id	sid	tid	token	lemma	pos
ejpam-3129	1	1	european	european	PROPN
ejpam-3129	1	2	journal	journal	PROPN
ejpam-3129	1	3	of	of	ADP
ejpam-3129	1	4	pure	pure	ADJ
ejpam-3129	1	5	and	and	CCONJ
ejpam-3129	1	6	applied	apply	VERB
ejpam-3129	1	7	mathematics	mathematic	NOUN
ejpam-3129	1	8	vol	vol	NOUN
ejpam-3129	1	9	.	.	PROPN
ejpam-3129	2	1	10	10	NUM
ejpam-3129	2	2	,	,	PUNCT
ejpam-3129	2	3	no	no	INTJ
ejpam-3129	2	4	.	.	NOUN
ejpam-3129	2	5	5	5	NUM
ejpam-3129	2	6	,	,	PUNCT
ejpam-3129	2	7	2017	2017	NUM
ejpam-3129	2	8	,	,	PUNCT
ejpam-3129	2	9	1099	1099	NUM
ejpam-3129	2	10	-	-	SYM
ejpam-3129	2	11	1111	1111	NUM
ejpam-3129	2	12	issn	issn	PROPN
ejpam-3129	2	13	1307	1307	NUM
ejpam-3129	2	14	-	-	SYM
ejpam-3129	2	15	5543	5543	NUM
ejpam-3129	2	16	–	–	PUNCT
ejpam-3129	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3129	2	18	published	publish	VERB
ejpam-3129	2	19	by	by	ADP
ejpam-3129	2	20	new	new	PROPN
ejpam-3129	2	21	york	york	PROPN
ejpam-3129	2	22	business	business	PROPN
ejpam-3129	2	23	global	global	PROPN
ejpam-3129	2	24	on	on	ADP
ejpam-3129	2	25	finsler	finsler	NOUN
ejpam-3129	2	26	s	s	NOUN
ejpam-3129	2	27	-	-	PUNCT
ejpam-3129	2	28	manifolds	manifold	VERB
ejpam-3129	2	29	parisa	parisa	PROPN
ejpam-3129	2	30	bahmandoust1	bahmandoust1	NOUN
ejpam-3129	2	31	,	,	PUNCT
ejpam-3129	2	32	dariush	dariush	PROPN
ejpam-3129	2	33	latifi1,∗	latifi1,∗	PROPN
ejpam-3129	2	34	1	1	NUM
ejpam-3129	2	35	department	department	NOUN
ejpam-3129	2	36	of	of	ADP
ejpam-3129	2	37	mathematics	mathematic	NOUN
ejpam-3129	2	38	,	,	PUNCT
ejpam-3129	2	39	university	university	NOUN
ejpam-3129	2	40	of	of	ADP
ejpam-3129	2	41	mohaghegh	mohaghegh	PROPN
ejpam-3129	2	42	ardabili	ardabili	PROPN
ejpam-3129	2	43	,	,	PUNCT
ejpam-3129	2	44	ardabil	ardabil	VERB
ejpam-3129	2	45	,	,	PUNCT
ejpam-3129	2	46	iran	iran	PROPN
ejpam-3129	2	47	abstract	abstract	NOUN
ejpam-3129	2	48	.	.	PUNCT
ejpam-3129	3	1	finsler	finsler	NOUN
ejpam-3129	3	2	s−manifolds	s−manifolds	PROPN
ejpam-3129	3	3	are	be	AUX
ejpam-3129	3	4	a	a	DET
ejpam-3129	3	5	generalization	generalization	NOUN
ejpam-3129	3	6	of	of	ADP
ejpam-3129	3	7	riemannian	riemannian	ADJ
ejpam-3129	3	8	s−manifolds	s−manifolds	PROPN
ejpam-3129	3	9	.	.	PUNCT
ejpam-3129	4	1	an	an	DET
ejpam-3129	4	2	important	important	ADJ
ejpam-3129	4	3	property	property	NOUN
ejpam-3129	4	4	of	of	ADP
ejpam-3129	4	5	such	such	ADJ
ejpam-3129	4	6	manifolds	manifold	NOUN
ejpam-3129	4	7	is	be	AUX
ejpam-3129	4	8	the	the	DET
ejpam-3129	4	9	homogeneity	homogeneity	NOUN
ejpam-3129	4	10	.	.	PUNCT
ejpam-3129	5	1	in	in	ADP
ejpam-3129	5	2	this	this	DET
ejpam-3129	5	3	paper	paper	NOUN
ejpam-3129	5	4	we	we	PRON
ejpam-3129	5	5	study	study	VERB
ejpam-3129	5	6	finsler	finsler	NOUN
ejpam-3129	5	7	s−manifolds	s−manifolds	PROPN
ejpam-3129	5	8	.	.	PUNCT
ejpam-3129	6	1	we	we	PRON
ejpam-3129	6	2	first	first	ADV
ejpam-3129	6	3	construct	construct	VERB
ejpam-3129	6	4	some	some	DET
ejpam-3129	6	5	example	example	NOUN
ejpam-3129	6	6	of	of	ADP
ejpam-3129	6	7	finsler	finsler	NOUN
ejpam-3129	6	8	s−manifolds	s−manifolds	ADP
ejpam-3129	6	9	which	which	PRON
ejpam-3129	6	10	are	be	AUX
ejpam-3129	6	11	neither	neither	CCONJ
ejpam-3129	6	12	riemannian	riemannian	ADJ
ejpam-3129	6	13	nor	nor	CCONJ
ejpam-3129	6	14	symmetric	symmetric	ADJ
ejpam-3129	6	15	.	.	PUNCT
ejpam-3129	7	1	then	then	ADV
ejpam-3129	7	2	we	we	PRON
ejpam-3129	7	3	consider	consider	VERB
ejpam-3129	7	4	symmetric	symmetric	ADJ
ejpam-3129	7	5	preserving	preserve	VERB
ejpam-3129	7	6	diffeomorphism	diffeomorphism	NOUN
ejpam-3129	7	7	of	of	ADP
