejpam-6204	315	2	g.	g.	PROPN
ejpam-6204	315	3	elgendi	elgendi	PROPN
ejpam-6204	315	4	,	,	PUNCT
ejpam-6204	315	5	a.	a.	NOUN
ejpam-6204	315	6	soleiman	soleiman	PROPN
ejpam-6204	315	7	/	/	SYM
ejpam-6204	315	8	eur	eur	PROPN
ejpam-6204	315	9	.	.	PUNCT
ejpam-6204	316	1	j.	j.	PROPN
ejpam-6204	316	2	pure	pure	PROPN
ejpam-6204	316	3	appl	appl	PROPN
ejpam-6204	316	4	.	.	PROPN
ejpam-6204	316	5	math	math	PROPN
ejpam-6204	316	6	,	,	PUNCT
ejpam-6204	316	7	18	18	NUM
ejpam-6204	316	8	(	(	PUNCT
ejpam-6204	316	9	3	3	NUM
ejpam-6204	316	10	)	)	PUNCT
ejpam-6204	316	11	(	(	PUNCT
ejpam-6204	316	12	2025	2025	NUM
ejpam-6204	316	13	)	)	PUNCT
ejpam-6204	316	14	,	,	PUNCT
ejpam-6204	316	15	6204	6204	NUM
ejpam-6204	316	16	13	13	NUM
ejpam-6204	316	17	of	of	ADP
ejpam-6204	316	18	18	18	NUM
ejpam-6204	316	19	4.2	4.2	NUM
ejpam-6204	316	20	.	.	PUNCT
ejpam-6204	317	1	spherically	spherically	PROPN
ejpam-6204	317	2	symmetric	symmetric	ADJ
ejpam-6204	317	3	metrics	metric	NOUN
ejpam-6204	317	4	a	a	DET
ejpam-6204	317	5	spherically	spherically	NOUN
ejpam-6204	317	6	symmetric	symmetric	ADJ
ejpam-6204	317	7	finsler	finsler	NOUN
ejpam-6204	317	8	metric	metric	ADJ
ejpam-6204	317	9	f	f	PROPN
ejpam-6204	317	10	on	on	ADP
ejpam-6204	317	11	bn(r0	bn(r0	ADJ
ejpam-6204	317	12	)	)	PUNCT
ejpam-6204	317	13	⊂	⊂	PROPN
ejpam-6204	317	14	rn	rn	PROPN
ejpam-6204	317	15	is	be	AUX
ejpam-6204	317	16	given	give	VERB
ejpam-6204	317	17	by	by	ADP
ejpam-6204	317	18	f	f	PROPN
ejpam-6204	317	19	(	(	PUNCT
ejpam-6204	317	20	x	x	PROPN
ejpam-6204	317	21	,	,	PUNCT
ejpam-6204	317	22	y	y	NOUN
ejpam-6204	317	23	)	)	PUNCT
ejpam-6204	317	24	=	=	SYM
ejpam-6204	317	25	u	u	PROPN
ejpam-6204	317	26	φ	φ	X
ejpam-6204	317	27	(	(	PUNCT
ejpam-6204	317	28	r	r	PROPN
ejpam-6204	317	29	,	,	PUNCT
ejpam-6204	317	30	s	s	PART
ejpam-6204	317	31	)	)	PUNCT
ejpam-6204	317	32	,	,	PUNCT
ejpam-6204	317	33	where	where	SCONJ
ejpam-6204	317	34	r	r	NOUN
ejpam-6204	317	35	=	=	SYM
ejpam-6204	317	36	|x|	|x|	PROPN
ejpam-6204	317	37	,	,	PUNCT
ejpam-6204	317	38	u	u	NOUN
ejpam-6204	317	39	=	=	SYM
ejpam-6204	317	40	|y|	|y|	PROPN
ejpam-6204	317	41	,	,	PUNCT
ejpam-6204	317	42	s	s	PART
ejpam-6204	317	43	=	=	PUNCT
ejpam-6204	317	44	⟨x	⟨x	VERB
ejpam-6204	317	45	,	,	PUNCT
ejpam-6204	317	46	y⟩	y⟩	NOUN
ejpam-6204	317	47	|y|	|y|	PROPN
ejpam-6204	317	48	,	,	PUNCT
ejpam-6204	317	49	|	|	ADV
ejpam-6204	317	50	·	·	PUNCT
ejpam-6204	317	51	|	|	ADV
ejpam-6204	317	52	denotes	denote	VERB
ejpam-6204	317	53	the	the	DET
ejpam-6204	317	54	standard	standard	ADJ
ejpam-6204	317	55	euclidean	euclidean	ADJ
ejpam-6204	317	56	norm	norm	NOUN
ejpam-6204	317	57	and	and	CCONJ
ejpam-6204	317	58	⟨	⟨	NOUN
ejpam-6204	317	59	·	·	NUM
ejpam-6204	317	60	,	,	PUNCT
ejpam-6204	317	61	·	·	PUNCT
ejpam-6204	317	62	⟩	⟩	NOUN
ejpam-6204	317	63	is	be	AUX
ejpam-6204	317	64	the	the	DET
ejpam-6204	317	65	standard	standard	ADJ
ejpam-6204	317	66	inner	inner	ADJ
ejpam-6204	317	67	product	product	NOUN
ejpam-6204	317	68	on	on	ADP
ejpam-6204	317	69	rn	rn	PROPN
ejpam-6204	317	70	,	,	PUNCT
ejpam-6204	317	71	for	for	ADP
ejpam-6204	317	72	more	more	ADJ
ejpam-6204	317	73	details	detail	NOUN
ejpam-6204	317	74	,	,	PUNCT
ejpam-6204	317	75	we	we	PRON
ejpam-6204	317	76	refer	refer	VERB
ejpam-6204	317	77	for	for	ADP
ejpam-6204	317	78	example	example	NOUN
ejpam-6204	317	79	to	to	ADP
ejpam-6204	317	80	[	[	X
ejpam-6204	317	81	23–25	23–25	NUM
ejpam-6204	317	82	]	]	PUNCT
ejpam-6204	317	83	.	.	PUNCT
ejpam-6204	318	1	moreover	moreover	ADV
ejpam-6204	318	2	,	,	PUNCT
ejpam-6204	318	3	the	the	DET
ejpam-6204	318	4	geodesic	geodesic	NOUN
ejpam-6204	318	5	spray	spray	NOUN
ejpam-6204	318	6	coefficients	coefficient	NOUN
ejpam-6204	318	7	gi	gi	NOUN
ejpam-6204	318	8	of	of	ADP
ejpam-6204	318	9	f	f	PROPN
ejpam-6204	318	10	are	be	AUX
ejpam-6204	318	11	given	give	VERB
ejpam-6204	318	12	by	by	ADP
ejpam-6204	318	13	gi	gi	NOUN
ejpam-6204	318	14	=	=	NOUN
ejpam-6204	318	15	upyi	upyi	ADJ
ejpam-6204	318	16	+	+	CCONJ
ejpam-6204	318	17	u2qxi	u2qxi	ADJ
ejpam-6204	318	18	,	,	PUNCT
ejpam-6204	318	19	(	(	PUNCT
ejpam-6204	318	20	32	32	NUM
ejpam-6204	318	21	)	)	PUNCT
ejpam-6204	318	22	where	where	SCONJ
ejpam-6204	318	23	the	the	DET
ejpam-6204	318	24	functions	function	NOUN
ejpam-6204	318	25	p	p	NOUN
ejpam-6204	318	26	and	and	CCONJ
ejpam-6204	318	27	q	q	NOUN
ejpam-6204	318	28	have	have	VERB
ejpam-6204	318	29	the	the	DET
ejpam-6204	318	30	following	follow	VERB
ejpam-6204	318	31	formulae	formulae	ADJ
ejpam-6204	318	32	q	q	PROPN
ejpam-6204	318	33	:	:	PUNCT
ejpam-6204	318	34	=	=	SYM
ejpam-6204	318	35	1	1	NUM
ejpam-6204	318	36	2r	2r	NUM
ejpam-6204	318	37	−φr	−φr	NOUN
ejpam-6204	318	38	+	+	CCONJ
ejpam-6204	318	39	sφrs	sφrs	NOUN
ejpam-6204	319	1	+	+	CCONJ
ejpam-6204	319	2	rφss	rφss	ADV
ejpam-6204	319	3	φ−	φ−	PROPN
ejpam-6204	319	4	sφs	sφs	VERB
ejpam-6204	319	5	+	+	CCONJ
ejpam-6204	319	6	(	(	PUNCT
ejpam-6204	319	7	r2	r2	PROPN
ejpam-6204	319	8	−	−	PROPN
ejpam-6204	319	9	s2)φss	s2)φss	ADV
ejpam-6204	319	10	,	,	PUNCT
ejpam-6204	319	11	p	p	X
ejpam-6204	319	12	:	:	PUNCT
ejpam-6204	319	13	=	=	NOUN
ejpam-6204	319	14	−q	−q	ADJ
ejpam-6204	319	15	φ	φ	PROPN
ejpam-6204	319	16	(	(	PUNCT
ejpam-6204	319	17	sφ+	sφ+	PROPN
ejpam-6204	319	18	(	(	PUNCT
ejpam-6204	319	19	r2	r2	PROPN
ejpam-6204	319	20	−	−	PROPN
ejpam-6204	319	21	s2)φs	s2)φs	NOUN
ejpam-6204	319	22	)	)	PUNCT
ejpam-6204	320	1	+	+	CCONJ
ejpam-6204	320	2	1	1	NUM
ejpam-6204	320	3	2rφ	2rφ	NOUN
ejpam-6204	320	4	(	(	PUNCT
ejpam-6204	320	5	sφr	sφr	NOUN
ejpam-6204	320	6	+	+	CCONJ
ejpam-6204	320	7	rφs	rφ	NOUN
ejpam-6204	320	8	)	)	PUNCT
ejpam-6204	320	9	.	.	PUNCT
ejpam-6204	321	1	(	(	PUNCT
ejpam-6204	321	2	33	33	NUM
ejpam-6204	321	3	)	)	PUNCT
ejpam-6204	321	4	the	the	DET
ejpam-6204	321	5	spray	spray	NOUN
ejpam-6204	321	6	s	s	VERB
ejpam-6204	321	7	of	of	ADP
ejpam-6204	321	8	a	a	DET
ejpam-6204	321	9	spherically	spherically	NOUN
ejpam-6204	321	10	symmetric	symmetric	ADJ
ejpam-6204	321	11	metric	metric	PROPN
ejpam-6204	321	12	f	f	PROPN
ejpam-6204	321	13	is	be	AUX
ejpam-6204	321	14	given	give	VERB
ejpam-6204	321	15	by	by	ADP
ejpam-6204	321	16	s	s	PART
ejpam-6204	321	17	=	=	PROPN
ejpam-6204	321	18	s0	s0	PROPN
ejpam-6204	321	19	−	−	PROPN
ejpam-6204	321	20	2pξ	2pξ	NOUN
ejpam-6204	321	21	,	,	PUNCT
ejpam-6204	321	22	where	where	SCONJ
ejpam-6204	321	23	s0	s0	PROPN
ejpam-6204	321	24	is	be	AUX
ejpam-6204	321	25	the	the	DET
ejpam-6204	321	26	spray	spray	NOUN
ejpam-6204	321	27	of	of	ADP
ejpam-6204	321	28	the	the	DET
ejpam-6204	321	29	euclidean	euclidean	ADJ
ejpam-6204	321	30	metric	metric	NOUN
ejpam-6204	321	31	and	and	CCONJ
ejpam-6204	321	32	pξ	pξ	ADP
ejpam-6204	321	33	=	=	SYM
ejpam-6204	321	34	upc	upc	PROPN
ejpam-6204	321	35	+	+	PROPN
ejpam-6204	321	36	u2qxi∂̇i	u2qxi∂̇i	PROPN
ejpam-6204	321	37	.	.	PROPN
ejpam-6204	321	38	from	from	ADP
ejpam-6204	321	39	which	which	PRON
ejpam-6204	321	40	we	we	PRON
ejpam-6204	321	41	get	get	VERB
ejpam-6204	321	42	the	the	DET
ejpam-6204	321	43	following	follow	VERB
ejpam-6204	321	44	known	know	VERB
ejpam-6204	321	45	corollary	corollary	NOUN
ejpam-6204	321	46	.	.	PUNCT
ejpam-6204	322	1	corollary	corollary	ADJ
ejpam-6204	322	2	4	4	NUM
ejpam-6204	322	3	.	.	PUNCT
ejpam-6204	323	1	the	the	DET
ejpam-6204	323	2	spray	spray	NOUN
ejpam-6204	323	3	of	of	ADP
ejpam-6204	323	4	a	a	DET
ejpam-6204	323	5	spherically	spherically	NOUN
ejpam-6204	323	6	symmetric	symmetric	ADJ
ejpam-6204	323	7	metric	metric	ADJ
ejpam-6204	323	8	f	f	PROPN
ejpam-6204	323	9	=	=	PUNCT
ejpam-6204	323	10	uφ(r	uφ(r	PROPN
ejpam-6204	323	11	,	,	PUNCT
ejpam-6204	323	12	s	s	PART
ejpam-6204	323	13	)	)	PUNCT
ejpam-6204	323	14	is	be	AUX
ejpam-6204	323	15	projectively	projectively	ADV
ejpam-6204	323	16	flat	flat	ADJ
ejpam-6204	323	17	if	if	SCONJ
ejpam-6204	324	1	and	and	CCONJ
ejpam-6204	324	2	only	only	ADV
ejpam-6204	324	3	if	if	SCONJ
ejpam-6204	324	4	q	q	PROPN
ejpam-6204	324	5	=	=	NOUN
ejpam-6204	324	6	0	0	NUM
ejpam-6204	324	7	.	.	NOUN
ejpam-6204	324	8	5	5	NUM
ejpam-6204	324	9	.	.	X
ejpam-6204	325	1	invariant	invariant	PROPN
ejpam-6204	325	2	jacobi	jacobi	PROPN
ejpam-6204	325	3	endomorphism	endomorphism	PROPN
ejpam-6204	325	4	and	and	CCONJ
ejpam-6204	325	5	curvature	curvature	VERB
ejpam-6204	325	6	in	in	ADP
ejpam-6204	325	7	this	this	DET
ejpam-6204	325	8	section	section	NOUN
ejpam-6204	325	9	,	,	PUNCT
ejpam-6204	325	10	under	under	ADP
ejpam-6204	325	11	the	the	DET
ejpam-6204	325	12	projective	projective	ADJ
ejpam-6204	325	13	-	-	PUNCT
ejpam-6204	325	14	like	like	ADJ
ejpam-6204	325	15	deformation	deformation	NOUN
ejpam-6204	325	16	(	(	PUNCT
ejpam-6204	325	17	18	18	NUM
ejpam-6204	325	18	)	)	PUNCT
ejpam-6204	325	19	,	,	PUNCT
ejpam-6204	325	20	we	we	PRON
ejpam-6204	325	21	study	study	VERB
ejpam-6204	325	22	some	some	DET
ejpam-6204	325	23	properties	property	NOUN
ejpam-6204	325	24	of	of	ADP
ejpam-6204	325	25	the	the	DET
ejpam-6204	325	26	jacobi	jacobi	PROPN
ejpam-6204	325	27	endomorphism	endomorphism	PROPN
ejpam-6204	325	28	,	,	PUNCT
ejpam-6204	325	29	barthel	barthel	PROPN
ejpam-6204	325	30	connection	connection	NOUN
ejpam-6204	325	31	,	,	PUNCT
ejpam-6204	325	32	and	and	CCONJ
ejpam-6204	325	33	the	the	DET
ejpam-6204	325	34	curvature	curvature	NOUN
ejpam-6204	325	35	of	of	ADP
ejpam-6204	325	36	barthel	barthel	PROPN
ejpam-6204	325	37	connection	connection	NOUN