ejpam-3129	7	8	finsler	finsler	NOUN
ejpam-3129	7	9	s−manifolds	s−manifold	NOUN
ejpam-3129	7	10	.	.	PUNCT
ejpam-3129	8	1	finally	finally	ADV
ejpam-3129	8	2	we	we	PRON
ejpam-3129	8	3	give	give	VERB
ejpam-3129	8	4	some	some	DET
ejpam-3129	8	5	algebraic	algebraic	ADJ
ejpam-3129	8	6	and	and	CCONJ
ejpam-3129	8	7	existence	existence	NOUN
ejpam-3129	8	8	theorem	theorem	NOUN
ejpam-3129	8	9	of	of	ADP
ejpam-3129	8	10	these	these	DET
ejpam-3129	8	11	spaces	space	NOUN
ejpam-3129	8	12	.	.	PUNCT
ejpam-3129	9	1	2010	2010	NUM
ejpam-3129	9	2	mathematics	mathematic	NOUN
ejpam-3129	9	3	subject	subject	NOUN
ejpam-3129	9	4	classifications	classification	NOUN
ejpam-3129	9	5	:	:	PUNCT
ejpam-3129	9	6	53c60	53c60	NUM
ejpam-3129	9	7	,	,	PUNCT
ejpam-3129	9	8	53c30	53c30	NUM
ejpam-3129	9	9	.	.	PUNCT
ejpam-3129	10	1	key	key	ADJ
ejpam-3129	10	2	words	word	NOUN
ejpam-3129	10	3	and	and	CCONJ
ejpam-3129	10	4	phrases	phrase	NOUN
ejpam-3129	10	5	:	:	PUNCT
ejpam-3129	10	6	finsler	finsler	NOUN
ejpam-3129	10	7	s−manifold	s−manifold	PROPN
ejpam-3129	10	8	,	,	PUNCT
ejpam-3129	10	9	symmetric	symmetric	ADJ
ejpam-3129	10	10	finsler	finsler	NOUN
ejpam-3129	10	11	space	space	NOUN
ejpam-3129	10	12	,	,	PUNCT
ejpam-3129	10	13	generalized	generalize	VERB
ejpam-3129	10	14	symmetric	symmetric	ADJ
ejpam-3129	10	15	space	space	NOUN
ejpam-3129	10	16	,	,	PUNCT
ejpam-3129	10	17	homogeneous	homogeneous	ADJ
ejpam-3129	10	18	finsler	finsler	NOUN
ejpam-3129	10	19	space	space	NOUN
ejpam-3129	10	20	.	.	PUNCT
ejpam-3129	11	1	1	1	X
ejpam-3129	11	2	.	.	X
ejpam-3129	11	3	introduction	introduction	NOUN
ejpam-3129	11	4	finsler	finsler	NOUN
ejpam-3129	11	5	manifold	manifold	PROPN
ejpam-3129	11	6	is	be	AUX
ejpam-3129	11	7	a	a	DET
ejpam-3129	11	8	generalization	generalization	NOUN
ejpam-3129	11	9	of	of	ADP
ejpam-3129	11	10	the	the	DET
ejpam-3129	11	11	riemannian	riemannian	ADJ
ejpam-3129	11	12	one	one	NOUN
ejpam-3129	11	13	,	,	PUNCT
ejpam-3129	11	14	in	in	ADP
ejpam-3129	11	15	the	the	DET
ejpam-3129	11	16	same	same	ADJ
ejpam-3129	11	17	as	as	SCONJ
ejpam-3129	11	18	riemannian	riemannian	ADJ
ejpam-3129	11	19	manifold	manifold	NOUN
ejpam-3129	11	20	is	be	AUX
ejpam-3129	11	21	for	for	ADP
ejpam-3129	11	22	the	the	DET
ejpam-3129	11	23	euclidean	euclidean	NOUN
ejpam-3129	11	24	.	.	PUNCT
ejpam-3129	12	1	a	a	DET
ejpam-3129	12	2	metric	metric	NOUN
ejpam-3129	12	3	depends	depend	VERB
ejpam-3129	12	4	on	on	ADP
ejpam-3129	12	5	the	the	DET
ejpam-3129	12	6	point	point	NOUN
ejpam-3129	12	7	and	and	CCONJ
ejpam-3129	12	8	the	the	DET
ejpam-3129	12	9	direction	direction	NOUN
ejpam-3129	12	10	.	.	PUNCT
ejpam-3129	13	1	a	a	DET
ejpam-3129	13	2	finsler	finsler	NOUN
ejpam-3129	13	3	metric	metric	ADJ
ejpam-3129	13	4	on	on	ADP
ejpam-3129	13	5	a	a	DET
ejpam-3129	13	6	manifold	manifold	NOUN
ejpam-3129	13	7	is	be	AUX
ejpam-3129	13	8	a	a	DET
ejpam-3129	13	9	family	family	NOUN
ejpam-3129	13	10	of	of	ADP
ejpam-3129	13	11	minkowski	minkowski	ADJ
ejpam-3129	13	12	norms	norm	NOUN
ejpam-3129	13	13	on	on	ADP
ejpam-3129	13	14	tangent	tangent	ADJ
ejpam-3129	13	15	spaces	space	NOUN
ejpam-3129	13	16	.	.	PUNCT
ejpam-3129	14	1	let	let	VERB
ejpam-3129	14	2	(	(	PUNCT
ejpam-3129	14	3	m	m	PROPN
ejpam-3129	14	4	,	,	PUNCT
ejpam-3129	14	5	f	f	PROPN
ejpam-3129	14	6	)	)	PUNCT
ejpam-3129	14	7	be	be	AUX
ejpam-3129	14	8	a	a	DET
ejpam-3129	14	9	finsler	finsler	NOUN
ejpam-3129	14	10	space	space	NOUN
ejpam-3129	14	11	,	,	PUNCT
ejpam-3129	14	12	where	where	SCONJ
ejpam-3129	14	13	f	f	PROPN
ejpam-3129	14	14	is	be	AUX
ejpam-3129	14	15	positively	positively	ADV
ejpam-3129	14	16	homogeneous	homogeneous	ADJ
ejpam-3129	14	17	of	of	ADP
ejpam-3129	14	18	degree	degree	NOUN
ejpam-3129	14	19	one	one	NUM
ejpam-3129	14	20	.	.	PUNCT
ejpam-3129	15	1	then	then	ADV
ejpam-3129	15	2	we	we	PRON
ejpam-3129	15	3	have	have	VERB
ejpam-3129	15	4	two	two	NUM
ejpam-3129	15	5	ways	way	NOUN
ejpam-3129	15	6	to	to	PART
ejpam-3129	15	7	define	define	VERB
ejpam-3129	15	8	the	the	DET
ejpam-3129	15	9	notion	notion	NOUN
ejpam-3129	15	10	of	of	ADP
ejpam-3129	15	11	an	an	DET
ejpam-3129	15	12	isometry	isometry	NOUN
ejpam-3129	15	13	of	of	ADP
ejpam-3129	15	14	(	(	PUNCT
ejpam-3129	15	15	m	m	PROPN
ejpam-3129	15	16	,	,	PUNCT
ejpam-3129	15	17	f	f	PROPN
ejpam-3129	15	18	)	)	PUNCT
ejpam-3129	15	19	.	.	PUNCT
ejpam-3129	16	1	on	on	ADP
ejpam-3129	16	2	the	the	DET
ejpam-3129	16	3	one	one	NUM
ejpam-3129	16	4	hand	hand	NOUN
ejpam-3129	16	5	,	,	PUNCT
ejpam-3129	16	6	we	we	PRON
ejpam-3129	16	7	call	call	VERB
ejpam-3129	16	8	a	a	DET
ejpam-3129	16	9	diffeomorphism	diffeomorphism	NOUN
ejpam-3129	16	10	σ	σ	NOUN
ejpam-3129	16	11	of	of	ADP
ejpam-3129	16	12	m	m	PROPN
ejpam-3129	16	13	onto	onto	ADP
ejpam-3129	16	14	itself	itself	PRON
ejpam-3129	16	15	an	an	DET
ejpam-3129	16	16	isometry	isometry	NOUN
ejpam-3129	16	17	if	if	SCONJ
ejpam-3129	16	18	f	f	PROPN
ejpam-3129	16	19	(	(	PUNCT
ejpam-3129	16	20	dσx(y	dσx(y	PROPN
ejpam-3129	16	21	)	)	PUNCT
ejpam-3129	16	22	)	)	PUNCT
ejpam-3129	17	1	=	=	SYM
ejpam-3129	17	2	f	f	PROPN
ejpam-3129	17	3	(	(	PUNCT
ejpam-3129	17	4	y	y	NOUN
ejpam-3129	17	5	)	)	PUNCT
ejpam-3129	17	6	,	,	PUNCT
ejpam-3129	17	7	for	for	ADP
ejpam-3129	17	8	any	any	DET
ejpam-3129	17	9	x	x	SYM
ejpam-3129	17	10	∈	∈	PROPN
ejpam-3129	17	11	m	m	NOUN
ejpam-3129	17	12	and	and	CCONJ
ejpam-3129	17	13	y	y	PROPN
ejpam-3129	17	14	∈	∈	PROPN
ejpam-3129	17	15	txm	txm	PROPN
ejpam-3129	17	16	.	.	PUNCT
ejpam-3129	18	1	on	on	ADP
ejpam-3129	18	2	the	the	DET
ejpam-3129	18	3	other	other	ADJ
ejpam-3129	18	4	hand	hand	NOUN
ejpam-3129	18	5	,	,	PUNCT
ejpam-3129	18	6	we	we	PRON
ejpam-3129	18	7	can	can	AUX
ejpam-3129	18	8	also	also	ADV
ejpam-3129	18	9	define	define	VERB
ejpam-3129	18	10	an	an	DET
ejpam-3129	18	11	isometry	isometry	NOUN
ejpam-3129	18	12	of	of	ADP
ejpam-3129	18	13	(	(	PUNCT
ejpam-3129	18	14	m	m	PROPN
ejpam-3129	18	15	,	,	PUNCT
ejpam-3129	18	16	f	f	PROPN
ejpam-3129	18	17	)	)	PUNCT
ejpam-3129	18	18	to	to	PART
ejpam-3129	18	19	be	be	AUX
ejpam-3129	18	20	a	a	DET
ejpam-3129	18	21	one	one	NUM
ejpam-3129	18	22	-	-	PUNCT
ejpam-3129	18	23	to	to	ADP
ejpam-3129	18	24	-	-	PUNCT
ejpam-3129	18	25	one	one	NUM
ejpam-3129	18	26	mapping	mapping	NOUN
ejpam-3129	18	27	of	of	ADP
ejpam-3129	18	28	m	m	PROPN
ejpam-3129	18	29	onto	onto	ADP
ejpam-3129	18	30	itself	itself	PRON
ejpam-3129	18	31	which	which	PRON
ejpam-3129	18	32	preserves	preserve	VERB
ejpam-3129	18	33	the	the	DET
ejpam-3129	18	34	distance	distance	NOUN
ejpam-3129	18	35	of	of	ADP
ejpam-3129	18	36	each	each	DET
ejpam-3129	18	37	pair	pair	NOUN
ejpam-3129	18	38	of	of	ADP
ejpam-3129	18	39	points	point	NOUN
ejpam-3129	18	40	of	of	ADP
ejpam-3129	18	41	m	m	PRON
ejpam-3129	18	42	.	.	PUNCT
ejpam-3129	19	1	it	it	PRON
ejpam-3129	19	2	is	be	AUX
ejpam-3129	19	3	well	well	ADV
ejpam-3129	19	4	known	know	VERB
ejpam-3129	19	5	that	that	SCONJ
ejpam-3129	19	6	the	the	DET
ejpam-3129	19	7	two	two	NUM
ejpam-3129	19	8	definitions	definition	NOUN
ejpam-3129	19	9	are	be	AUX
ejpam-3129	19	10	equivalent	equivalent	ADJ
ejpam-3129	19	11	if	if	SCONJ
ejpam-3129	19	12	the	the	DET
ejpam-3129	19	13	metric	metric	ADJ
ejpam-3129	19	14	f	f	PROPN