ejpam-6204	325	38	[	[	X
ejpam-6204	325	39	26	26	NUM
ejpam-6204	325	40	,	,	PUNCT
ejpam-6204	325	41	27	27	NUM
ejpam-6204	325	42	]	]	PUNCT
ejpam-6204	325	43	.	.	PUNCT
ejpam-6204	326	1	using	use	VERB
ejpam-6204	326	2	the	the	DET
ejpam-6204	326	3	property	property	NOUN
ejpam-6204	326	4	(	(	PUNCT
ejpam-6204	326	5	13	13	NUM
ejpam-6204	326	6	)	)	PUNCT
ejpam-6204	326	7	3r	3r	NOUN
ejpam-6204	326	8	=	=	PUNCT
ejpam-6204	327	1	[	[	X
ejpam-6204	327	2	j	j	PROPN
ejpam-6204	327	3	,	,	PUNCT
ejpam-6204	327	4	φ	φ	PROPN
ejpam-6204	327	5	]	]	X
ejpam-6204	327	6	,	,	PUNCT
ejpam-6204	327	7	φ	φ	PROPN
ejpam-6204	327	8	=	=	SYM
ejpam-6204	327	9	isr	isr	PROPN
ejpam-6204	327	10	,	,	PUNCT
ejpam-6204	327	11	we	we	PRON
ejpam-6204	327	12	have	have	VERB
ejpam-6204	327	13	the	the	DET
ejpam-6204	327	14	following	follow	VERB
ejpam-6204	327	15	theorem	theorem	VERB
ejpam-6204	327	16	.	.	PUNCT
ejpam-6204	327	17	theorem	theorem	NOUN
ejpam-6204	327	18	3	3	NUM
ejpam-6204	327	19	.	.	PUNCT
ejpam-6204	328	1	under	under	ADP
ejpam-6204	328	2	the	the	DET
ejpam-6204	328	3	general	general	ADJ
ejpam-6204	328	4	deformation	deformation	NOUN
ejpam-6204	328	5	(	(	PUNCT
ejpam-6204	328	6	18	18	NUM
ejpam-6204	328	7	)	)	PUNCT
ejpam-6204	328	8	,	,	PUNCT
ejpam-6204	328	9	the	the	DET
ejpam-6204	328	10	jacobi	jacobi	PROPN
ejpam-6204	328	11	endomorphism	endomorphism	PROPN
ejpam-6204	328	12	φ	φ	PROPN
ejpam-6204	328	13	is	be	AUX
ejpam-6204	328	14	invariant	invariant	ADJ
ejpam-6204	328	15	if	if	SCONJ
ejpam-6204	328	16	and	and	CCONJ
ejpam-6204	328	17	only	only	ADV
ejpam-6204	328	18	if	if	SCONJ
ejpam-6204	328	19	the	the	DET
ejpam-6204	328	20	curvature	curvature	NOUN
ejpam-6204	328	21	r	r	NOUN
ejpam-6204	328	22	is	be	AUX
ejpam-6204	328	23	invariant	invariant	ADJ
ejpam-6204	328	24	.	.	PUNCT
ejpam-6204	329	1	s.	s.	PROPN
ejpam-6204	329	2	g.	g.	PROPN
ejpam-6204	329	3	elgendi	elgendi	PROPN
ejpam-6204	329	4	,	,	PUNCT
ejpam-6204	329	5	a.	a.	NOUN
ejpam-6204	329	6	soleiman	soleiman	PROPN
ejpam-6204	329	7	/	/	SYM
ejpam-6204	329	8	eur	eur	PROPN
ejpam-6204	329	9	.	.	PUNCT
ejpam-6204	330	1	j.	j.	PROPN
ejpam-6204	330	2	pure	pure	PROPN
ejpam-6204	330	3	appl	appl	PROPN
ejpam-6204	330	4	.	.	PROPN
ejpam-6204	330	5	math	math	PROPN
ejpam-6204	330	6	,	,	PUNCT
ejpam-6204	330	7	18	18	NUM
ejpam-6204	330	8	(	(	PUNCT
ejpam-6204	330	9	3	3	NUM
ejpam-6204	330	10	)	)	PUNCT
ejpam-6204	330	11	(	(	PUNCT
ejpam-6204	330	12	2025	2025	NUM
ejpam-6204	330	13	)	)	PUNCT
ejpam-6204	330	14	,	,	PUNCT
ejpam-6204	330	15	6204	6204	NUM
ejpam-6204	330	16	14	14	NUM
ejpam-6204	330	17	of	of	ADP
ejpam-6204	330	18	18	18	NUM
ejpam-6204	330	19	proof	proof	NOUN
ejpam-6204	330	20	.	.	PUNCT
ejpam-6204	331	1	let	let	VERB
ejpam-6204	331	2	s	s	PRON
ejpam-6204	331	3	be	be	AUX
ejpam-6204	331	4	a	a	DET
ejpam-6204	331	5	spray	spray	NOUN
ejpam-6204	331	6	on	on	ADP
ejpam-6204	331	7	a	a	DET
ejpam-6204	331	8	manifold	manifold	ADJ
ejpam-6204	331	9	m	m	NOUN
ejpam-6204	331	10	with	with	ADP
ejpam-6204	331	11	the	the	DET
ejpam-6204	331	12	jacobi	jacobi	PROPN
ejpam-6204	331	13	endomorphism	endomorphism	PROPN
ejpam-6204	331	14	φ	φ	PROPN
ejpam-6204	331	15	and	and	CCONJ
ejpam-6204	331	16	curvature	curvature	PROPN
ejpam-6204	331	17	r.	r.	PROPN
ejpam-6204	331	18	now	now	ADV
ejpam-6204	331	19	,	,	PUNCT
ejpam-6204	331	20	consider	consider	VERB
ejpam-6204	331	21	the	the	DET
ejpam-6204	331	22	general	general	ADJ
ejpam-6204	331	23	deformation	deformation	NOUN
ejpam-6204	331	24	(	(	PUNCT
ejpam-6204	331	25	18	18	NUM
ejpam-6204	331	26	)	)	PUNCT
ejpam-6204	331	27	of	of	ADP
ejpam-6204	331	28	s.	s.	PROPN
ejpam-6204	331	29	assume	assume	VERB
ejpam-6204	331	30	that	that	SCONJ
ejpam-6204	331	31	φ	φ	PROPN
ejpam-6204	331	32	is	be	AUX
ejpam-6204	331	33	invarinat	invarinat	NOUN
ejpam-6204	331	34	under	under	ADP
ejpam-6204	331	35	the	the	DET
ejpam-6204	331	36	deforamtion	deforamtion	NOUN
ejpam-6204	331	37	(	(	PUNCT
ejpam-6204	331	38	18	18	NUM
ejpam-6204	331	39	)	)	PUNCT
ejpam-6204	331	40	,	,	PUNCT
ejpam-6204	332	1	that	that	ADV
ejpam-6204	332	2	is	is	ADV
ejpam-6204	332	3	,	,	PUNCT
ejpam-6204	332	4	φ̃	φ̃	PROPN
ejpam-6204	332	5	=	=	SYM
ejpam-6204	332	6	φ	φ	PROPN
ejpam-6204	332	7	.	.	PUNCT
ejpam-6204	333	1	then	then	ADV
ejpam-6204	333	2	,	,	PUNCT
ejpam-6204	333	3	we	we	PRON
ejpam-6204	333	4	have	have	VERB
ejpam-6204	333	5	3r̃	3r̃	NUM
ejpam-6204	333	6	=	=	SYM
ejpam-6204	334	1	[	[	X
ejpam-6204	334	2	j	j	X
ejpam-6204	334	3	,	,	PUNCT
ejpam-6204	334	4	φ̃	φ̃	PROPN
ejpam-6204	334	5	]	]	X
ejpam-6204	334	6	=	=	SYM
ejpam-6204	335	1	[	[	X
ejpam-6204	335	2	j	j	PROPN
ejpam-6204	335	3	,	,	PUNCT
ejpam-6204	335	4	φ	φ	NOUN
ejpam-6204	335	5	]	]	X
ejpam-6204	335	6	=	=	SYM
ejpam-6204	335	7	3r	3r	NUM
ejpam-6204	335	8	.	.	PUNCT
ejpam-6204	336	1	that	that	PRON
ejpam-6204	336	2	is	is	ADV
ejpam-6204	336	3	,	,	PUNCT
ejpam-6204	336	4	the	the	DET
ejpam-6204	336	5	curvature	curvature	NOUN
ejpam-6204	336	6	r	r	NOUN
ejpam-6204	336	7	is	be	AUX
ejpam-6204	336	8	invariant	invariant	ADJ
ejpam-6204	336	9	.	.	PUNCT
ejpam-6204	337	1	conversely	conversely	ADV
ejpam-6204	337	2	,	,	PUNCT
ejpam-6204	337	3	let	let	VERB
ejpam-6204	337	4	r	r	PRON
ejpam-6204	337	5	be	be	AUX
ejpam-6204	337	6	invariant	invariant	ADJ
ejpam-6204	337	7	,	,	PUNCT
ejpam-6204	337	8	then	then	ADV
ejpam-6204	337	9	we	we	PRON
ejpam-6204	337	10	get	get	VERB
ejpam-6204	337	11	φ̃	φ̃	PROPN
ejpam-6204	337	12	=	=	PRON
ejpam-6204	337	13	i	i	PRON
ejpam-6204	337	14	s̃	s̃	PROPN
ejpam-6204	337	15	r̃	r̃	PROPN
ejpam-6204	337	16	=	=	SYM
ejpam-6204	338	1	is−2ξr	is−2ξr	NUM
ejpam-6204	338	2	=	=	SYM
ejpam-6204	338	3	isr−	isr−	PROPN
ejpam-6204	338	4	2iζr	2iζr	PROPN
ejpam-6204	338	5	=	=	SYM
ejpam-6204	338	6	φ−	φ−	PROPN
ejpam-6204	338	7	2iξr	2iξr	PROPN
ejpam-6204	338	8	.	.	PUNCT
ejpam-6204	339	1	but	but	CCONJ
ejpam-6204	339	2	using	use	VERB
ejpam-6204	339	3	the	the	DET
ejpam-6204	339	4	fact	fact	NOUN
ejpam-6204	339	5	that	that	SCONJ
ejpam-6204	339	6	r	r	NOUN
ejpam-6204	339	7	is	be	AUX
ejpam-6204	339	8	semi	semi	ADJ
ejpam-6204	339	9	-	-	ADJ
ejpam-6204	339	10	basic	basic	ADJ
ejpam-6204	339	11	,	,	PUNCT
ejpam-6204	339	12	we	we	PRON
ejpam-6204	339	13	have	have	VERB
ejpam-6204	339	14	iζr	iζr	NOUN
ejpam-6204	339	15	=	=	SYM
ejpam-6204	339	16	0	0	X
ejpam-6204	339	17	.	.	PUNCT
ejpam-6204	340	1	consequently	consequently	ADV
ejpam-6204	340	2	,	,	PUNCT
ejpam-6204	340	3	φ̃	φ̃	PROPN
ejpam-6204	340	4	=	=	SYM
ejpam-6204	340	5	φ	φ	PROPN
ejpam-6204	340	6	,	,	PUNCT
ejpam-6204	340	7	i.e.	i.e.	X
ejpam-6204	340	8	,	,	PUNCT
ejpam-6204	340	9	φ	φ	PROPN
ejpam-6204	340	10	is	be	AUX
ejpam-6204	340	11	invariant	invariant	ADJ
ejpam-6204	340	12	.	.	PUNCT
ejpam-6204	341	1	proposition	proposition	NOUN
ejpam-6204	341	2	3	3	NUM
ejpam-6204	341	3	.	.	PUNCT
ejpam-6204	342	1	under	under	ADP
ejpam-6204	342	2	the	the	DET
ejpam-6204	342	3	projective	projective	ADJ
ejpam-6204	342	4	-	-	PUNCT
ejpam-6204	342	5	like	like	ADJ
ejpam-6204	342	6	deformation	deformation	NOUN
ejpam-6204	342	7	(	(	PUNCT
ejpam-6204	342	8	18	18	NUM
ejpam-6204	342	9	)	)	PUNCT
ejpam-6204	342	10	,	,	PUNCT
ejpam-6204	342	11	with	with	ADP
ejpam-6204	342	12	deformation	deformation	NOUN
ejpam-6204	342	13	factor	factor	NOUN
ejpam-6204	342	14	p(x	p(x	PROPN
ejpam-6204	342	15	,	,	PUNCT
ejpam-6204	342	16	y	y	PROPN
ejpam-6204	342	17	)	)	PUNCT
ejpam-6204	342	18	,	,	PUNCT
ejpam-6204	342	19	the	the	DET
ejpam-6204	342	20	curvature	curvature	NOUN
ejpam-6204	342	21	barthel	barthel	PROPN
ejpam-6204	342	22	connection	connection	PROPN
ejpam-6204	342	23	r	r	NOUN
ejpam-6204	342	24	is	be	AUX
ejpam-6204	342	25	invariant	invariant	ADJ
ejpam-6204	342	26	if	if	SCONJ
ejpam-6204	342	27	and	and	CCONJ
ejpam-6204	342	28	only	only	ADV
ejpam-6204	342	29	if	if	SCONJ
ejpam-6204	342	30	the	the	DET
ejpam-6204	342	31	vertical	vertical	ADJ
ejpam-6204	342	32	one	one	NUM
ejpam-6204	342	33	form	form	NOUN
ejpam-6204	342	34	l	l	NOUN
ejpam-6204	342	35	satisfies	satisfy	VERB
ejpam-6204	342	36	the	the	DET
ejpam-6204	342	37	following	follow	VERB
ejpam-6204	342	38	relation	relation	NOUN
ejpam-6204	342	39	[	[	X
ejpam-6204	342	40	h	h	X
ejpam-6204	342	41	,	,	PUNCT
ejpam-6204	342	42	l	l	NOUN
ejpam-6204	342	43	]	]	X
ejpam-6204	342	44	=	=	SYM
ejpam-6204	342	45	1	1	NUM
ejpam-6204	342	46	2	2	NUM
ejpam-6204	343	1	[	[	X
ejpam-6204	343	2	l	l	NOUN
ejpam-6204	343	3	,	,	PUNCT
ejpam-6204	343	4	l	l	NOUN
ejpam-6204	343	5	]	]	X
ejpam-6204	343	6	,	,	PUNCT
ejpam-6204	343	7	where	where	SCONJ
ejpam-6204	343	8	h	h	NOUN
ejpam-6204	343	9	is	be	AUX
ejpam-6204	343	10	the	the	DET
ejpam-6204	343	11	corresponding	corresponding	ADJ
ejpam-6204	343	12	horizontal	horizontal	ADJ
ejpam-6204	343	13	projection	projection	NOUN
ejpam-6204	343	14	of	of	ADP
ejpam-6204	343	15	the	the	DET
ejpam-6204	343	16	spray	spray	NOUN
ejpam-6204	343	17	s.	s.	PROPN
ejpam-6204	343	18	proof	proof	PROPN
ejpam-6204	343	19	.	.	PUNCT
ejpam-6204	344	1	the	the	DET
ejpam-6204	344	2	proof	proof	NOUN
ejpam-6204	344	3	is	be	AUX
ejpam-6204	344	4	clear	clear	ADJ
ejpam-6204	344	5	and	and	CCONJ
ejpam-6204	344	6	we	we	PRON
ejpam-6204	344	7	omit	omit	VERB
ejpam-6204	344	8	it	it	PRON
ejpam-6204	344	9	.	.	PUNCT
ejpam-6204	345	1	from	from	ADP
ejpam-6204	345	2	which	which	PRON
ejpam-6204	345	3	together	together	ADV
ejpam-6204	345	4	with	with	ADP
ejpam-6204	345	5	theorem	theorem	ADJ