ejpam-3129	19	15	is	be	AUX
ejpam-3129	19	16	riemannian	riemannian	ADJ
ejpam-3129	19	17	.	.	PUNCT
ejpam-3129	20	1	the	the	DET
ejpam-3129	20	2	equivalence	equivalence	NOUN
ejpam-3129	20	3	of	of	ADP
ejpam-3129	20	4	these	these	DET
ejpam-3129	20	5	two	two	NUM
ejpam-3129	20	6	definitions	definition	NOUN
ejpam-3129	20	7	in	in	ADP
ejpam-3129	20	8	the	the	DET
ejpam-3129	20	9	general	general	ADJ
ejpam-3129	20	10	finsler	finsler	NOUN
ejpam-3129	20	11	case	case	NOUN
ejpam-3129	20	12	is	be	AUX
ejpam-3129	20	13	a	a	DET
ejpam-3129	20	14	result	result	NOUN
ejpam-3129	20	15	of	of	ADP
ejpam-3129	20	16	s.	s.	PROPN
ejpam-3129	20	17	deng	deng	PROPN
ejpam-3129	20	18	and	and	CCONJ
ejpam-3129	20	19	z.	z.	PROPN
ejpam-3129	20	20	hou	hou	PROPN
ejpam-3129	21	1	[	[	X
ejpam-3129	21	2	2	2	NUM
ejpam-3129	21	3	]	]	PUNCT
ejpam-3129	21	4	.	.	PUNCT
ejpam-3129	22	1	using	use	VERB
ejpam-3129	22	2	these	these	DET
ejpam-3129	22	3	result	result	NOUN
ejpam-3129	22	4	,	,	PUNCT
ejpam-3129	22	5	they	they	PRON
ejpam-3129	22	6	proved	prove	VERB
ejpam-3129	22	7	that	that	SCONJ
ejpam-3129	22	8	the	the	DET
ejpam-3129	22	9	group	group	NOUN
ejpam-3129	22	10	of	of	ADP
ejpam-3129	22	11	isometries	isometry	NOUN
ejpam-3129	22	12	i(m	i(m	NOUN
ejpam-3129	22	13	,	,	PUNCT
ejpam-3129	22	14	f	f	PROPN
ejpam-3129	22	15	)	)	PUNCT
ejpam-3129	22	16	of	of	ADP
ejpam-3129	22	17	a	a	DET
ejpam-3129	22	18	finsler	finsler	NOUN
ejpam-3129	22	19	space	space	NOUN
ejpam-3129	22	20	(	(	PUNCT
ejpam-3129	22	21	m	m	PROPN
ejpam-3129	22	22	,	,	PUNCT
ejpam-3129	22	23	f	f	PROPN
ejpam-3129	22	24	)	)	PUNCT
ejpam-3129	22	25	is	be	AUX
ejpam-3129	22	26	a	a	DET
ejpam-3129	22	27	lie	lie	NOUN
ejpam-3129	22	28	transformation	transformation	NOUN
ejpam-3129	22	29	group	group	NOUN
ejpam-3129	22	30	of	of	ADP
ejpam-3129	22	31	m	m	PROPN
ejpam-3129	22	32	and	and	CCONJ
ejpam-3129	22	33	for	for	ADP
ejpam-3129	22	34	any	any	DET
ejpam-3129	22	35	point	point	NOUN
ejpam-3129	22	36	x	x	PUNCT
ejpam-3129	22	37	∈	∈	NOUN
ejpam-3129	22	38	m	m	NOUN
ejpam-3129	22	39	,	,	PUNCT
ejpam-3129	22	40	the	the	DET
ejpam-3129	22	41	isotropic	isotropic	NOUN
ejpam-3129	22	42	subgroup	subgroup	NOUN
ejpam-3129	22	43	ix(m	ix(m	NUM
ejpam-3129	22	44	,	,	PUNCT
ejpam-3129	22	45	f	f	PROPN
ejpam-3129	22	46	)	)	PUNCT
ejpam-3129	22	47	is	be	AUX
ejpam-3129	22	48	a	a	DET
ejpam-3129	22	49	compact	compact	ADJ
ejpam-3129	22	50	subgroup	subgroup	NOUN
ejpam-3129	22	51	of	of	ADP
ejpam-3129	22	52	i(m	i(m	NOUN
ejpam-3129	22	53	,	,	PUNCT
ejpam-3129	22	54	f	f	PROPN
ejpam-3129	22	55	)	)	PUNCT
ejpam-3129	22	56	.	.	PUNCT
ejpam-3129	23	1	these	these	DET
ejpam-3129	23	2	results	result	NOUN
ejpam-3129	23	3	are	be	AUX
ejpam-3129	23	4	important	important	ADJ
ejpam-3129	23	5	to	to	PART
ejpam-3129	23	6	study	study	VERB
ejpam-3129	23	7	homogenous	homogenous	ADJ
ejpam-3129	23	8	and	and	CCONJ
ejpam-3129	23	9	symmetric	symmetric	ADJ
ejpam-3129	23	10	finsler	finsler	NOUN
ejpam-3129	23	11	spaces	space	NOUN
ejpam-3129	23	12	,	,	PUNCT
ejpam-3129	23	13	for	for	ADP
ejpam-3129	23	14	example	example	NOUN
ejpam-3129	23	15	[	[	X
ejpam-3129	23	16	3	3	NUM
ejpam-3129	23	17	,	,	PUNCT
ejpam-3129	23	18	4	4	NUM
ejpam-3129	23	19	,	,	PUNCT
ejpam-3129	23	20	5	5	NUM
ejpam-3129	23	21	,	,	PUNCT
ejpam-3129	23	22	12	12	NUM
ejpam-3129	23	23	,	,	PUNCT
ejpam-3129	23	24	13	13	NUM
ejpam-3129	23	25	,	,	PUNCT
ejpam-3129	23	26	14	14	NUM
ejpam-3129	23	27	]	]	PUNCT
ejpam-3129	23	28	.	.	PUNCT
ejpam-3129	24	1	symmetric	symmetric	ADJ
ejpam-3129	24	2	spaces	space	NOUN
ejpam-3129	24	3	and	and	CCONJ
ejpam-3129	24	4	generalized	generalize	VERB