ejpam-6204	345	6	3	3	NUM
ejpam-6204	345	7	,	,	PUNCT
ejpam-6204	345	8	we	we	PRON
ejpam-6204	345	9	conclude	conclude	VERB
ejpam-6204	345	10	that	that	PRON
ejpam-6204	345	11	theorem	theorem	VERB
ejpam-6204	345	12	4	4	NUM
ejpam-6204	345	13	.	.	PUNCT
ejpam-6204	346	1	under	under	ADP
ejpam-6204	346	2	the	the	DET
ejpam-6204	346	3	projective	projective	ADJ
ejpam-6204	346	4	-	-	PUNCT
ejpam-6204	346	5	like	like	ADJ
ejpam-6204	346	6	deformation	deformation	NOUN
ejpam-6204	346	7	(	(	PUNCT
ejpam-6204	346	8	18	18	NUM
ejpam-6204	346	9	)	)	PUNCT
ejpam-6204	346	10	,	,	PUNCT
ejpam-6204	346	11	with	with	ADP
ejpam-6204	346	12	deformation	deformation	NOUN
ejpam-6204	346	13	factor	factor	NOUN
ejpam-6204	346	14	p(x	p(x	PROPN
ejpam-6204	346	15	,	,	PUNCT
ejpam-6204	346	16	y	y	PROPN
ejpam-6204	346	17	)	)	PUNCT
ejpam-6204	346	18	,	,	PUNCT
ejpam-6204	346	19	the	the	DET
ejpam-6204	346	20	following	follow	VERB
ejpam-6204	346	21	assertions	assertion	NOUN
ejpam-6204	346	22	are	be	AUX
ejpam-6204	346	23	equivalent	equivalent	ADJ
ejpam-6204	346	24	(	(	PUNCT
ejpam-6204	346	25	i	i	NOUN
ejpam-6204	346	26	)	)	PUNCT
ejpam-6204	346	27	the	the	DET
ejpam-6204	346	28	vertical	vertical	ADJ
ejpam-6204	346	29	one	one	NUM
ejpam-6204	346	30	form	form	NOUN
ejpam-6204	346	31	l	l	NOUN
ejpam-6204	346	32	satisfies	satisfie	NOUN
ejpam-6204	347	1	[	[	X
ejpam-6204	347	2	h	h	NOUN
ejpam-6204	347	3	,	,	PUNCT
ejpam-6204	347	4	l	l	NOUN
ejpam-6204	347	5	]	]	X
ejpam-6204	347	6	=	=	SYM
ejpam-6204	347	7	1	1	NUM
ejpam-6204	347	8	2	2	NUM
ejpam-6204	347	9	[	[	X
ejpam-6204	347	10	l	l	NOUN
ejpam-6204	347	11	,	,	PUNCT
ejpam-6204	347	12	l	l	NOUN
ejpam-6204	347	13	]	]	PUNCT
ejpam-6204	347	14	.	.	PUNCT
ejpam-6204	348	1	(	(	PUNCT
ejpam-6204	348	2	ii	ii	X
ejpam-6204	348	3	)	)	PUNCT
ejpam-6204	348	4	the	the	DET
ejpam-6204	348	5	jacobi	jacobi	PROPN
ejpam-6204	348	6	endomorphism	endomorphism	PROPN
ejpam-6204	348	7	φ	φ	PROPN
ejpam-6204	348	8	is	be	AUX
ejpam-6204	348	9	invariant	invariant	ADJ
ejpam-6204	348	10	.	.	PUNCT
ejpam-6204	349	1	(	(	PUNCT
ejpam-6204	349	2	iii	iii	X
ejpam-6204	349	3	)	)	PUNCT
ejpam-6204	349	4	the	the	DET
ejpam-6204	349	5	curvature	curvature	NOUN
ejpam-6204	349	6	barthel	barthel	PROPN
ejpam-6204	349	7	connection	connection	PROPN
ejpam-6204	349	8	r	r	NOUN
ejpam-6204	349	9	is	be	AUX
ejpam-6204	349	10	invariant	invariant	ADJ
ejpam-6204	349	11	.	.	PUNCT
ejpam-6204	350	1	proposition	proposition	NOUN
ejpam-6204	350	2	4	4	NUM
ejpam-6204	350	3	.	.	PUNCT
ejpam-6204	351	1	the	the	DET
ejpam-6204	351	2	projective	projective	ADJ
ejpam-6204	351	3	deformation	deformation	NOUN
ejpam-6204	351	4	(	(	PUNCT
ejpam-6204	351	5	27	27	NUM
ejpam-6204	351	6	)	)	PUNCT
ejpam-6204	351	7	preserves	preserve	VERB
ejpam-6204	351	8	the	the	DET
ejpam-6204	351	9	curvature	curvature	NOUN
ejpam-6204	351	10	the	the	DET
ejpam-6204	351	11	projective	projective	ADJ
ejpam-6204	351	12	factor	factor	NOUN
ejpam-6204	351	13	p	p	NOUN
ejpam-6204	351	14	is	be	AUX
ejpam-6204	351	15	a	a	DET
ejpam-6204	351	16	funk	funk	NOUN
ejpam-6204	351	17	function	function	NOUN
ejpam-6204	351	18	,	,	PUNCT
ejpam-6204	351	19	that	that	ADV
ejpam-6204	351	20	is	is	ADV
ejpam-6204	351	21	,	,	PUNCT
ejpam-6204	351	22	dhp	dhp	PROPN
ejpam-6204	351	23	=	=	PROPN
ejpam-6204	351	24	pdjp	pdjp	PROPN
ejpam-6204	351	25	.	.	PUNCT
ejpam-6204	352	1	proof	proof	NOUN
ejpam-6204	352	2	.	.	PUNCT
ejpam-6204	353	1	it	it	PRON
ejpam-6204	353	2	is	be	AUX
ejpam-6204	353	3	easy	easy	ADJ
ejpam-6204	353	4	to	to	PART
ejpam-6204	353	5	see	see	VERB
ejpam-6204	353	6	that	that	SCONJ
ejpam-6204	353	7	the	the	DET
ejpam-6204	353	8	curvature	curvature	NOUN
ejpam-6204	353	9	of	of	ADP
ejpam-6204	353	10	a	a	DET
ejpam-6204	353	11	spray	spray	NOUN
ejpam-6204	353	12	s	s	VERB
ejpam-6204	353	13	is	be	AUX
ejpam-6204	353	14	preserved	preserve	VERB
ejpam-6204	353	15	under	under	ADP
ejpam-6204	353	16	any	any	DET
ejpam-6204	353	17	deformation	deformation	NOUN
ejpam-6204	353	18	of	of	ADP
ejpam-6204	353	19	s	s	PRON
ejpam-6204	353	20	if	if	SCONJ
ejpam-6204	353	21	and	and	CCONJ
ejpam-6204	354	1	only	only	ADV
ejpam-6204	354	2	if	if	SCONJ
ejpam-6204	354	3	r̃	r̃	PROPN
ejpam-6204	354	4	=	=	SYM
ejpam-6204	354	5	r	r	NOUN
ejpam-6204	354	6	,	,	PUNCT
ejpam-6204	354	7	that	that	PRON
ejpam-6204	354	8	is	be	AUX
ejpam-6204	354	9	djdhp	djdhp	PROPN
ejpam-6204	354	10	⊗	⊗	PROPN
ejpam-6204	354	11	c	c	PROPN
ejpam-6204	355	1	+	+	CCONJ
ejpam-6204	355	2	(	(	PUNCT
ejpam-6204	355	3	pdjp	pdjp	ADJ
ejpam-6204	355	4	−	−	PROPN
ejpam-6204	355	5	dhp	dhp	PROPN
ejpam-6204	355	6	)	)	PUNCT
ejpam-6204	355	7	∧	∧	PROPN
ejpam-6204	355	8	j	j	PROPN
ejpam-6204	355	9	=	=	SYM
ejpam-6204	355	10	0	0	PROPN
ejpam-6204	355	11	.	.	PUNCT
ejpam-6204	356	1	the	the	DET
ejpam-6204	356	2	above	above	ADJ
ejpam-6204	356	3	equation	equation	NOUN
ejpam-6204	356	4	is	be	AUX
ejpam-6204	356	5	satisfied	satisfied	ADJ
ejpam-6204	356	6	if	if	SCONJ
ejpam-6204	356	7	and	and	CCONJ
ejpam-6204	356	8	only	only	ADV
ejpam-6204	356	9	if	if	SCONJ
ejpam-6204	356	10	pdjp	pdjp	ADJ
ejpam-6204	356	11	−	−	PROPN
ejpam-6204	356	12	dhp	dhp	PROPN
ejpam-6204	356	13	=	=	PROPN
ejpam-6204	356	14	0	0	PROPN
ejpam-6204	356	15	.	.	PUNCT
ejpam-6204	357	1	s.	s.	PROPN
ejpam-6204	357	2	g.	g.	PROPN
ejpam-6204	357	3	elgendi	elgendi	PROPN
ejpam-6204	357	4	,	,	PUNCT
ejpam-6204	357	5	a.	a.	NOUN
ejpam-6204	357	6	soleiman	soleiman	PROPN
ejpam-6204	357	7	/	/	SYM
ejpam-6204	357	8	eur	eur	PROPN
ejpam-6204	357	9	.	.	PUNCT
ejpam-6204	358	1	j.	j.	PROPN
ejpam-6204	358	2	pure	pure	PROPN
ejpam-6204	358	3	appl	appl	PROPN
ejpam-6204	358	4	.	.	PROPN
ejpam-6204	358	5	math	math	PROPN
ejpam-6204	358	6	,	,	PUNCT
ejpam-6204	358	7	18	18	NUM
ejpam-6204	358	8	(	(	PUNCT
ejpam-6204	358	9	3	3	NUM
ejpam-6204	358	10	)	)	PUNCT
ejpam-6204	358	11	(	(	PUNCT
ejpam-6204	358	12	2025	2025	NUM
ejpam-6204	358	13	)	)	PUNCT
ejpam-6204	358	14	,	,	PUNCT
ejpam-6204	358	15	6204	6204	NUM
ejpam-6204	358	16	15	15	NUM
ejpam-6204	358	17	of	of	ADP
ejpam-6204	358	18	18	18	NUM
ejpam-6204	358	19	in	in	ADP
ejpam-6204	358	20	the	the	DET
ejpam-6204	358	21	following	follow	VERB
ejpam-6204	358	22	two	two	NUM
ejpam-6204	358	23	examples	example	NOUN
ejpam-6204	358	24	,	,	PUNCT
ejpam-6204	358	25	for	for	ADP
ejpam-6204	358	26	simplicity	simplicity	NOUN
ejpam-6204	358	27	,	,	PUNCT
ejpam-6204	358	28	we	we	PRON
ejpam-6204	358	29	consider	consider	VERB
ejpam-6204	358	30	s̃	s̃	PROPN
ejpam-6204	358	31	=	=	SYM
ejpam-6204	358	32	s	s	PART
ejpam-6204	358	33	−	−	PROPN
ejpam-6204	358	34	2pξ	2pξ	NOUN
ejpam-6204	358	35	=	=	PUNCT
ejpam-6204	358	36	s	s	PART
ejpam-6204	358	37	−	−	NOUN
ejpam-6204	358	38	2ζ	2ζ	NOUN
ejpam-6204	358	39	,	,	PUNCT
ejpam-6204	358	40	where	where	SCONJ
ejpam-6204	358	41	we	we	PRON
ejpam-6204	358	42	set	set	VERB
ejpam-6204	358	43	ζ	ζ	NOUN
ejpam-6204	358	44	=	=	PUNCT
ejpam-6204	358	45	pξ	pξ	NOUN
ejpam-6204	358	46	.	.	PUNCT
ejpam-6204	359	1	for	for	ADP
ejpam-6204	359	2	calculations	calculation	NOUN
ejpam-6204	359	3	,	,	PUNCT
ejpam-6204	359	4	we	we	PRON
ejpam-6204	359	5	use	use	VERB
ejpam-6204	359	6	the	the	DET
ejpam-6204	359	7	finsler	finsler	NOUN
ejpam-6204	359	8	package	package	NOUN
ejpam-6204	360	1	[	[	X
ejpam-6204	360	2	28	28	NUM
ejpam-6204	360	3	]	]	PUNCT
ejpam-6204	360	4	,	,	PUNCT
ejpam-6204	360	5	moreover	moreover	ADV
ejpam-6204	360	6	,	,	PUNCT
ejpam-6204	360	7	pdf	pdf	NOUN
ejpam-6204	360	8	and	and	CCONJ
ejpam-6204	360	9	maple	maple	NOUN
ejpam-6204	360	10	files	file	NOUN
ejpam-6204	360	11	of	of	ADP
ejpam-6204	360	12	the	the	DET
ejpam-6204	360	13	calculation	calculation	NOUN
ejpam-6204	360	14	are	be	AUX
ejpam-6204	360	15	posted	post	VERB
ejpam-6204	360	16	on	on	ADP
ejpam-6204	360	17	https://github.com/salahelgendi/calculations-for-the-paper-deformation-of-sprays.git	https://github.com/salahelgendi/calculations-for-the-paper-deformation-of-sprays.git	NOUN
ejpam-6204	360	18	example	example	NOUN
ejpam-6204	360	19	2	2	X
ejpam-6204	360	20	.	.	X
ejpam-6204	360	21	consider	consider	VERB
ejpam-6204	360	22	m	m	VERB
ejpam-6204	360	23	=	=	PRON
ejpam-6204	360	24	{	{	PUNCT
ejpam-6204	360	25	(	(	PUNCT
ejpam-6204	360	26	x1	x1	PROPN
ejpam-6204	360	27	,	,	PUNCT
ejpam-6204	360	28	x2	x2	ADJ
ejpam-6204	360	29	)	)	PUNCT
ejpam-6204	360	30	∈	∈	PROPN
ejpam-6204	360	31	r2	r2	NOUN
ejpam-6204	360	32	:	:	PUNCT
ejpam-6204	361	1	x1	x1	PROPN
ejpam-6204	361	2	>	>	X
ejpam-6204	361	3	0	0	PUNCT
ejpam-6204	362	1	with	with	ADP
ejpam-6204	362	2	the	the	DET
ejpam-6204	362	3	finsler	finsler	NOUN
ejpam-6204	362	4	function	function	NOUN
ejpam-6204	363	1	f	f	PROPN
ejpam-6204	363	2	f	f	PROPN
ejpam-6204	363	3	=	=	PUNCT
ejpam-6204	363	4	√	√	PROPN
ejpam-6204	363	5	x1((y1)2	x1((y1)2	PROPN
ejpam-6204	363	6	+	+	CCONJ
ejpam-6204	363	7	(	(	PUNCT
ejpam-6204	363	8	y2)2	y2)2	INTJ
ejpam-6204	363	9	)	)	PUNCT
ejpam-6204	363	10	,	,	PUNCT
ejpam-6204	363	11	where	where	SCONJ
ejpam-6204	363	12	(	(	PUNCT
ejpam-6204	363	13	x1	x1	ADJ
ejpam-6204	363	14	,	,	PUNCT
ejpam-6204	363	15	x2	x2	PROPN
ejpam-6204	363	16	;	;	PUNCT
ejpam-6204	363	17	y1	y1	NOUN
ejpam-6204	363	18	,	,	PUNCT
ejpam-6204	363	19	y2	y2	NOUN
ejpam-6204	363	20	)	)	PUNCT
ejpam-6204	363	21	∈	∈	PROPN
ejpam-6204	363	22	tr2	tr2	NOUN
ejpam-6204	363	23	=	=	SYM
ejpam-6204	363	24	r4	r4	NOUN
ejpam-6204	363	25	.	.	PUNCT
ejpam-6204	364	1	the	the	DET
ejpam-6204	364	2	coefficients	coefficient	NOUN
ejpam-6204	364	3	gi	gi	INTJ
ejpam-6204	364	4	of	of	ADP
ejpam-6204	364	5	the	the	DET
ejpam-6204	364	6	geodesic	geodesic	ADJ
ejpam-6204	364	7	spray	spray	NOUN
ejpam-6204	364	8	are	be	AUX
ejpam-6204	364	9	given	give	VERB
ejpam-6204	364	10	by	by	ADP
ejpam-6204	364	11	g1	g1	NOUN
ejpam-6204	364	12	=	=	SYM
ejpam-6204	364	13	1	1	NUM
ejpam-6204	364	14	4	4	NUM
ejpam-6204	364	15	(	(	PUNCT
ejpam-6204	364	16	y1)2	y1)2	NUM
ejpam-6204	364	17	−	−	PROPN
ejpam-6204	364	18	(	(	PUNCT
ejpam-6204	364	19	y2)2	y2)2	NOUN
ejpam-6204	364	20	x1	x1	PROPN
ejpam-6204	364	21	,	,	PUNCT
ejpam-6204	364	22	g2	g2	PROPN
ejpam-6204	364	23	=	=	NOUN
ejpam-6204	364	24	1	1	NUM
ejpam-6204	364	25	4	4	NUM
ejpam-6204	364	26	y1y2	y1y2	NUM
ejpam-6204	364	27	x1	x1	NUM
ejpam-6204	364	28	.	.	PUNCT
ejpam-6204	365	1	the	the	DET
ejpam-6204	365	2	components	component	NOUN
ejpam-6204	365	3	of	of	ADP
ejpam-6204	365	4	the	the	DET
ejpam-6204	365	5	jacobi	jacobi	PROPN
ejpam-6204	365	6	endomorphism	endomorphism	PROPN
ejpam-6204	365	7	are	be	AUX
ejpam-6204	365	8	given	give	VERB
ejpam-6204	365	9	by	by	ADP
ejpam-6204	365	10	r1	r1	PROPN
ejpam-6204	365	11	1	1	NUM
ejpam-6204	365	12	=	=	SYM
ejpam-6204	365	13	−1	−1	NOUN
ejpam-6204	365	14	2	2	NUM
ejpam-6204	365	15	(	(	PUNCT
ejpam-6204	365	16	y2)2)2	y2)2)2	NOUN
ejpam-6204	365	17	(	(	PUNCT
ejpam-6204	365	18	x1)2	x1)2	PROPN
ejpam-6204	365	19	,	,	PUNCT
ejpam-6204	365	20	r1	r1	NOUN
ejpam-6204	365	21	2	2	NUM
ejpam-6204	365	22	=	=	SYM
ejpam-6204	365	23	1	1	NUM
ejpam-6204	365	24	2	2	NUM
ejpam-6204	365	25	y1y2)2	y1y2)2	NOUN
ejpam-6204	365	26	(	(	PUNCT
ejpam-6204	365	27	x1)2	x1)2	PROPN
ejpam-6204	365	28	,	,	PUNCT
ejpam-6204	365	29	r2	r2	PROPN
ejpam-6204	365	30	1	1	NUM
ejpam-6204	365	31	=	=	SYM
ejpam-6204	365	32	1	1	NUM
ejpam-6204	365	33	2	2	NUM
ejpam-6204	365	34	y1y2)2	y1y2)2	NOUN
ejpam-6204	365	35	(	(	PUNCT
ejpam-6204	365	36	x1)2	x1)2	PROPN
ejpam-6204	365	37	,	,	PUNCT
ejpam-6204	365	38	r2	r2	PROPN
ejpam-6204	365	39	2	2	NUM
ejpam-6204	365	40	=	=	SYM
ejpam-6204	365	41	−1	−1	NOUN
ejpam-6204	365	42	2	2	NUM
ejpam-6204	365	43	(	(	PUNCT
ejpam-6204	365	44	y1)2	y1)2	PROPN
ejpam-6204	365	45	(	(	PUNCT
ejpam-6204	365	46	x1)2	x1)2	PROPN
ejpam-6204	365	47	.	.	PUNCT
ejpam-6204	366	1	now	now	ADV
ejpam-6204	366	2	,	,	PUNCT
ejpam-6204	366	3	consider	consider	VERB
ejpam-6204	366	4	the	the	DET
ejpam-6204	366	5	conformal	conformal	ADJ
ejpam-6204	366	6	transformation	transformation	NOUN
ejpam-6204	366	7	f̃	f̃	PROPN
ejpam-6204	366	8	=	=	PUNCT
ejpam-6204	367	1	e−	e−	PROPN
ejpam-6204	367	2	1	1	NUM
ejpam-6204	367	3	2	2	NUM
ejpam-6204	367	4	(	(	PUNCT
ejpam-6204	367	5	(	(	PUNCT
ejpam-6204	367	6	x1)2−(x2)2+x1+x2))f	x1)2−(x2)2+x1+x2))f	PROPN
ejpam-6204	367	7	.	.	PUNCT
ejpam-6204	368	1	then	then	ADV
ejpam-6204	368	2	the	the	DET
ejpam-6204	368	3	spray	spray	NOUN
ejpam-6204	368	4	coefficients	coefficient	NOUN
ejpam-6204	368	5	of	of	ADP
ejpam-6204	368	6	f̃	f̃	PROPN
ejpam-6204	368	7	are	be	AUX
ejpam-6204	368	8	given	give	VERB
ejpam-6204	368	9	by	by	ADP
ejpam-6204	368	10	g̃1	g̃1	NOUN
ejpam-6204	368	11	=	=	SYM
ejpam-6204	368	12	g1	g1	PROPN
ejpam-6204	368	13	−	−	PROPN
ejpam-6204	368	14	1	1	NUM
ejpam-6204	368	15	4	4	NUM
ejpam-6204	368	16	2(x1)2(y1)2	2(x1)2(y1)2	NUM
ejpam-6204	368	17	−	−	PROPN
ejpam-6204	368	18	2(x1)2(y2)2	2(x1)2(y2)2	PROPN
ejpam-6204	368	19	−	−	PROPN
ejpam-6204	368	20	4x1x2y1y2	4x1x2y1y2	NUM
ejpam-6204	369	1	+	+	CCONJ
ejpam-6204	369	2	x1(y1)2	x1(y1)2	X
ejpam-6204	369	3	+	+	CCONJ
ejpam-6204	370	1	2x1y1y2	2x1y1y2	NUM
ejpam-6204	370	2	−	−	NOUN
ejpam-6204	370	3	x1(y2)2	x1(y2)2	NOUN
ejpam-6204	370	4	x1	x1	X
ejpam-6204	370	5	.	.	PUNCT
ejpam-6204	371	1	g̃2	g̃2	VERB
ejpam-6204	371	2	=	=	SYM
ejpam-6204	371	3	g2	g2	PROPN
ejpam-6204	371	4	−	−	NOUN
ejpam-6204	371	5	1	1	NUM
ejpam-6204	371	6	4	4	NUM
ejpam-6204	371	7	4(x1)2y1y2	4(x1)2y1y2	NUM
ejpam-6204	372	1	+	+	CCONJ
ejpam-6204	372	2	2x1x2(y1)2	2x1x2(y1)2	NUM
ejpam-6204	372	3	−	−	NOUN
ejpam-6204	372	4	2x1x2(y2)2	2x1x2(y2)2	NUM
ejpam-6204	372	5	−	−	NOUN
ejpam-6204	372	6	x1(y1)2	x1(y1)2	PROPN
ejpam-6204	373	1	+	+	CCONJ
ejpam-6204	373	2	2x1y1y2	2x1y1y2	NUM
ejpam-6204	373	3	+	+	NUM
ejpam-6204	373	4	x1(y2)2	x1(y2)2	NOUN
ejpam-6204	374	1	x1	x1	INTJ
ejpam-6204	374	2	.	.	PUNCT
ejpam-6204	375	1	we	we	PRON
ejpam-6204	375	2	can	can	AUX
ejpam-6204	375	3	write	write	VERB
ejpam-6204	375	4	s̃	s̃	PROPN
ejpam-6204	375	5	=	=	SYM
ejpam-6204	375	6	s	s	PART
ejpam-6204	375	7	−	−	PROPN
ejpam-6204	375	8	2pξ	2pξ	NOUN
ejpam-6204	375	9	=	=	PUNCT
ejpam-6204	375	10	s	s	PART
ejpam-6204	375	11	−	−	NOUN
ejpam-6204	375	12	2ζ	2ζ	NOUN
ejpam-6204	375	13	,	,	PUNCT
ejpam-6204	375	14	then	then	ADV
ejpam-6204	375	15	the	the	DET
ejpam-6204	375	16	coefficients	coefficient	NOUN
ejpam-6204	375	17	g̃i	g̃i	ADV
ejpam-6204	375	18	as	as	SCONJ
ejpam-6204	375	19	follows	follow	VERB
ejpam-6204	375	20	:	:	PUNCT
ejpam-6204	375	21	g̃1	g̃1	NOUN
ejpam-6204	375	22	=	=	PUNCT
ejpam-6204	375	23	g1	g1	PROPN
ejpam-6204	375	24	+	+	CCONJ
ejpam-6204	375	25	ζ1	ζ1	NOUN
ejpam-6204	375	26	,	,	PUNCT
ejpam-6204	375	27	g̃2	g̃2	PROPN
ejpam-6204	375	28	=	=	SYM
ejpam-6204	375	29	g2	g2	PROPN
ejpam-6204	375	30	+	+	CCONJ
ejpam-6204	375	31	ζ2	ζ2	NOUN
ejpam-6204	375	32	.	.	PUNCT
ejpam-6204	376	1	hence	hence	ADV
ejpam-6204	376	2	the	the	DET
ejpam-6204	376	3	vector	vector	NOUN
ejpam-6204	376	4	ζ	ζ	NOUN
ejpam-6204	376	5	is	be	AUX
ejpam-6204	376	6	given	give	VERB
ejpam-6204	376	7	by	by	ADP
ejpam-6204	376	8	ζ	ζ	NOUN
ejpam-6204	376	9	=	=	SYM
ejpam-6204	376	10	ζ1∂̇1	ζ1∂̇1	PROPN
ejpam-6204	376	11	+	+	CCONJ
ejpam-6204	376	12	ζ2∂̇2	ζ2∂̇2	PROPN
ejpam-6204	376	13	where	where	SCONJ
ejpam-6204	376	14	ζ1	ζ1	NOUN
ejpam-6204	376	15	=	=	NOUN
ejpam-6204	376	16	−1	−1	NOUN
ejpam-6204	376	17	4	4	NUM
ejpam-6204	376	18	2(x1)2(y1)2	2(x1)2(y1)2	NUM
ejpam-6204	376	19	−	−	PROPN
ejpam-6204	376	20	2(x1)2(y2)2	2(x1)2(y2)2	PROPN
ejpam-6204	376	21	−	−	PROPN
ejpam-6204	376	22	4x1x2y1y2	4x1x2y1y2	NUM
ejpam-6204	376	23	+	+	CCONJ
ejpam-6204	377	1	x1(y1)2	x1(y1)2	X
ejpam-6204	378	1	+	+	CCONJ
ejpam-6204	379	1	2x1y1y2	2x1y1y2	NUM
ejpam-6204	379	2	−	−	NOUN
ejpam-6204	379	3	x1(y2)2	x1(y2)2	NOUN
ejpam-6204	379	4	x1	x1	ADJ
ejpam-6204	379	5	ζ2	ζ2	NOUN
ejpam-6204	379	6	=	=	SYM
ejpam-6204	379	7	−1	−1	NOUN
ejpam-6204	379	8	4	4	NUM
ejpam-6204	379	9	4(x1)2y1y2	4(x1)2y1y2	NUM
ejpam-6204	380	1	+	+	CCONJ
ejpam-6204	380	2	2x1x2(y1)2	2x1x2(y1)2	NUM
ejpam-6204	380	3	−	−	NOUN
ejpam-6204	380	4	2x1x2(y2)2	2x1x2(y2)2	NUM
ejpam-6204	380	5	−	−	NOUN
ejpam-6204	380	6	x1(y1)2	x1(y1)2	PROPN
ejpam-6204	381	1	+	+	CCONJ
ejpam-6204	381	2	2x1y1y2	2x1y1y2	NUM
ejpam-6204	381	3	+	+	NUM
ejpam-6204	381	4	x1(y2)2	x1(y2)2	NOUN
ejpam-6204	381	5	x1	x1	PROPN
ejpam-6204	381	6	s.	s.	PROPN
ejpam-6204	381	7	g.	g.	PROPN
ejpam-6204	381	8	elgendi	elgendi	PROPN
ejpam-6204	381	9	,	,	PUNCT
ejpam-6204	381	10	a.	a.	NOUN
ejpam-6204	381	11	soleiman	soleiman	PROPN
ejpam-6204	381	12	/	/	SYM
ejpam-6204	381	13	eur	eur	PROPN
ejpam-6204	381	14	.	.	PUNCT
ejpam-6204	382	1	j.	j.	PROPN
ejpam-6204	382	2	pure	pure	PROPN
ejpam-6204	382	3	appl	appl	PROPN
ejpam-6204	382	4	.	.	PROPN
ejpam-6204	382	5	math	math	PROPN
ejpam-6204	382	6	,	,	PUNCT
ejpam-6204	382	7	18	18	NUM
ejpam-6204	382	8	(	(	PUNCT
ejpam-6204	382	9	3	3	NUM
ejpam-6204	382	10	)	)	PUNCT
ejpam-6204	382	11	(	(	PUNCT
ejpam-6204	382	12	2025	2025	NUM
ejpam-6204	382	13	)	)	PUNCT
ejpam-6204	382	14	,	,	PUNCT
ejpam-6204	382	15	6204	6204	NUM
ejpam-6204	382	16	16	16	NUM
ejpam-6204	382	17	of	of	ADP
ejpam-6204	382	18	18	18	NUM
ejpam-6204	382	19	the	the	DET
ejpam-6204	382	20	components	component	NOUN
ejpam-6204	382	21	of	of	ADP
ejpam-6204	382	22	ri	ri	PROPN
ejpam-6204	382	23	j	j	PROPN
ejpam-6204	382	24	of	of	ADP
ejpam-6204	382	25	the	the	DET
ejpam-6204	382	26	jacobi	jacobi	PROPN
ejpam-6204	382	27	endomorphism	endomorphism	PROPN
ejpam-6204	382	28	are	be	AUX
ejpam-6204	382	29	equal	equal	ADJ
ejpam-6204	382	30	since	since	SCONJ
ejpam-6204	382	31	the	the	DET
ejpam-6204	382	32	jacobi	jacobi	PROPN
ejpam-6204	382	33	endomorphism	endomorphism	PROPN
ejpam-6204	382	34	is	be	AUX
ejpam-6204	382	35	preserved	preserve	VERB
ejpam-6204	382	36	under	under	ADP
ejpam-6204	382	37	this	this	DET
ejpam-6204	382	38	transformation	transformation	NOUN
ejpam-6204	382	39	,	,	PUNCT
ejpam-6204	382	40	moreover	moreover	ADV
ejpam-6204	382	41	the	the	DET
ejpam-6204	382	42	components	component	NOUN
ejpam-6204	382	43	of	of	ADP
ejpam-6204	382	44	r̃i	r̃i	NOUN
ejpam-6204	382	45	j	j	PROPN
ejpam-6204	382	46	are	be	AUX
ejpam-6204	382	47	given	give	VERB
ejpam-6204	382	48	by	by	ADP
ejpam-6204	382	49	r̃1	r̃1	PROPN
ejpam-6204	382	50	1	1	NUM
ejpam-6204	382	51	=	=	SYM
ejpam-6204	382	52	r1	r1	NOUN
ejpam-6204	382	53	1	1	NUM
ejpam-6204	382	54	=	=	SYM
ejpam-6204	382	55	1	1	NUM
ejpam-6204	382	56	2	2	NUM
ejpam-6204	382	57	(	(	PUNCT
ejpam-6204	382	58	y2)2	y2)2	X
ejpam-6204	382	59	(	(	PUNCT
ejpam-6204	382	60	x1)2	x1)2	PROPN
ejpam-6204	382	61	,	,	PUNCT
ejpam-6204	382	62	r̃1	r̃1	NOUN
ejpam-6204	382	63	2	2	NUM
ejpam-6204	382	64	=	=	SYM
ejpam-6204	382	65	r1	r1	NOUN
ejpam-6204	382	66	2	2	NUM
ejpam-6204	382	67	=	=	SYM
ejpam-6204	382	68	−1	−1	NOUN
ejpam-6204	382	69	2	2	NUM
ejpam-6204	382	70	y1y2	y1y2	PROPN
ejpam-6204	382	71	(	(	PUNCT
ejpam-6204	382	72	x1)2	x1)2	PROPN
ejpam-6204	382	73	,	,	PUNCT
ejpam-6204	382	74	r̃1	r̃1	NOUN