ejpam-3129	24	5	symmetric	symmetric	ADJ
ejpam-3129	24	6	spaces	space	NOUN
ejpam-3129	24	7	have	have	AUX
ejpam-3129	24	8	appeared	appear	VERB
ejpam-3129	24	9	to	to	PART
ejpam-3129	24	10	be	be	AUX
ejpam-3129	24	11	very	very	ADV
ejpam-3129	24	12	rich	rich	ADJ
ejpam-3129	24	13	in	in	ADP
ejpam-3129	24	14	content	content	NOUN
ejpam-3129	24	15	,	,	PUNCT
ejpam-3129	24	16	stimulating	stimulate	VERB
ejpam-3129	24	17	the	the	DET
ejpam-3129	24	18	research	research	NOUN
ejpam-3129	24	19	in	in	ADP
ejpam-3129	24	20	lie	lie	NOUN
ejpam-3129	24	21	groups	group	NOUN
ejpam-3129	24	22	,	,	PUNCT
ejpam-3129	24	23	mechanics	mechanic	NOUN
ejpam-3129	24	24	,	,	PUNCT
ejpam-3129	24	25	physics	physics	NOUN
ejpam-3129	24	26	,	,	PUNCT
ejpam-3129	24	27	gravity	gravity	NOUN
ejpam-3129	24	28	etc	etc	X
ejpam-3129	24	29	.	.	PUNCT
ejpam-3129	25	1	the	the	DET
ejpam-3129	25	2	definition	definition	NOUN
ejpam-3129	25	3	of	of	ADP
ejpam-3129	25	4	symmetric	symmetric	ADJ
ejpam-3129	25	5	finsler	finsler	NOUN
ejpam-3129	25	6	space	space	NOUN
ejpam-3129	25	7	is	be	AUX
ejpam-3129	25	8	a	a	DET
ejpam-3129	25	9	naturall	naturall	ADJ
ejpam-3129	25	10	generalization	generalization	NOUN
ejpam-3129	25	11	of	of	ADP
ejpam-3129	25	12	e.	e.	PROPN
ejpam-3129	25	13	cartan	cartan	PROPN
ejpam-3129	25	14	’s	’s	PART
ejpam-3129	25	15	definition	definition	NOUN
ejpam-3129	25	16	of	of	ADP
ejpam-3129	25	17	riemannian	riemannian	ADJ
ejpam-3129	25	18	symmetric	symmetric	ADJ
ejpam-3129	25	19	spaces	space	NOUN
ejpam-3129	25	20	[	[	X
ejpam-3129	25	21	8	8	NUM
ejpam-3129	25	22	]	]	PUNCT
ejpam-3129	25	23	.	.	PUNCT
ejpam-3129	26	1	we	we	PRON
ejpam-3129	26	2	call	call	VERB
ejpam-3129	26	3	a	a	DET
ejpam-3129	26	4	finsler	finsler	NOUN
ejpam-3129	26	5	space	space	NOUN
ejpam-3129	26	6	(	(	PUNCT
ejpam-3129	26	7	m	m	PROPN
ejpam-3129	26	8	,	,	PUNCT
ejpam-3129	26	9	f	f	PROPN
ejpam-3129	26	10	)	)	PUNCT
ejpam-3129	26	11	a	a	DET
ejpam-3129	26	12	symmetric	symmetric	ADJ
ejpam-3129	26	13	∗corresponding	∗corresponde	VERB
ejpam-3129	26	14	author	author	NOUN
ejpam-3129	26	15	.	.	PUNCT
ejpam-3129	27	1	email	email	NOUN
ejpam-3129	27	2	addresses	address	NOUN
ejpam-3129	27	3	:	:	PUNCT
ejpam-3129	27	4	bahmandoust.p@uma.ac.ir	bahmandoust.p@uma.ac.ir	X
ejpam-3129	27	5	(	(	PUNCT
ejpam-3129	27	6	p.	p.	NOUN
ejpam-3129	27	7	bahmandoust	bahmandoust	PROPN
ejpam-3129	27	8	)	)	PUNCT
ejpam-3129	27	9	,	,	PUNCT
ejpam-3129	27	10	latifi@uma.ac.ir	latifi@uma.ac.ir	PROPN
ejpam-3129	27	11	(	(	PUNCT
ejpam-3129	27	12	d.	d.	PROPN
ejpam-3129	27	13	latifi	latifi	PROPN
ejpam-3129	27	14	)	)	PUNCT
ejpam-3129	27	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3129	28	1	1099	1099	NUM
ejpam-3129	28	2	c	c	NOUN
ejpam-3129	28	3	©	©	PROPN
ejpam-3129	28	4	2017	2017	NUM
ejpam-3129	28	5	ejpam	ejpam	VERB
ejpam-3129	28	6	all	all	DET
ejpam-3129	28	7	rights	right	NOUN
ejpam-3129	28	8	reserved	reserve	VERB
ejpam-3129	28	9	.	.	PUNCT
ejpam-3129	29	1	p.	p.	NOUN
ejpam-3129	29	2	bahmandoust	bahmandoust	NOUN
ejpam-3129	29	3	,	,	PUNCT
ejpam-3129	29	4	d.	d.	PROPN
ejpam-3129	29	5	latifi	latifi	PROPN
ejpam-3129	29	6	/	/	SYM
ejpam-3129	29	7	eur	eur	PROPN
ejpam-3129	29	8	.	.	PUNCT
ejpam-3129	30	1	j.	j.	PROPN
ejpam-3129	30	2	pure	pure	PROPN
ejpam-3129	30	3	appl	appl	PROPN
ejpam-3129	30	4	.	.	PROPN
ejpam-3129	30	5	math	math	PROPN
ejpam-3129	30	6	,	,	PUNCT
ejpam-3129	30	7	10	10	NUM
ejpam-3129	30	8	(	(	PUNCT
ejpam-3129	30	9	5	5	NUM
ejpam-3129	30	10	)	)	PUNCT
ejpam-3129	30	11	(	(	PUNCT
ejpam-3129	30	12	2017	2017	NUM
ejpam-3129	30	13	)	)	PUNCT
ejpam-3129	30	14	,	,	PUNCT