ejpam-6204	382	75	2	2	NUM
ejpam-6204	382	76	=	=	SYM
ejpam-6204	382	77	r2	r2	NOUN
ejpam-6204	382	78	1	1	NUM
ejpam-6204	382	79	=	=	SYM
ejpam-6204	382	80	−1	−1	NOUN
ejpam-6204	382	81	2	2	NUM
ejpam-6204	382	82	y1y2	y1y2	PROPN
ejpam-6204	382	83	(	(	PUNCT
ejpam-6204	382	84	x1)2	x1)2	PROPN
ejpam-6204	382	85	,	,	PUNCT
ejpam-6204	382	86	r̃1	r̃1	NOUN
ejpam-6204	382	87	2	2	NUM
ejpam-6204	382	88	=	=	SYM
ejpam-6204	382	89	r2	r2	NOUN
ejpam-6204	382	90	2	2	NUM
ejpam-6204	382	91	=	=	SYM
ejpam-6204	382	92	1	1	NUM
ejpam-6204	382	93	2	2	NUM
ejpam-6204	382	94	(	(	PUNCT
ejpam-6204	382	95	y1)2	y1)2	PROPN
ejpam-6204	382	96	(	(	PUNCT
ejpam-6204	382	97	x1)2	x1)2	PROPN
ejpam-6204	382	98	.	.	PUNCT
ejpam-6204	383	1	the	the	DET
ejpam-6204	383	2	components	component	NOUN
ejpam-6204	383	3	of	of	ADP
ejpam-6204	383	4	ri	ri	PROPN
ejpam-6204	383	5	jk	jk	PROPN
ejpam-6204	383	6	of	of	ADP
ejpam-6204	383	7	the	the	DET
ejpam-6204	383	8	curvature	curvature	NOUN
ejpam-6204	383	9	is	be	AUX
ejpam-6204	383	10	preserved	preserve	VERB
ejpam-6204	383	11	under	under	ADP
ejpam-6204	383	12	this	this	DET
ejpam-6204	383	13	transformation	transformation	NOUN
ejpam-6204	383	14	,	,	PUNCT
ejpam-6204	383	15	moreover	moreover	ADV
ejpam-6204	383	16	the	the	DET
ejpam-6204	383	17	components	component	NOUN
ejpam-6204	383	18	of	of	ADP
ejpam-6204	383	19	r̃i	r̃i	NOUN
ejpam-6204	383	20	jk	jk	PROPN
ejpam-6204	383	21	are	be	AUX
ejpam-6204	383	22	given	give	VERB
ejpam-6204	383	23	by	by	ADP
ejpam-6204	383	24	r̃1	r̃1	PROPN
ejpam-6204	383	25	12	12	NUM
ejpam-6204	383	26	=	=	SYM
ejpam-6204	383	27	r1	r1	NOUN
ejpam-6204	383	28	12	12	NUM
ejpam-6204	383	29	=	=	SYM
ejpam-6204	383	30	−1	−1	NOUN
ejpam-6204	383	31	2	2	NUM
ejpam-6204	383	32	y2	y2	NOUN
ejpam-6204	383	33	(	(	PUNCT
ejpam-6204	383	34	x1)2	x1)2	PROPN
ejpam-6204	383	35	,	,	PUNCT
ejpam-6204	383	36	r̃1	r̃1	PROPN
ejpam-6204	383	37	21	21	NUM
ejpam-6204	383	38	=	=	SYM
ejpam-6204	383	39	r1	r1	NOUN
ejpam-6204	383	40	21	21	NUM
ejpam-6204	383	41	=	=	SYM
ejpam-6204	383	42	1	1	NUM
ejpam-6204	383	43	2	2	NUM
ejpam-6204	383	44	y2	y2	NOUN
ejpam-6204	383	45	(	(	PUNCT
ejpam-6204	383	46	x1)2	x1)2	PROPN
ejpam-6204	383	47	,	,	PUNCT
ejpam-6204	383	48	r̃2	r̃2	PROPN
ejpam-6204	383	49	12	12	NUM
ejpam-6204	383	50	=	=	SYM
ejpam-6204	383	51	r2	r2	NOUN
ejpam-6204	383	52	12	12	NUM
ejpam-6204	383	53	=	=	SYM
ejpam-6204	383	54	1	1	NUM
ejpam-6204	383	55	2	2	NUM
ejpam-6204	383	56	y1	y1	NOUN
ejpam-6204	383	57	(	(	PUNCT
ejpam-6204	383	58	x1)2	x1)2	PROPN
ejpam-6204	383	59	,	,	PUNCT
ejpam-6204	383	60	r̃2	r̃2	PROPN
ejpam-6204	383	61	21	21	NUM
ejpam-6204	383	62	=	=	SYM
ejpam-6204	383	63	r2	r2	PROPN
ejpam-6204	383	64	21	21	NUM
ejpam-6204	383	65	=	=	SYM
ejpam-6204	383	66	−1	−1	NOUN
ejpam-6204	383	67	2	2	NUM
ejpam-6204	383	68	y1	y1	NOUN
ejpam-6204	383	69	(	(	PUNCT
ejpam-6204	383	70	x1)2	x1)2	NUM
ejpam-6204	383	71	.	.	PUNCT
ejpam-6204	384	1	example	example	NOUN
ejpam-6204	385	1	3	3	X
ejpam-6204	385	2	.	.	X
ejpam-6204	385	3	consider	consider	VERB
ejpam-6204	385	4	m	m	NOUN
ejpam-6204	385	5	=	=	VERB
ejpam-6204	385	6	r3	r3	PROPN
ejpam-6204	385	7	with	with	ADP
ejpam-6204	385	8	the	the	DET
ejpam-6204	385	9	finsler	finsler	NOUN
ejpam-6204	385	10	function	function	NOUN
ejpam-6204	385	11	f	f	PROPN
ejpam-6204	385	12	f	f	PROPN
ejpam-6204	385	13	=	=	SYM
ejpam-6204	385	14	4	4	NUM
ejpam-6204	385	15	√	√	NUM
ejpam-6204	385	16	(	(	PUNCT
ejpam-6204	385	17	y1)4	y1)4	PROPN
ejpam-6204	385	18	+	+	CCONJ
ejpam-6204	385	19	(	(	PUNCT
ejpam-6204	385	20	y2)4	y2)4	INTJ
ejpam-6204	385	21	+	+	CCONJ
ejpam-6204	385	22	(	(	PUNCT
ejpam-6204	385	23	y3)4	y3)4	NOUN
ejpam-6204	385	24	,	,	PUNCT
ejpam-6204	385	25	where	where	SCONJ
ejpam-6204	385	26	(	(	PUNCT
ejpam-6204	385	27	x1	x1	ADJ
ejpam-6204	385	28	,	,	PUNCT
ejpam-6204	385	29	x2	x2	PROPN
ejpam-6204	385	30	,	,	PUNCT
ejpam-6204	385	31	x3	x3	ADJ
ejpam-6204	385	32	;	;	PUNCT
ejpam-6204	385	33	y1	y1	NOUN
ejpam-6204	385	34	,	,	PUNCT
ejpam-6204	385	35	y2	y2	PROPN
ejpam-6204	385	36	,	,	PUNCT
ejpam-6204	385	37	y3	y3	PROPN
ejpam-6204	385	38	)	)	PUNCT
ejpam-6204	385	39	∈	∈	PROPN
ejpam-6204	385	40	tr3	tr3	NOUN
ejpam-6204	385	41	=	=	PROPN
ejpam-6204	385	42	r6	r6	PROPN
ejpam-6204	385	43	.	.	PUNCT
ejpam-6204	386	1	the	the	DET
ejpam-6204	386	2	coefficients	coefficient	NOUN
ejpam-6204	386	3	gi	gi	INTJ
ejpam-6204	386	4	of	of	ADP
ejpam-6204	386	5	the	the	DET
ejpam-6204	386	6	geodesic	geodesic	ADJ
ejpam-6204	386	7	spray	spray	NOUN
ejpam-6204	386	8	are	be	AUX
ejpam-6204	386	9	given	give	VERB
ejpam-6204	386	10	by	by	ADP
ejpam-6204	386	11	gi	gi	NOUN
ejpam-6204	386	12	=	=	SYM
ejpam-6204	386	13	0	0	X
ejpam-6204	386	14	.	.	PUNCT
ejpam-6204	387	1	the	the	DET
ejpam-6204	387	2	components	component	NOUN
ejpam-6204	387	3	of	of	ADP
ejpam-6204	387	4	the	the	DET
ejpam-6204	387	5	jacobi	jacobi	PROPN
ejpam-6204	387	6	endomorphism	endomorphism	PROPN
ejpam-6204	387	7	are	be	AUX
ejpam-6204	387	8	given	give	VERB
ejpam-6204	387	9	by	by	ADP
ejpam-6204	387	10	ri	ri	PROPN
ejpam-6204	387	11	j	j	PROPN
ejpam-6204	387	12	=	=	SYM
ejpam-6204	387	13	0	0	PROPN
ejpam-6204	387	14	,	,	PUNCT
ejpam-6204	387	15	ri	ri	PROPN
ejpam-6204	387	16	jk	jk	PROPN
ejpam-6204	387	17	=	=	PUNCT
ejpam-6204	388	1	0	0	X
ejpam-6204	388	2	.	.	PUNCT
ejpam-6204	389	1	now	now	ADV
ejpam-6204	389	2	,	,	PUNCT
ejpam-6204	389	3	consider	consider	VERB
ejpam-6204	389	4	the	the	DET
ejpam-6204	389	5	deformation	deformation	NOUN
ejpam-6204	389	6	of	of	ADP
ejpam-6204	389	7	f	f	PROPN
ejpam-6204	389	8	as	as	SCONJ
ejpam-6204	389	9	follows	follow	VERB
ejpam-6204	389	10	f̃	f̃	PROPN
ejpam-6204	389	11	=	=	PUNCT
ejpam-6204	389	12	4	4	NUM
ejpam-6204	389	13	√	√	NUM
ejpam-6204	389	14	f1(x1)(y1)4	f1(x1)(y1)4	PROPN
ejpam-6204	390	1	+	+	CCONJ
ejpam-6204	390	2	f2(x2)(y2)4	f2(x2)(y2)4	PUNCT
ejpam-6204	390	3	+	+	NUM
ejpam-6204	390	4	f3(x3)(y3)4	f3(x3)(y3)4	X
ejpam-6204	390	5	.	.	PUNCT
ejpam-6204	390	6	then	then	ADV
ejpam-6204	390	7	the	the	DET
ejpam-6204	390	8	spray	spray	NOUN
ejpam-6204	390	9	coefficients	coefficient	NOUN
ejpam-6204	390	10	of	of	ADP
ejpam-6204	390	11	f̃	f̃	PROPN
ejpam-6204	390	12	are	be	AUX
ejpam-6204	390	13	given	give	VERB
ejpam-6204	390	14	by	by	ADP
ejpam-6204	390	15	g̃1	g̃1	NOUN
ejpam-6204	390	16	=	=	PUNCT
ejpam-6204	390	17	(	(	PUNCT
ejpam-6204	390	18	y1)2	y1)2	PROPN
ejpam-6204	390	19	8f1(x1	8f1(x1	NUM
ejpam-6204	390	20	)	)	PUNCT
ejpam-6204	390	21	df1(x	df1(x	PROPN
ejpam-6204	390	22	1	1	NUM
ejpam-6204	390	23	)	)	PUNCT
ejpam-6204	390	24	dx1	dx1	PROPN
ejpam-6204	390	25	,	,	PUNCT
ejpam-6204	390	26	g̃2	g̃2	PROPN
ejpam-6204	390	27	=	=	SYM
ejpam-6204	390	28	(	(	PUNCT
ejpam-6204	390	29	y2)2	y2)2	NOUN
ejpam-6204	390	30	8f2(x2	8f2(x2	NUM
ejpam-6204	390	31	)	)	PUNCT
ejpam-6204	390	32	df2(x	df2(x	PROPN
ejpam-6204	390	33	2	2	X
ejpam-6204	390	34	)	)	PUNCT
ejpam-6204	390	35	dx2	dx2	NOUN
ejpam-6204	390	36	,	,	PUNCT
ejpam-6204	390	37	g̃3	g̃3	PROPN
ejpam-6204	390	38	=	=	SYM
ejpam-6204	390	39	(	(	PUNCT
ejpam-6204	390	40	y3)2	y3)2	PROPN
ejpam-6204	390	41	8f3(x3	8f3(x3	NUM
ejpam-6204	390	42	)	)	PUNCT
ejpam-6204	390	43	df3(x	df3(x	PROPN
ejpam-6204	390	44	3	3	NUM
ejpam-6204	390	45	)	)	PUNCT
ejpam-6204	390	46	dx3	dx3	PROPN
ejpam-6204	390	47	.	.	PUNCT
ejpam-6204	391	1	consider	consider	VERB
ejpam-6204	391	2	s̃	s̃	PROPN
ejpam-6204	391	3	=	=	SYM
ejpam-6204	391	4	s	s	PART
ejpam-6204	391	5	−	−	PROPN
ejpam-6204	391	6	2pξ	2pξ	NOUN
ejpam-6204	391	7	=	=	PUNCT
ejpam-6204	391	8	s	s	PART
ejpam-6204	391	9	−	−	NOUN
ejpam-6204	391	10	2ζ	2ζ	NOUN
ejpam-6204	391	11	,	,	PUNCT
ejpam-6204	391	12	then	then	ADV
ejpam-6204	391	13	the	the	DET
ejpam-6204	391	14	coefficients	coefficient	NOUN
ejpam-6204	391	15	g̃i	g̃i	ADV
ejpam-6204	391	16	as	as	SCONJ
ejpam-6204	391	17	follows	follow	VERB
ejpam-6204	391	18	:	:	PUNCT
ejpam-6204	391	19	g̃1	g̃1	NOUN
ejpam-6204	391	20	=	=	PUNCT
ejpam-6204	391	21	g1	g1	PROPN
ejpam-6204	391	22	+	+	CCONJ
ejpam-6204	391	23	ζ1	ζ1	NOUN
ejpam-6204	391	24	,	,	PUNCT
ejpam-6204	391	25	g̃2	g̃2	PROPN
ejpam-6204	391	26	=	=	SYM
ejpam-6204	391	27	g2	g2	PROPN
ejpam-6204	391	28	+	+	CCONJ
ejpam-6204	391	29	ζ2	ζ2	NOUN
ejpam-6204	391	30	,	,	PUNCT
ejpam-6204	391	31	g̃3	g̃3	NOUN
ejpam-6204	391	32	=	=	SYM
ejpam-6204	391	33	g3	g3	PROPN
ejpam-6204	391	34	+	+	NUM
ejpam-6204	391	35	ζ3	ζ3	NOUN
ejpam-6204	391	36	.	.	PUNCT
ejpam-6204	392	1	hence	hence	ADV
ejpam-6204	392	2	the	the	DET
ejpam-6204	392	3	vector	vector	NOUN
ejpam-6204	392	4	ζ	ζ	NOUN
ejpam-6204	392	5	is	be	AUX
ejpam-6204	392	6	given	give	VERB
ejpam-6204	392	7	by	by	ADP
ejpam-6204	392	8	ζ	ζ	NOUN
ejpam-6204	392	9	=	=	SYM
ejpam-6204	392	10	ζ1∂̇1	ζ1∂̇1	PROPN
ejpam-6204	392	11	+	+	CCONJ
ejpam-6204	392	12	ζ2∂̇2	ζ2∂̇2	PROPN
ejpam-6204	392	13	+	+	PUNCT
ejpam-6204	393	1	ζ3∂̇3	ζ3∂̇3	PROPN
ejpam-6204	393	2	where	where	SCONJ
ejpam-6204	393	3	ζ1	ζ1	NOUN
ejpam-6204	393	4	=	=	SYM
ejpam-6204	393	5	(	(	PUNCT
ejpam-6204	393	6	y1)2	y1)2	PROPN
ejpam-6204	393	7	8f1(x1	8f1(x1	NUM
ejpam-6204	393	8	)	)	PUNCT
ejpam-6204	393	9	df1(x	df1(x	PROPN
ejpam-6204	393	10	1	1	NUM
ejpam-6204	393	11	)	)	PUNCT
ejpam-6204	393	12	dx1	dx1	PROPN
ejpam-6204	393	13	,	,	PUNCT
ejpam-6204	393	14	ζ2	ζ2	NOUN
ejpam-6204	393	15	=	=	SYM
ejpam-6204	393	16	(	(	PUNCT
ejpam-6204	393	17	y2)2	y2)2	NOUN
ejpam-6204	393	18	8f2(x2	8f2(x2	NUM
ejpam-6204	393	19	)	)	PUNCT
ejpam-6204	393	20	df2(x	df2(x	PROPN
ejpam-6204	393	21	2	2	X
ejpam-6204	393	22	)	)	PUNCT
ejpam-6204	393	23	dx2	dx2	NOUN
ejpam-6204	393	24	,	,	PUNCT
ejpam-6204	393	25	ζ3	ζ3	NOUN
ejpam-6204	393	26	=	=	SYM
ejpam-6204	393	27	(	(	PUNCT
ejpam-6204	393	28	y3)2	y3)2	PROPN
ejpam-6204	393	29	8f3(x3	8f3(x3	NUM
ejpam-6204	393	30	)	)	PUNCT
ejpam-6204	393	31	df3(x	df3(x	PROPN
ejpam-6204	393	32	3	3	NUM
ejpam-6204	393	33	)	)	PUNCT
ejpam-6204	393	34	dx3	dx3	PROPN
ejpam-6204	393	35	.	.	PUNCT
ejpam-6204	394	1	the	the	DET
ejpam-6204	394	2	components	component	NOUN
ejpam-6204	394	3	of	of	ADP
ejpam-6204	394	4	ri	ri	PROPN
ejpam-6204	394	5	j	j	PROPN
ejpam-6204	394	6	of	of	ADP
ejpam-6204	394	7	the	the	DET
ejpam-6204	394	8	jacobi	jacobi	PROPN
ejpam-6204	394	9	endomorphism	endomorphism	PROPN
ejpam-6204	394	10	are	be	AUX
ejpam-6204	394	11	equal	equal	ADJ
ejpam-6204	394	12	since	since	SCONJ
ejpam-6204	394	13	the	the	DET
ejpam-6204	394	14	jacobi	jacobi	PROPN
ejpam-6204	394	15	endomorphism	endomorphism	PROPN
ejpam-6204	394	16	is	be	AUX
ejpam-6204	394	17	preserved	preserve	VERB
ejpam-6204	394	18	under	under	ADP
ejpam-6204	394	19	this	this	DET
ejpam-6204	394	20	transformation	transformation	NOUN
ejpam-6204	394	21	.	.	PUNCT
ejpam-6204	395	1	that	that	PRON
ejpam-6204	395	2	is	is	ADV
ejpam-6204	395	3	,	,	PUNCT
ejpam-6204	395	4	we	we	PRON
ejpam-6204	395	5	have	have	VERB
ejpam-6204	395	6	r̃i	r̃i	NOUN
ejpam-6204	395	7	j	j	PROPN
ejpam-6204	395	8	=	=	SYM
ejpam-6204	395	9	ri	ri	PROPN
ejpam-6204	395	10	j	j	PROPN
ejpam-6204	395	11	=	=	SYM
ejpam-6204	395	12	0	0	PROPN
ejpam-6204	395	13	,	,	PUNCT
ejpam-6204	395	14	r̃i	r̃i	ADP
ejpam-6204	395	15	jk	jk	NOUN
ejpam-6204	395	16	=	=	SYM
ejpam-6204	395	17	ri	ri	PROPN
ejpam-6204	395	18	jk	jk	PROPN
ejpam-6204	395	19	=	=	PUNCT
ejpam-6204	395	20	0	0	PROPN
ejpam-6204	395	21	.	.	PUNCT
ejpam-6204	396	1	s.	s.	PROPN
ejpam-6204	396	2	g.	g.	PROPN
ejpam-6204	396	3	elgendi	elgendi	PROPN
ejpam-6204	396	4	,	,	PUNCT
ejpam-6204	396	5	a.	a.	NOUN
ejpam-6204	396	6	soleiman	soleiman	PROPN
ejpam-6204	396	7	/	/	SYM
ejpam-6204	396	8	eur	eur	PROPN
ejpam-6204	396	9	.	.	PUNCT
ejpam-6204	397	1	j.	j.	PROPN
ejpam-6204	397	2	pure	pure	PROPN
ejpam-6204	397	3	appl	appl	PROPN
ejpam-6204	397	4	.	.	PROPN
ejpam-6204	397	5	math	math	PROPN
ejpam-6204	397	6	,	,	PUNCT
ejpam-6204	397	7	18	18	NUM
ejpam-6204	397	8	(	(	PUNCT
ejpam-6204	397	9	3	3	NUM
ejpam-6204	397	10	)	)	PUNCT
ejpam-6204	397	11	(	(	PUNCT
ejpam-6204	397	12	2025	2025	NUM
ejpam-6204	397	13	)	)	PUNCT
ejpam-6204	397	14	,	,	PUNCT
ejpam-6204	397	15	6204	6204	NUM
ejpam-6204	397	16	17	17	NUM
ejpam-6204	397	17	of	of	ADP
ejpam-6204	397	18	18	18	NUM
ejpam-6204	397	19	acknowledgements	acknowledgement	NOUN
ejpam-6204	397	20	the	the	DET
ejpam-6204	397	21	authors	author	NOUN
ejpam-6204	397	22	sincerely	sincerely	ADV
ejpam-6204	397	23	thank	thank	VERB
ejpam-6204	397	24	the	the	DET
ejpam-6204	397	25	referee	referee	NOUN
ejpam-6204	397	26	for	for	ADP
ejpam-6204	397	27	their	their	PRON
ejpam-6204	397	28	constructive	constructive	ADJ
ejpam-6204	397	29	comments	comment	NOUN
ejpam-6204	397	30	and	and	CCONJ
ejpam-6204	397	31	helpful	helpful	ADJ
ejpam-6204	397	32	suggestions	suggestion	NOUN
ejpam-6204	397	33	,	,	PUNCT
ejpam-6204	397	34	which	which	PRON
ejpam-6204	397	35	have	have	AUX
ejpam-6204	397	36	enhanced	enhance	VERB
ejpam-6204	397	37	the	the	DET
ejpam-6204	397	38	quality	quality	NOUN
ejpam-6204	397	39	of	of	ADP
ejpam-6204	397	40	the	the	DET
ejpam-6204	397	41	paper	paper	NOUN
ejpam-6204	397	42	.	.	PUNCT
ejpam-6204	398	1	references	reference	NOUN
ejpam-6204	398	2	[	[	X
ejpam-6204	398	3	1	1	NUM
ejpam-6204	398	4	]	]	PUNCT
ejpam-6204	398	5	p.	p.	PROPN
ejpam-6204	398	6	l.	l.	PROPN
ejpam-6204	398	7	antonelli	antonelli	PROPN
ejpam-6204	398	8	,	,	PUNCT
ejpam-6204	398	9	r.	r.	PROPN
ejpam-6204	398	10	ingarden	ingarden	PROPN
ejpam-6204	398	11	,	,	PUNCT
ejpam-6204	398	12	and	and	CCONJ
ejpam-6204	398	13	m.	m.	PROPN
ejpam-6204	398	14	matsumoto	matsumoto	PROPN
ejpam-6204	398	15	.	.	PUNCT
ejpam-6204	399	1	the	the	DET
ejpam-6204	399	2	theory	theory	NOUN
ejpam-6204	399	3	of	of	ADP
ejpam-6204	399	4	sprays	spray	NOUN
ejpam-6204	399	5	and	and	CCONJ
ejpam-6204	399	6	finsler	finsler	NOUN
ejpam-6204	399	7	spaces	space	NOUN
ejpam-6204	399	8	with	with	ADP
ejpam-6204	399	9	applications	application	NOUN
ejpam-6204	399	10	in	in	ADP
ejpam-6204	399	11	physics	physics	NOUN
ejpam-6204	399	12	and	and	CCONJ
ejpam-6204	399	13	biology	biology	NOUN
ejpam-6204	399	14	.	.	PUNCT
ejpam-6204	400	1	kluwer	kluwer	NOUN
ejpam-6204	400	2	academic	academic	ADJ
ejpam-6204	400	3	publishers	publisher	NOUN
ejpam-6204	400	4	,	,	PUNCT
ejpam-6204	400	5	netherlands	netherlands	PROPN
ejpam-6204	400	6	,	,	PUNCT
ejpam-6204	400	7	1993	1993	NUM
ejpam-6204	400	8	.	.	PUNCT
ejpam-6204	401	1	[	[	X
ejpam-6204	401	2	2	2	NUM
ejpam-6204	401	3	]	]	PUNCT
ejpam-6204	401	4	i.	i.	NOUN
ejpam-6204	401	5	bucataru	bucataru	PROPN
ejpam-6204	401	6	and	and	CCONJ
ejpam-6204	401	7	z.	z.	PROPN
ejpam-6204	401	8	muzsnay	muzsnay	PROPN
ejpam-6204	401	9	.	.	PROPN
ejpam-6204	402	1	projective	projective	PROPN
ejpam-6204	402	2	metrizability	metrizability	NOUN
ejpam-6204	402	3	and	and	CCONJ
ejpam-6204	402	4	formal	formal	ADJ
ejpam-6204	402	5	integrability	integrability	NOUN
ejpam-6204	402	6	.	.	PUNCT
ejpam-6204	403	1	sigma	sigma	PROPN
ejpam-6204	403	2	,	,	PUNCT
ejpam-6204	403	3	7	7	NUM
ejpam-6204	403	4	,	,	PUNCT
ejpam-6204	403	5	2011	2011	NUM
ejpam-6204	403	6	.	.	PUNCT
ejpam-6204	404	1	[	[	X
ejpam-6204	404	2	3	3	NUM
ejpam-6204	404	3	]	]	X
ejpam-6204	404	4	i.	i.	NOUN
ejpam-6204	404	5	bucataru	bucataru	PROPN
ejpam-6204	404	6	and	and	CCONJ
ejpam-6204	404	7	z.	z.	PROPN
ejpam-6204	404	8	muzsnay	muzsnay	PROPN
ejpam-6204	404	9	.	.	PROPN
ejpam-6204	405	1	projective	projective	PROPN
ejpam-6204	405	2	and	and	CCONJ
ejpam-6204	405	3	finsler	finsler	NOUN
ejpam-6204	405	4	metrizability	metrizability	NOUN
ejpam-6204	405	5	:	:	PUNCT
ejpam-6204	405	6	parameterizationrigidity	parameterizationrigidity	NOUN
ejpam-6204	405	7	of	of	ADP
ejpam-6204	405	8	the	the	DET
ejpam-6204	405	9	geodesics	geodesic	NOUN
ejpam-6204	405	10	.	.	PUNCT
ejpam-6204	406	1	int	int	NOUN
ejpam-6204	406	2	.	.	PUNCT
ejpam-6204	407	1	j.	j.	PROPN
ejpam-6204	407	2	math	math	PROPN
ejpam-6204	407	3	.	.	PROPN
ejpam-6204	407	4	,	,	PUNCT
ejpam-6204	407	5	23(9	23(9	NUM
ejpam-6204	407	6	)	)	PUNCT
ejpam-6204	407	7	,	,	PUNCT
ejpam-6204	407	8	2012	2012	NUM
ejpam-6204	407	9	.	.	PUNCT
ejpam-6204	408	1	[	[	X
ejpam-6204	408	2	4	4	X
ejpam-6204	408	3	]	]	PUNCT
ejpam-6204	408	4	s.	s.	PROPN
ejpam-6204	408	5	s.	s.	PROPN
ejpam-6204	408	6	chern	chern	PROPN
ejpam-6204	408	7	and	and	CCONJ
ejpam-6204	408	8	z.	z.	PROPN
ejpam-6204	408	9	shen	shen	PROPN
ejpam-6204	408	10	.	.	PUNCT
ejpam-6204	409	1	riemann	riemann	PROPN
ejpam-6204	409	2	-	-	PUNCT
ejpam-6204	409	3	finsler	finsler	NOUN
ejpam-6204	409	4	geometry	geometry	NOUN
ejpam-6204	409	5	.	.	PUNCT
ejpam-6204	410	1	world	world	NOUN
ejpam-6204	410	2	scientific	scientific	ADJ
ejpam-6204	410	3	publishers	publisher	NOUN
ejpam-6204	410	4	,	,	PUNCT
ejpam-6204	410	5	2004	2004	NUM
ejpam-6204	410	6	.	.	PUNCT
ejpam-6204	411	1	[	[	X
ejpam-6204	411	2	5	5	NUM
ejpam-6204	411	3	]	]	PUNCT
ejpam-6204	411	4	m.	m.	NOUN
ejpam-6204	411	5	crampin	crampin	NOUN
ejpam-6204	411	6	and	and	CCONJ
ejpam-6204	411	7	d.	d.	PROPN
ejpam-6204	411	8	j.	j.	PROPN
ejpam-6204	411	9	saunders	saunders	PROPN
ejpam-6204	411	10	.	.	PUNCT
ejpam-6204	412	1	affine	affine	PROPN
ejpam-6204	412	2	and	and	CCONJ
ejpam-6204	412	3	projective	projective	ADJ
ejpam-6204	412	4	transformations	transformation	NOUN
ejpam-6204	412	5	of	of	ADP
ejpam-6204	412	6	berwald	berwald	NOUN
ejpam-6204	412	7	connections	connection	NOUN
ejpam-6204	412	8	.	.	PUNCT
ejpam-6204	413	1	differ	differ	VERB
ejpam-6204	413	2	.	.	PUNCT
ejpam-6204	414	1	geom	geom	PROPN
ejpam-6204	414	2	.	.	PUNCT
ejpam-6204	415	1	appl	appl	PROPN
ejpam-6204	415	2	.	.	PROPN
ejpam-6204	415	3	,	,	PUNCT
ejpam-6204	416	1	25:235–250	25:235–250	NUM
ejpam-6204	416	2	,	,	PUNCT
ejpam-6204	416	3	2007	2007	NUM
ejpam-6204	416	4	.	.	PUNCT
ejpam-6204	417	1	[	[	X
ejpam-6204	417	2	6	6	NUM
ejpam-6204	417	3	]	]	PUNCT
ejpam-6204	417	4	s.	s.	PROPN
ejpam-6204	417	5	g.	g.	PROPN
ejpam-6204	417	6	elgendi	elgendi	PROPN
ejpam-6204	417	7	and	and	CCONJ
ejpam-6204	417	8	z.	z.	PROPN
ejpam-6204	417	9	muzsnay	muzsnay	PROPN
ejpam-6204	417	10	.	.	PUNCT
ejpam-6204	418	1	metrizability	metrizability	NOUN
ejpam-6204	418	2	of	of	ADP
ejpam-6204	418	3	1	1	NUM
ejpam-6204	418	4	-	-	PUNCT
ejpam-6204	418	5	form	form	NOUN
ejpam-6204	418	6	projective	projective	ADJ
ejpam-6204	418	7	deformation	deformation	NOUN
ejpam-6204	418	8	of	of	ADP
ejpam-6204	418	9	sprays	spray	NOUN
ejpam-6204	418	10	.	.	PUNCT
ejpam-6204	419	1	submitted	submit	VERB
ejpam-6204	419	2	,	,	PUNCT
ejpam-6204	419	3	2025	2025	NUM
ejpam-6204	419	4	.	.	PUNCT
ejpam-6204	420	1	[	[	X
ejpam-6204	420	2	7	7	NUM
ejpam-6204	420	3	]	]	X
ejpam-6204	420	4	m.	m.	NOUN
ejpam-6204	420	5	matsumoto	matsumoto	PROPN
ejpam-6204	420	6	.	.	PUNCT
ejpam-6204	421	1	projective	projective	ADJ
ejpam-6204	421	2	changes	change	NOUN
ejpam-6204	421	3	of	of	ADP
ejpam-6204	421	4	finsler	finsler	NOUN
ejpam-6204	421	5	metrics	metric	NOUN
ejpam-6204	421	6	and	and	CCONJ
ejpam-6204	421	7	projectively	projectively	ADV