ejpam-3129	30	15	1099	1099	NUM
ejpam-3129	30	16	-	-	SYM
ejpam-3129	30	17	1111	1111	NUM
ejpam-3129	30	18	1100	1100	NUM
ejpam-3129	30	19	finsler	finsler	NOUN
ejpam-3129	30	20	space	space	NOUN
ejpam-3129	30	21	if	if	SCONJ
ejpam-3129	30	22	for	for	ADP
ejpam-3129	30	23	any	any	DET
ejpam-3129	30	24	point	point	NOUN
ejpam-3129	30	25	p	p	NOUN
ejpam-3129	30	26	∈m	∈m	NOUN
ejpam-3129	30	27	there	there	ADV
ejpam-3129	30	28	exists	exist	VERB
ejpam-3129	30	29	an	an	DET
ejpam-3129	30	30	involutive	involutive	ADJ
ejpam-3129	30	31	isometry	isometry	NOUN
ejpam-3129	30	32	sp	sp	ADP
ejpam-3129	30	33	of	of	ADP
ejpam-3129	30	34	(	(	PUNCT
ejpam-3129	30	35	m	m	PROPN
ejpam-3129	30	36	,	,	PUNCT
ejpam-3129	30	37	f	f	PROPN
ejpam-3129	30	38	)	)	PUNCT
ejpam-3129	30	39	such	such	ADJ
ejpam-3129	30	40	that	that	SCONJ
ejpam-3129	30	41	p	p	NOUN
ejpam-3129	30	42	is	be	AUX
ejpam-3129	30	43	an	an	DET
ejpam-3129	30	44	isolated	isolated	ADJ
ejpam-3129	30	45	fixed	fix	VERB
ejpam-3129	30	46	point	point	NOUN
ejpam-3129	30	47	of	of	ADP
ejpam-3129	30	48	sp	sp	NOUN
ejpam-3129	30	49	,	,	PUNCT
ejpam-3129	30	50	[	[	X
ejpam-3129	30	51	6	6	NUM
ejpam-3129	30	52	,	,	PUNCT
ejpam-3129	30	53	5	5	NUM
ejpam-3129	30	54	,	,	PUNCT
ejpam-3129	30	55	9	9	NUM
ejpam-3129	30	56	,	,	PUNCT
ejpam-3129	30	57	12	12	NUM
ejpam-3129	30	58	]	]	PUNCT
ejpam-3129	30	59	.	.	PUNCT
ejpam-3129	31	1	affine	affine	NOUN
ejpam-3129	31	2	and	and	CCONJ
ejpam-3129	31	3	riemannian	riemannian	ADJ
ejpam-3129	31	4	s−manifold	s−manifold	NOUN
ejpam-3129	31	5	were	be	AUX
ejpam-3129	31	6	first	first	ADV
ejpam-3129	31	7	defined	define	VERB
ejpam-3129	31	8	in	in	ADP
ejpam-3129	31	9	[	[	X
ejpam-3129	31	10	18	18	NUM
ejpam-3129	31	11	]	]	PUNCT
ejpam-3129	31	12	following	follow	VERB
ejpam-3129	31	13	the	the	DET
ejpam-3129	31	14	introduction	introduction	NOUN
ejpam-3129	31	15	of	of	ADP
ejpam-3129	31	16	generalized	generalized	ADJ
ejpam-3129	31	17	riemannian	riemannian	ADJ
ejpam-3129	31	18	symmetric	symmetric	ADJ
ejpam-3129	31	19	spaces	space	NOUN
ejpam-3129	31	20	in	in	ADP
ejpam-3129	31	21	[	[	X
ejpam-3129	31	22	19	19	NUM
ejpam-3129	31	23	]	]	PUNCT
ejpam-3129	31	24	.	.	PUNCT
ejpam-3129	32	1	they	they	PRON
ejpam-3129	32	2	form	form	VERB
ejpam-3129	32	3	a	a	DET
ejpam-3129	32	4	more	more	ADV
ejpam-3129	32	5	general	general	ADJ
ejpam-3129	32	6	class	class	NOUN
ejpam-3129	32	7	than	than	ADP
ejpam-3129	32	8	the	the	DET
ejpam-3129	32	9	symmetric	symmetric	ADJ
ejpam-3129	32	10	spaces	space	NOUN
ejpam-3129	32	11	[	[	X
ejpam-3129	32	12	11	11	NUM
ejpam-3129	32	13	]	]	PUNCT
ejpam-3129	32	14	.	.	PUNCT
ejpam-3129	33	1	an	an	DET
ejpam-3129	33	2	isometry	isometry	NOUN
ejpam-3129	33	3	of	of	ADP
ejpam-3129	33	4	(	(	PUNCT
ejpam-3129	33	5	m	m	PROPN
ejpam-3129	33	6	,	,	PUNCT
ejpam-3129	33	7	f	f	PROPN
ejpam-3129	33	8	)	)	PUNCT
ejpam-3129	33	9	with	with	ADP
ejpam-3129	33	10	an	an	DET
ejpam-3129	33	11	isolated	isolated	ADJ
ejpam-3129	33	12	fixed	fix	VERB
ejpam-3129	33	13	point	point	NOUN
ejpam-3129	33	14	x	x	PUNCT
ejpam-3129	33	15	∈m	∈m	NOUN
ejpam-3129	33	16	is	be	AUX
ejpam-3129	33	17	called	call	VERB
ejpam-3129	33	18	a	a	DET
ejpam-3129	33	19	symmetry	symmetry	NOUN
ejpam-3129	33	20	of	of	ADP
ejpam-3129	33	21	(	(	PUNCT
ejpam-3129	33	22	m	m	PROPN
ejpam-3129	33	23	,	,	PUNCT
ejpam-3129	33	24	f	f	PROPN
ejpam-3129	33	25	)	)	PUNCT
ejpam-3129	33	26	at	at	ADP
ejpam-3129	33	27	x.	x.	NOUN
ejpam-3129	33	28	a	a	DET
ejpam-3129	33	29	family	family	NOUN
ejpam-3129	33	30	{	{	PUNCT
ejpam-3129	33	31	sx|x	sx|x	PROPN
ejpam-3129	33	32	∈	∈	PROPN
ejpam-3129	33	33	m	m	NOUN
ejpam-3129	33	34	}	}	PUNCT
ejpam-3129	33	35	of	of	ADP
ejpam-3129	33	36	symmetries	symmetry	NOUN
ejpam-3129	33	37	of	of	ADP
ejpam-3129	33	38	a	a	DET
ejpam-3129	33	39	connected	connected	ADJ
ejpam-3129	33	40	finsler	finsler	NOUN
ejpam-3129	33	41	space	space	NOUN
ejpam-3129	33	42	(	(	PUNCT
ejpam-3129	33	43	m	m	PROPN
ejpam-3129	33	44	,	,	PUNCT
ejpam-3129	33	45	f	f	PROPN
ejpam-3129	33	46	)	)	PUNCT
ejpam-3129	33	47	is	be	AUX
ejpam-3129	33	48	called	call	VERB
ejpam-3129	33	49	an	an	DET
ejpam-3129	33	50	s−structure	s−structure	NOUN
ejpam-3129	33	51	of	of	ADP
ejpam-3129	33	52	(	(	PUNCT
ejpam-3129	33	53	m	m	PROPN
ejpam-3129	33	54	,	,	PUNCT
ejpam-3129	33	55	f	f	PROPN
ejpam-3129	33	56	)	)	PUNCT
ejpam-3129	33	57	,	,	PUNCT
ejpam-3129	34	1	[	[	X
ejpam-3129	34	2	7	7	NUM
ejpam-3129	34	3	]	]	PUNCT
ejpam-3129	34	4	.	.	PUNCT
ejpam-3129	34	5	σ−spaces	σ−space	NOUN
ejpam-3129	34	6	and	and	CCONJ
ejpam-3129	34	7	reduced	reduce	VERB
ejpam-3129	34	8	σ−spaces	σ−space	NOUN
ejpam-3129	34	9	were	be	AUX
ejpam-3129	34	10	first	first	ADV
ejpam-3129	34	11	introduced	introduce	VERB
ejpam-3129	34	12	by	by	ADP
ejpam-3129	34	13	loos	loo	NOUN
ejpam-3129	34	14	as	as	ADP
ejpam-3129	34	15	a	a	DET
ejpam-3129	34	16	generalization	generalization	NOUN
ejpam-3129	34	17	of	of	ADP
ejpam-3129	34	18	reflection	reflection	NOUN
ejpam-3129	34	19	spaces	space	NOUN
ejpam-3129	34	20	and	and	CCONJ
ejpam-3129	34	21	symmetric	symmetric	ADJ
ejpam-3129	34	22	spaces	space	NOUN
ejpam-3129	34	23	[	[	X
ejpam-3129	34	24	20	20	NUM
ejpam-3129	34	25	]	]	PUNCT
ejpam-3129	34	26	.	.	PUNCT
ejpam-3129	35	1	he	he	PRON
ejpam-3129	35	2	then	then	ADV
ejpam-3129	35	3	proved	prove	VERB
ejpam-3129	35	4	that	that	SCONJ
ejpam-3129	35	5	any	any	DET
ejpam-3129	35	6	σ−space	σ−space	NOUN
ejpam-3129	35	7	with	with	ADP
ejpam-3129	35	8	compact	compact	ADJ
ejpam-3129	35	9	σ	σ	PROPN
ejpam-3129	35	10	is	be	AUX
ejpam-3129	35	11	a	a	DET
ejpam-3129	35	12	fibre	fibre	NOUN
ejpam-3129	35	13	bundle	bundle	NOUN
ejpam-3129	35	14	over	over	ADP
ejpam-3129	35	15	a	a	DET
ejpam-3129	35	16	reduced	reduced	ADJ
ejpam-3129	35	17	σ−space	σ−space	PROPN
ejpam-3129	35	18	.	.	PUNCT
ejpam-3129	36	1	basic	basic	ADJ
ejpam-3129	36	2	properties	property	NOUN
ejpam-3129	36	3	of	of	ADP
ejpam-3129	36	4	any	any	DET
ejpam-3129	36	5	reduced	reduce	VERB
ejpam-3129	36	6	σ−space	σ−space	NOUN
ejpam-3129	36	7	m	m	VERB
ejpam-3129	36	8	and	and	CCONJ
ejpam-3129	36	9	affine	affine	VERB
ejpam-3129	36	10	and	and	CCONJ
ejpam-3129	36	11	riemannian	riemannian	ADJ
ejpam-3129	36	12	σ−space	σ−space	PROPN
ejpam-3129	36	13	and	and	CCONJ
ejpam-3129	36	14	finsler	finsler	NOUN
ejpam-3129	36	15	σ−space	σ−space	PROPN
ejpam-3129	36	16	was	be	AUX
ejpam-3129	36	17	given	give	VERB
ejpam-3129	36	18	in	in	ADP
ejpam-3129	36	19	[	[	X
ejpam-3129	36	20	15	15	NUM
ejpam-3129	36	21	,	,	PUNCT
ejpam-3129	36	22	21	21	NUM
ejpam-3129	36	23	]	]	PUNCT
ejpam-3129	36	24	.	.	PUNCT
ejpam-3129	37	1	in	in	ADP
ejpam-3129	37	2	this	this	DET
ejpam-3129	37	3	paper	paper	NOUN
ejpam-3129	37	4	we	we	PRON
ejpam-3129	37	5	are	be	AUX
ejpam-3129	37	6	concerned	concerned	ADJ
ejpam-3129	37	7	with	with	ADP
ejpam-3129	37	8	properties	property	NOUN
ejpam-3129	37	9	of	of	ADP
ejpam-3129	37	10	finsler	finsler	NOUN
ejpam-3129	37	11	spaces	space	NOUN
ejpam-3129	37	12	admitting	admit	VERB
ejpam-3129	37	13	such	such	DET
ejpam-3129	37	14	an	an	DET
ejpam-3129	37	15	s−structure	s−structure	NOUN
ejpam-3129	37	16	.	.	PUNCT
ejpam-3129	38	1	we	we	PRON
ejpam-3129	38	2	construct	construct	VERB
ejpam-3129	38	3	some	some	DET