ejpam-6204	421	8	flat	flat	ADJ
ejpam-6204	421	9	finsler	finsler	NOUN
ejpam-6204	421	10	spaces	space	NOUN
ejpam-6204	421	11	.	.	PUNCT
ejpam-6204	422	1	tensor	tensor	NOUN
ejpam-6204	422	2	,	,	PUNCT
ejpam-6204	422	3	n.	n.	PROPN
ejpam-6204	422	4	s.	s.	PROPN
ejpam-6204	422	5	,	,	PUNCT
ejpam-6204	422	6	34:303–315	34:303–315	PROPN
ejpam-6204	422	7	,	,	PUNCT
ejpam-6204	422	8	1980	1980	NUM
ejpam-6204	422	9	.	.	PUNCT
ejpam-6204	423	1	[	[	X
ejpam-6204	423	2	8	8	NUM
ejpam-6204	423	3	]	]	PUNCT
ejpam-6204	423	4	m.	m.	NOUN
ejpam-6204	423	5	matsumoto	matsumoto	PROPN
ejpam-6204	423	6	.	.	PUNCT
ejpam-6204	424	1	projectively	projectively	ADV
ejpam-6204	424	2	flat	flat	ADJ
ejpam-6204	424	3	finsler	finsler	NOUN
ejpam-6204	424	4	spaces	space	VERB
ejpam-6204	424	5	with	with	ADP
ejpam-6204	424	6	(	(	PUNCT
ejpam-6204	424	7	α	α	NOUN
ejpam-6204	424	8	,	,	PUNCT
ejpam-6204	424	9	β)-metric	β)-metric	PUNCT
ejpam-6204	424	10	.	.	PUNCT
ejpam-6204	425	1	rep	rep	PROPN
ejpam-6204	425	2	.	.	PROPN
ejpam-6204	425	3	math	math	PROPN
ejpam-6204	425	4	.	.	PUNCT
ejpam-6204	426	1	phys	phy	NOUN
ejpam-6204	426	2	.	.	PUNCT
ejpam-6204	426	3	,	,	PUNCT
ejpam-6204	426	4	30:15–20	30:15–20	NUM
ejpam-6204	426	5	,	,	PUNCT
ejpam-6204	426	6	1991	1991	NUM
ejpam-6204	426	7	.	.	PUNCT
ejpam-6204	427	1	[	[	X
ejpam-6204	427	2	9	9	NUM
ejpam-6204	427	3	]	]	PUNCT
ejpam-6204	427	4	z.	z.	PROPN
ejpam-6204	427	5	shen	shen	PROPN
ejpam-6204	427	6	.	.	PUNCT
ejpam-6204	427	7	differential	differential	ADJ
ejpam-6204	427	8	geometry	geometry	NOUN
ejpam-6204	427	9	of	of	ADP
ejpam-6204	427	10	spray	spray	NOUN
ejpam-6204	427	11	and	and	CCONJ
ejpam-6204	427	12	finsler	finsler	NOUN
ejpam-6204	427	13	spaces	space	NOUN
ejpam-6204	427	14	.	.	PUNCT
ejpam-6204	428	1	springer	springer	NOUN
ejpam-6204	428	2	,	,	PUNCT
ejpam-6204	428	3	2001	2001	NUM
ejpam-6204	428	4	.	.	PUNCT
ejpam-6204	429	1	[	[	X
ejpam-6204	429	2	10	10	NUM
ejpam-6204	429	3	]	]	X
ejpam-6204	429	4	j.	j.	PROPN
ejpam-6204	429	5	szilasi	szilasi	PROPN
ejpam-6204	429	6	and	and	CCONJ
ejpam-6204	429	7	sz	sz	NOUN
ejpam-6204	429	8	.	.	PUNCT
ejpam-6204	430	1	vattamány	vattamány	VERB
ejpam-6204	430	2	.	.	PUNCT
ejpam-6204	431	1	on	on	ADP
ejpam-6204	431	2	the	the	DET
ejpam-6204	431	3	projective	projective	ADJ
ejpam-6204	431	4	geometry	geometry	NOUN
ejpam-6204	431	5	of	of	ADP
ejpam-6204	431	6	sprays	spray	NOUN
ejpam-6204	431	7	.	.	PUNCT
ejpam-6204	432	1	differ	differ	VERB
ejpam-6204	432	2	.	.	PUNCT
ejpam-6204	433	1	geom	geom	PROPN
ejpam-6204	433	2	.	.	PUNCT
ejpam-6204	434	1	appl	appl	PROPN
ejpam-6204	434	2	.	.	PROPN
ejpam-6204	434	3	,	,	PUNCT
ejpam-6204	434	4	12:185–206	12:185–206	NUM
ejpam-6204	434	5	,	,	PUNCT
ejpam-6204	434	6	2000	2000	NUM
ejpam-6204	434	7	.	.	PUNCT
ejpam-6204	435	1	[	[	X
ejpam-6204	435	2	11	11	NUM
ejpam-6204	435	3	]	]	X
ejpam-6204	435	4	g.	g.	PROPN
ejpam-6204	435	5	yang	yang	PROPN
ejpam-6204	435	6	.	.	PUNCT
ejpam-6204	436	1	some	some	DET
ejpam-6204	436	2	classes	class	NOUN
ejpam-6204	436	3	of	of	ADP
ejpam-6204	436	4	sprays	spray	NOUN
ejpam-6204	436	5	in	in	ADP
ejpam-6204	436	6	projective	projective	ADJ
ejpam-6204	436	7	spray	spray	NOUN
ejpam-6204	436	8	geometry	geometry	NOUN
ejpam-6204	436	9	.	.	PUNCT
ejpam-6204	437	1	diff	diff	PROPN
ejpam-6204	437	2	.	.	PUNCT
ejpam-6204	438	1	geom	geom	PROPN
ejpam-6204	438	2	.	.	PUNCT
ejpam-6204	439	1	appl	appl	PROPN
ejpam-6204	439	2	.	.	PROPN
ejpam-6204	439	3	,	,	PUNCT
ejpam-6204	440	1	29:606–614	29:606–614	NUM
ejpam-6204	440	2	,	,	PUNCT
ejpam-6204	440	3	2011	2011	NUM
ejpam-6204	440	4	.	.	PUNCT
ejpam-6204	441	1	[	[	X
ejpam-6204	441	2	12	12	NUM
ejpam-6204	441	3	]	]	PUNCT
ejpam-6204	441	4	t.	t.	PROPN
ejpam-6204	441	5	yamada	yamada	PROPN
ejpam-6204	441	6	.	.	PUNCT
ejpam-6204	442	1	on	on	ADP
ejpam-6204	442	2	projective	projective	ADJ
ejpam-6204	442	3	changes	change	NOUN
ejpam-6204	442	4	in	in	ADP
ejpam-6204	442	5	finsler	finsler	NOUN
ejpam-6204	442	6	spaces	space	NOUN
ejpam-6204	442	7	.	.	PUNCT
ejpam-6204	443	1	tensor	tensor	NOUN
ejpam-6204	443	2	,	,	PUNCT
ejpam-6204	443	3	n.	n.	PROPN
ejpam-6204	443	4	s.	s.	PROPN
ejpam-6204	443	5	,	,	PUNCT
ejpam-6204	443	6	52:189–198	52:189–198	PROPN
ejpam-6204	443	7	,	,	PUNCT
ejpam-6204	443	8	1993	1993	NUM
ejpam-6204	443	9	.	.	PUNCT
ejpam-6204	444	1	[	[	X
ejpam-6204	444	2	13	13	NUM
ejpam-6204	444	3	]	]	X
ejpam-6204	444	4	h.	h.	PROPN
ejpam-6204	444	5	rund	rund	PROPN
ejpam-6204	444	6	.	.	PUNCT
ejpam-6204	445	1	the	the	DET
ejpam-6204	445	2	differential	differential	ADJ
ejpam-6204	445	3	geometry	geometry	NOUN
ejpam-6204	445	4	of	of	ADP
ejpam-6204	445	5	finsler	finsler	NOUN
ejpam-6204	445	6	spaces	space	NOUN
ejpam-6204	445	7	.	.	PUNCT
ejpam-6204	446	1	springer	springer	NOUN
ejpam-6204	446	2	-	-	PUNCT
ejpam-6204	446	3	verlag	verlag	PROPN
ejpam-6204	446	4	,	,	PUNCT
ejpam-6204	446	5	berlin	berlin	PROPN
ejpam-6204	446	6	,	,	PUNCT
ejpam-6204	446	7	1959	1959	NUM
ejpam-6204	446	8	.	.	PUNCT
ejpam-6204	447	1	[	[	X
ejpam-6204	447	2	14	14	NUM
ejpam-6204	447	3	]	]	X
ejpam-6204	447	4	nabil	nabil	PROPN
ejpam-6204	447	5	l.	l.	PROPN
ejpam-6204	447	6	youssef	youssef	PROPN
ejpam-6204	447	7	.	.	PUNCT
ejpam-6204	448	1	semi	semi	ADJ
ejpam-6204	448	2	-	-	ADJ
ejpam-6204	448	3	projective	projective	ADJ
ejpam-6204	448	4	changes	change	NOUN
ejpam-6204	448	5	.	.	PUNCT
ejpam-6204	449	1	tensor	tensor	NOUN
ejpam-6204	449	2	,	,	PUNCT
ejpam-6204	449	3	n.	n.	PROPN
ejpam-6204	449	4	s.	s.	PROPN
ejpam-6204	449	5	,	,	PUNCT
ejpam-6204	449	6	55:131–141	55:131–141	NUM
ejpam-6204	449	7	,	,	PUNCT
ejpam-6204	449	8	1994	1994	NUM
ejpam-6204	449	9	.	.	PUNCT
ejpam-6204	450	1	[	[	X
ejpam-6204	450	2	15	15	NUM
ejpam-6204	450	3	]	]	X
ejpam-6204	450	4	l.	l.	PROPN
ejpam-6204	450	5	r.	r.	PROPN
ejpam-6204	450	6	del	del	PROPN
ejpam-6204	450	7	castillo	castillo	PROPN
ejpam-6204	450	8	.	.	PUNCT
ejpam-6204	451	1	tenseurs	tenseur	NOUN
ejpam-6204	451	2	de	de	ADP
ejpam-6204	451	3	weyl	weyl	X
ejpam-6204	451	4	d’une	d’une	ADJ
ejpam-6204	451	5	gerbe	gerbe	NOUN
ejpam-6204	451	6	de	de	ADP
ejpam-6204	451	7	directions	direction	NOUN
ejpam-6204	451	8	.	.	PUNCT
ejpam-6204	452	1	c.	c.	PROPN
ejpam-6204	452	2	r.	r.	PROPN
ejpam-6204	452	3	acad	acad	PROPN
ejpam-6204	452	4	.	.	PUNCT
ejpam-6204	453	1	sci	sci	PROPN
ejpam-6204	453	2	.	.	PROPN
ejpam-6204	453	3	paris	paris	PROPN
ejpam-6204	453	4	,	,	PUNCT
ejpam-6204	453	5	ser	ser	PROPN
ejpam-6204	453	6	.	.	PUNCT
ejpam-6204	454	1	a	a	DET
ejpam-6204	454	2	,	,	PUNCT
ejpam-6204	454	3	282:595–598	282:595–598	NUM
ejpam-6204	454	4	,	,	PUNCT
ejpam-6204	454	5	1976	1976	NUM
ejpam-6204	454	6	.	.	PUNCT
ejpam-6204	455	1	[	[	X
ejpam-6204	455	2	16	16	NUM
ejpam-6204	455	3	]	]	X
ejpam-6204	455	4	j.	j.	PROPN
ejpam-6204	455	5	grifone	grifone	PROPN
ejpam-6204	455	6	.	.	PUNCT
ejpam-6204	456	1	structure	structure	NOUN
ejpam-6204	456	2	presque	presque	ADJ
ejpam-6204	456	3	-	-	PUNCT
ejpam-6204	456	4	tangente	tangente	NOUN
ejpam-6204	456	5	et	et	NOUN
ejpam-6204	456	6	connexions	connexion	NOUN
ejpam-6204	456	7	,	,	PUNCT
ejpam-6204	456	8	i.	i.	PROPN
ejpam-6204	456	9	annales	annales	PROPN
ejpam-6204	456	10	de	de	PROPN
ejpam-6204	456	11	l’institut	l’institut	PROPN
ejpam-6204	456	12	fourier	fourier	NOUN
ejpam-6204	456	13	(	(	PUNCT
ejpam-6204	456	14	grenoble	grenoble	ADJ
ejpam-6204	456	15	)	)	PUNCT
ejpam-6204	456	16	,	,	PUNCT
ejpam-6204	456	17	22(1):287–334	22(1):287–334	PROPN
ejpam-6204	456	18	,	,	PUNCT
ejpam-6204	456	19	1972	1972	NUM
ejpam-6204	456	20	.	.	PUNCT
ejpam-6204	457	1	[	[	X
ejpam-6204	457	2	17	17	NUM
ejpam-6204	457	3	]	]	PUNCT
ejpam-6204	457	4	a.	a.	NOUN
ejpam-6204	457	5	frölicher	frölicher	PROPN
ejpam-6204	457	6	and	and	CCONJ
ejpam-6204	457	7	a.	a.	PROPN
ejpam-6204	457	8	nijenhuis	nijenhuis	PROPN
ejpam-6204	457	9	.	.	PUNCT
ejpam-6204	458	1	theory	theory	NOUN
ejpam-6204	458	2	of	of	ADP
ejpam-6204	458	3	vector	vector	NOUN
ejpam-6204	458	4	-	-	PUNCT
ejpam-6204	458	5	valued	value	VERB
ejpam-6204	458	6	differential	differential	NOUN
ejpam-6204	458	7	forms	form	NOUN
ejpam-6204	458	8	i.	i.	PROPN
ejpam-6204	458	9	ann	ann	PROPN
ejpam-6204	458	10	.	.	PUNCT
ejpam-6204	459	1	proc	proc	PROPN
ejpam-6204	459	2	.	.	PUNCT
ejpam-6204	460	1	kon	kon	PROPN
ejpam-6204	460	2	.	.	PUNCT
ejpam-6204	460	3	ned	ned	PROPN
ejpam-6204	460	4	.	.	PROPN
ejpam-6204	460	5	akad	akad	PROPN
ejpam-6204	460	6	.	.	PUNCT
ejpam-6204	460	7	,	,	PUNCT
ejpam-6204	460	8	59:338–359	59:338–359	NUM
ejpam-6204	460	9	,	,	PUNCT
ejpam-6204	460	10	1956	1956	NUM
ejpam-6204	460	11	.	.	PUNCT
ejpam-6204	461	1	[	[	X
ejpam-6204	461	2	18	18	NUM
ejpam-6204	461	3	]	]	PUNCT
ejpam-6204	461	4	m.	m.	NOUN
ejpam-6204	461	5	hashiguchi	hashiguchi	PROPN
ejpam-6204	461	6	.	.	PUNCT
ejpam-6204	462	1	on	on	ADP
ejpam-6204	462	2	conformal	conformal	ADJ
ejpam-6204	462	3	transformations	transformation	NOUN
ejpam-6204	462	4	of	of	ADP
ejpam-6204	462	5	finsler	finsler	NOUN
ejpam-6204	462	6	metrics	metric	NOUN
ejpam-6204	462	7	.	.	PUNCT
ejpam-6204	463	1	j.	j.	PROPN
ejpam-6204	463	2	math	math	PROPN
ejpam-6204	463	3	.	.	PUNCT
ejpam-6204	464	1	kyoto	kyoto	PROPN
ejpam-6204	464	2	univ	univ	PROPN
ejpam-6204	464	3	.	.	PROPN
ejpam-6204	464	4	,	,	PUNCT
ejpam-6204	464	5	16:25–50	16:25–50	NUM
ejpam-6204	464	6	,	,	PUNCT
ejpam-6204	464	7	1976	1976	NUM
ejpam-6204	464	8	.	.	PUNCT
ejpam-6204	465	1	[	[	X
ejpam-6204	465	2	19	19	NUM
ejpam-6204	465	3	]	]	PUNCT
ejpam-6204	465	4	z.	z.	PROPN
ejpam-6204	465	5	muzsnay	muzsnay	PROPN
ejpam-6204	465	6	.	.	PUNCT
ejpam-6204	466	1	the	the	DET
ejpam-6204	466	2	euler	euler	NOUN
ejpam-6204	466	3	-	-	PUNCT
ejpam-6204	466	4	lagrange	lagrange	NOUN
ejpam-6204	466	5	pde	pde	NOUN
ejpam-6204	466	6	and	and	CCONJ
ejpam-6204	466	7	finsler	finsler	NOUN
ejpam-6204	466	8	metrizability	metrizability	NOUN
ejpam-6204	466	9	.	.	PUNCT
ejpam-6204	467	1	houston	houston	PROPN
ejpam-6204	467	2	j.	j.	PROPN
ejpam-6204	467	3	math	math	PROPN
ejpam-6204	467	4	.	.	PUNCT
ejpam-6204	467	5	,	,	PUNCT
ejpam-6204	467	6	32:79–98	32:79–98	NUM
ejpam-6204	467	7	,	,	PUNCT
ejpam-6204	467	8	2006	2006	NUM
ejpam-6204	467	9	.	.	PUNCT
ejpam-6204	468	1	s.	s.	PROPN
ejpam-6204	468	2	g.	g.	PROPN
ejpam-6204	468	3	elgendi	elgendi	PROPN
ejpam-6204	468	4	,	,	PUNCT
ejpam-6204	468	5	a.	a.	NOUN
ejpam-6204	468	6	soleiman	soleiman	PROPN
ejpam-6204	468	7	/	/	SYM
ejpam-6204	468	8	eur	eur	PROPN
ejpam-6204	468	9	.	.	PUNCT
ejpam-6204	469	1	j.	j.	PROPN
ejpam-6204	469	2	pure	pure	PROPN
ejpam-6204	469	3	appl	appl	PROPN
ejpam-6204	469	4	.	.	PROPN
ejpam-6204	469	5	math	math	PROPN
ejpam-6204	469	6	,	,	PUNCT
ejpam-6204	469	7	18	18	NUM
ejpam-6204	469	8	(	(	PUNCT
ejpam-6204	469	9	3	3	NUM
ejpam-6204	469	10	)	)	PUNCT
ejpam-6204	469	11	(	(	PUNCT
ejpam-6204	469	12	2025	2025	NUM
ejpam-6204	469	13	)	)	PUNCT
ejpam-6204	469	14	,	,	PUNCT
ejpam-6204	469	15	6204	6204	NUM
ejpam-6204	469	16	18	18	NUM
ejpam-6204	469	17	of	of	ADP
ejpam-6204	469	18	18	18	NUM
ejpam-6204	469	19	[	[	SYM
ejpam-6204	469	20	20	20	NUM
ejpam-6204	469	21	]	]	PUNCT
ejpam-6204	469	22	z.	z.	PROPN
ejpam-6204	469	23	shen	shen	PROPN
ejpam-6204	469	24	.	.	PUNCT
ejpam-6204	470	1	on	on	ADP
ejpam-6204	470	2	a	a	DET
ejpam-6204	470	3	class	class	NOUN
ejpam-6204	470	4	of	of	ADP
ejpam-6204	470	5	landsberg	landsberg	PROPN
ejpam-6204	470	6	metrics	metric	NOUN
ejpam-6204	470	7	in	in	ADP
ejpam-6204	470	8	finsler	finsler	NOUN
ejpam-6204	470	9	geometry	geometry	NOUN
ejpam-6204	470	10	.	.	PUNCT
ejpam-6204	471	1	canad	canad	PROPN
ejpam-6204	471	2	.	.	PUNCT
ejpam-6204	472	1	j.	j.	PROPN
ejpam-6204	472	2	math	math	PROPN
ejpam-6204	472	3	.	.	PUNCT
ejpam-6204	472	4	,	,	PUNCT
ejpam-6204	473	1	61:1357–1374	61:1357–1374	NUM
ejpam-6204	473	2	,	,	PUNCT
ejpam-6204	473	3	2009	2009	NUM
ejpam-6204	473	4	.	.	PUNCT
ejpam-6204	474	1	[	[	X
ejpam-6204	474	2	21	21	NUM
ejpam-6204	474	3	]	]	X
ejpam-6204	474	4	c.	c.	PROPN
ejpam-6204	474	5	shibata	shibata	PROPN
ejpam-6204	474	6	.	.	PUNCT
ejpam-6204	475	1	on	on	ADP
ejpam-6204	475	2	invariant	invariant	ADJ
ejpam-6204	475	3	tensors	tensor	NOUN
ejpam-6204	475	4	of	of	ADP
ejpam-6204	475	5	β	β	NOUN
ejpam-6204	475	6	-	-	NOUN
ejpam-6204	475	7	changes	change	NOUN
ejpam-6204	475	8	of	of	ADP
ejpam-6204	475	9	finsler	finsler	NOUN
ejpam-6204	475	10	metrics	metric	NOUN
ejpam-6204	475	11	.	.	PUNCT
ejpam-6204	476	1	j.	j.	PROPN
ejpam-6204	476	2	math	math	PROPN
ejpam-6204	476	3	.	.	PUNCT
ejpam-6204	477	1	kyoto	kyoto	PROPN
ejpam-6204	477	2	univ	univ	PROPN
ejpam-6204	477	3	.	.	PROPN
ejpam-6204	477	4	,	,	PUNCT
ejpam-6204	478	1	24:163–188	24:163–188	PROPN
ejpam-6204	478	2	,	,	PUNCT
ejpam-6204	478	3	1984	1984	NUM
ejpam-6204	478	4	.	.	PUNCT
ejpam-6204	479	1	[	[	X
ejpam-6204	479	2	22	22	NUM
ejpam-6204	479	3	]	]	PUNCT
ejpam-6204	479	4	s.	s.	PROPN
ejpam-6204	479	5	g.	g.	PROPN
ejpam-6204	479	6	elgendi	elgendi	PROPN
ejpam-6204	479	7	.	.	PUNCT
ejpam-6204	480	1	parallel	parallel	VERB
ejpam-6204	480	2	one	one	NUM
ejpam-6204	480	3	forms	form	NOUN
ejpam-6204	480	4	on	on	ADP
ejpam-6204	480	5	special	special	ADJ
ejpam-6204	480	6	finsler	finsler	NOUN
ejpam-6204	480	7	manifolds	manifold	NOUN
ejpam-6204	480	8	.	.	PUNCT
ejpam-6204	481	1	aims	aim	VERB
ejpam-6204	481	2	mathematics	mathematic	NOUN
ejpam-6204	481	3	,	,	PUNCT
ejpam-6204	481	4	9(12):34356–34371	9(12):34356–34371	NUM
ejpam-6204	481	5	,	,	PUNCT
ejpam-6204	481	6	2024	2024	NUM
ejpam-6204	481	7	.	.	PUNCT
ejpam-6204	482	1	[	[	X
ejpam-6204	482	2	23	23	NUM
ejpam-6204	482	3	]	]	X
ejpam-6204	482	4	s.	s.	PROPN
ejpam-6204	482	5	g.	g.	PROPN
ejpam-6204	482	6	elgendi	elgendi	PROPN
ejpam-6204	482	7	.	.	PUNCT
ejpam-6204	483	1	on	on	ADP
ejpam-6204	483	2	the	the	DET
ejpam-6204	483	3	classification	classification	NOUN
ejpam-6204	483	4	of	of	ADP
ejpam-6204	483	5	landsberg	landsberg	PROPN
ejpam-6204	483	6	spherically	spherically	PROPN
ejpam-6204	483	7	symmetric	symmetric	ADJ
ejpam-6204	483	8	finsler	finsler	NOUN
ejpam-6204	483	9	metrics	metric	NOUN
ejpam-6204	483	10	.	.	PUNCT
ejpam-6204	484	1	int	int	NOUN
ejpam-6204	484	2	.	.	PUNCT
ejpam-6204	485	1	j.	j.	PROPN
ejpam-6204	485	2	geom	geom	PROPN
ejpam-6204	485	3	.	.	PUNCT
ejpam-6204	486	1	methods	methods	PROPN
ejpam-6204	486	2	mod	mod	PROPN
ejpam-6204	486	3	.	.	PUNCT
ejpam-6204	487	1	phys	phy	NOUN
ejpam-6204	487	2	.	.	PUNCT
ejpam-6204	487	3	,	,	PUNCT
ejpam-6204	487	4	18	18	NUM
ejpam-6204	487	5	,	,	PUNCT
ejpam-6204	487	6	2021	2021	NUM
ejpam-6204	487	7	.	.	PUNCT
ejpam-6204	488	1	[	[	X
ejpam-6204	488	2	24	24	NUM
ejpam-6204	488	3	]	]	X
ejpam-6204	488	4	x.	x.	PROPN
ejpam-6204	488	5	mo	mo	PROPN
ejpam-6204	488	6	and	and	CCONJ
ejpam-6204	488	7	l.	l.	PROPN
ejpam-6204	488	8	zhou	zhou	PROPN
ejpam-6204	488	9	.	.	PUNCT
ejpam-6204	489	1	the	the	DET
ejpam-6204	489	2	curvatures	curvature	NOUN
ejpam-6204	489	3	of	of	ADP
ejpam-6204	489	4	spherically	spherically	NOUN
ejpam-6204	489	5	symmetric	symmetric	ADJ
ejpam-6204	489	6	finsler	finsler	NOUN
ejpam-6204	489	7	metrics	metric	NOUN
ejpam-6204	489	8	in	in	ADP
ejpam-6204	489	9	rn	rn	PROPN
ejpam-6204	489	10	.	.	PUNCT
ejpam-6204	490	1	arxiv:1202.4543v4	arxiv:1202.4543v4	PROPN
ejpam-6204	491	1	[	[	X
ejpam-6204	491	2	math.dg	math.dg	X
ejpam-6204	491	3	]	]	PUNCT
ejpam-6204	491	4	.	.	PUNCT
ejpam-6204	492	1	[	[	X
ejpam-6204	492	2	25	25	NUM
ejpam-6204	492	3	]	]	X
ejpam-6204	492	4	c.	c.	PROPN
ejpam-6204	492	5	yu	yu	PROPN
ejpam-6204	492	6	and	and	CCONJ
ejpam-6204	492	7	h.	h.	PROPN
ejpam-6204	492	8	zhu	zhu	PROPN
ejpam-6204	492	9	.	.	PUNCT
ejpam-6204	493	1	on	on	ADP
ejpam-6204	493	2	a	a	DET
ejpam-6204	493	3	new	new	ADJ
ejpam-6204	493	4	class	class	NOUN
ejpam-6204	493	5	of	of	ADP
ejpam-6204	493	6	finsler	finsler	NOUN
ejpam-6204	493	7	metrics	metric	NOUN
ejpam-6204	493	8	.	.	PUNCT
ejpam-6204	494	1	differ	differ	VERB
ejpam-6204	494	2	.	.	PUNCT
ejpam-6204	495	1	geom	geom	PROPN
ejpam-6204	495	2	.	.	PUNCT
ejpam-6204	496	1	appl	appl	PROPN
ejpam-6204	496	2	.	.	PROPN
ejpam-6204	496	3	,	,	PUNCT
ejpam-6204	496	4	29:244–554	29:244–554	PROPN
ejpam-6204	496	5	,	,	PUNCT
ejpam-6204	496	6	2011	2011	NUM
ejpam-6204	496	7	.	.	PUNCT
ejpam-6204	497	1	[	[	X
ejpam-6204	497	2	26	26	NUM
ejpam-6204	497	3	]	]	PUNCT
ejpam-6204	497	4	j.	j.	PROPN
ejpam-6204	497	5	grifone	grifone	PROPN
ejpam-6204	497	6	.	.	PUNCT
ejpam-6204	498	1	structure	structure	NOUN
ejpam-6204	498	2	presque	presque	ADJ
ejpam-6204	498	3	-	-	PUNCT
ejpam-6204	498	4	tangente	tangente	NOUN
ejpam-6204	498	5	et	et	NOUN
ejpam-6204	498	6	connexions	connexion	NOUN
ejpam-6204	498	7	,	,	PUNCT
ejpam-6204	498	8	ii	ii	PROPN
ejpam-6204	498	9	.	.	PROPN
ejpam-6204	498	10	annales	annales	PROPN
ejpam-6204	498	11	de	de	PROPN
ejpam-6204	498	12	l’institut	l’institut	PROPN
ejpam-6204	498	13	fourier	fourier	NOUN
ejpam-6204	498	14	(	(	PUNCT
ejpam-6204	498	15	grenoble	grenoble	ADJ
ejpam-6204	498	16	)	)	PUNCT
ejpam-6204	498	17	,	,	PUNCT
ejpam-6204	498	18	22(3):291–338	22(3):291–338	PROPN
ejpam-6204	498	19	,	,	PUNCT
ejpam-6204	498	20	1972	1972	NUM
ejpam-6204	498	21	.	.	PUNCT
ejpam-6204	499	1	[	[	X
ejpam-6204	499	2	27	27	NUM
ejpam-6204	499	3	]	]	X
ejpam-6204	499	4	j.	j.	PROPN
ejpam-6204	499	5	klein	klein	PROPN
ejpam-6204	499	6	and	and	CCONJ
ejpam-6204	499	7	a.	a.	NOUN
ejpam-6204	499	8	voutier	voutier	NOUN
ejpam-6204	499	9	.	.	PUNCT
ejpam-6204	500	1	formes	forme	NOUN
ejpam-6204	500	2	extérieures	extérieure	VERB
ejpam-6204	500	3	génératrices	génératrices	PROPN
ejpam-6204	500	4	de	de	NOUN
ejpam-6204	500	5	sprays	spray	NOUN
ejpam-6204	500	6	.	.	PUNCT
ejpam-6204	501	1	annales	annales	PROPN
ejpam-6204	501	2	de	de	ADP
ejpam-6204	501	3	l’institut	l’institut	PROPN
ejpam-6204	501	4	fourier	fourier	NOUN
ejpam-6204	501	5	(	(	PUNCT
ejpam-6204	501	6	grenoble	grenoble	ADJ
ejpam-6204	501	7	)	)	PUNCT
ejpam-6204	501	8	,	,	PUNCT
ejpam-6204	501	9	18(1):241–260	18(1):241–260	NUM
ejpam-6204	501	10	,	,	PUNCT
ejpam-6204	501	11	1968	1968	NUM
ejpam-6204	501	12	.	.	PUNCT
ejpam-6204	502	1	[	[	X
ejpam-6204	502	2	28	28	NUM
ejpam-6204	502	3	]	]	X
ejpam-6204	502	4	nabil	nabil	PROPN
ejpam-6204	502	5	l.	l.	PROPN
ejpam-6204	502	6	youssef	youssef	PROPN
ejpam-6204	502	7	and	and	CCONJ
ejpam-6204	502	8	s.	s.	PROPN
ejpam-6204	502	9	g.	g.	PROPN
ejpam-6204	502	10	elgendi	elgendi	PROPN
ejpam-6204	502	11	.	.	PUNCT
ejpam-6204	503	1	new	new	ADJ
ejpam-6204	503	2	finsler	finsler	NOUN
ejpam-6204	503	3	package	package	NOUN
ejpam-6204	503	4	.	.	PUNCT
ejpam-6204	504	1	comput	comput	NOUN
ejpam-6204	504	2	.	.	PUNCT
ejpam-6204	505	1	phys	phy	NOUN
ejpam-6204	505	2	.	.	PUNCT
ejpam-6204	506	1	commun	commun	PROPN
ejpam-6204	506	2	.	.	PROPN
ejpam-6204	506	3	,	,	PUNCT
ejpam-6204	506	4	185(3):986–997	185(3):986–997	NUM
ejpam-6204	506	5	,	,	PUNCT
ejpam-6204	506	6	2014	2014	NUM
ejpam-6204	506	7	.	.	PUNCT