ejpam-3129	38	4	example	example	NOUN
ejpam-3129	38	5	of	of	ADP
ejpam-3129	38	6	finsler	finsler	NOUN
ejpam-3129	38	7	s−manifolds	s−manifolds	ADP
ejpam-3129	38	8	which	which	PRON
ejpam-3129	38	9	are	be	AUX
ejpam-3129	38	10	neither	neither	CCONJ
ejpam-3129	38	11	riemannian	riemannian	ADJ
ejpam-3129	38	12	nor	nor	CCONJ
ejpam-3129	38	13	symmetric	symmetric	ADJ
ejpam-3129	38	14	.	.	PUNCT
ejpam-3129	39	1	then	then	ADV
ejpam-3129	39	2	we	we	PRON
ejpam-3129	39	3	study	study	VERB
ejpam-3129	39	4	symmetry	symmetry	NOUN
ejpam-3129	39	5	preserving	preserve	VERB
ejpam-3129	39	6	diffeomorphism	diffeomorphism	NOUN
ejpam-3129	39	7	of	of	ADP
ejpam-3129	39	8	finsler	finsler	NOUN
ejpam-3129	39	9	s−manifolds	s−manifolds	PROPN
ejpam-3129	39	10	and	and	CCONJ
ejpam-3129	39	11	show	show	VERB
ejpam-3129	39	12	that	that	SCONJ
ejpam-3129	39	13	the	the	DET
ejpam-3129	39	14	group	group	NOUN
ejpam-3129	39	15	of	of	ADP
ejpam-3129	39	16	symmetry	symmetry	NOUN
ejpam-3129	39	17	preserving	preserve	VERB
ejpam-3129	39	18	diffeomorphism	diffeomorphism	NOUN
ejpam-3129	39	19	is	be	AUX
ejpam-3129	39	20	a	a	DET
ejpam-3129	39	21	transitive	transitive	ADJ
ejpam-3129	39	22	group	group	NOUN
ejpam-3129	39	23	.	.	PUNCT
ejpam-3129	40	1	we	we	PRON
ejpam-3129	40	2	then	then	ADV
ejpam-3129	40	3	study	study	VERB
ejpam-3129	40	4	some	some	DET
ejpam-3129	40	5	existence	existence	NOUN
ejpam-3129	40	6	theorems	theorem	NOUN
ejpam-3129	40	7	and	and	CCONJ
ejpam-3129	40	8	consider	consider	VERB
ejpam-3129	40	9	some	some	DET
ejpam-3129	40	10	geometric	geometric	ADJ
ejpam-3129	40	11	properties	property	NOUN
ejpam-3129	40	12	of	of	ADP
ejpam-3129	40	13	finsler	finsler	NOUN
ejpam-3129	40	14	s−manifolds	s−manifold	NOUN
ejpam-3129	40	15	.	.	NOUN
ejpam-3129	41	1	2	2	X
ejpam-3129	41	2	.	.	X
ejpam-3129	41	3	preliminaries	preliminary	NOUN
ejpam-3129	41	4	let	let	VERB
ejpam-3129	41	5	m	m	PRON
ejpam-3129	41	6	be	be	AUX
ejpam-3129	41	7	an	an	DET
ejpam-3129	41	8	n−dimensional	n−dimensional	ADJ
ejpam-3129	41	9	smooth	smooth	ADJ
ejpam-3129	41	10	manifold	manifold	NOUN
ejpam-3129	41	11	without	without	ADP
ejpam-3129	41	12	boundary	boundary	NOUN
ejpam-3129	41	13	and	and	CCONJ
ejpam-3129	41	14	tm	tm	NOUN
ejpam-3129	41	15	denote	denote	VERB
ejpam-3129	41	16	its	its	PRON
ejpam-3129	41	17	tangent	tangent	NOUN
ejpam-3129	41	18	bundle	bundle	NOUN
ejpam-3129	41	19	.	.	PUNCT
ejpam-3129	42	1	a	a	DET
ejpam-3129	42	2	finsler	finsler	NOUN
ejpam-3129	42	3	structure	structure	NOUN
ejpam-3129	42	4	on	on	ADP
ejpam-3129	42	5	m	m	PROPN
ejpam-3129	42	6	is	be	AUX
ejpam-3129	42	7	a	a	DET
ejpam-3129	42	8	map	map	NOUN
ejpam-3129	42	9	f	f	NOUN
ejpam-3129	42	10	:	:	PUNCT
ejpam-3129	42	11	tm	tm	PROPN
ejpam-3129	42	12	−→	−→	PROPN
ejpam-3129	42	13	[	[	X
ejpam-3129	42	14	0,∞	0,∞	NOUN
ejpam-3129	42	15	)	)	PUNCT
ejpam-3129	42	16	which	which	PRON
ejpam-3129	42	17	has	have	VERB
ejpam-3129	42	18	the	the	DET
ejpam-3129	42	19	following	follow	VERB
ejpam-3129	42	20	properties	property	NOUN
ejpam-3129	42	21	[	[	X
ejpam-3129	42	22	1	1	NUM
ejpam-3129	42	23	]	]	X
ejpam-3129	42	24	:	:	PUNCT
ejpam-3129	42	25	(	(	PUNCT
ejpam-3129	42	26	i	i	NOUN
ejpam-3129	42	27	)	)	PUNCT
ejpam-3129	42	28	f	f	PROPN
ejpam-3129	42	29	is	be	AUX
ejpam-3129	42	30	smooth	smooth	ADJ
ejpam-3129	42	31	on	on	ADP
ejpam-3129	42	32	t̃m	t̃m	NOUN
ejpam-3129	42	33	:	:	PUNCT
ejpam-3129	42	34	=	=	SYM
ejpam-3129	42	35	tm\{0	tm\{0	ADJ
ejpam-3129	42	36	}	}	PUNCT
ejpam-3129	42	37	.	.	PUNCT
ejpam-3129	43	1	(	(	PUNCT
ejpam-3129	43	2	ii	ii	X
ejpam-3129	43	3	)	)	PUNCT
ejpam-3129	43	4	f	f	NOUN
ejpam-3129	43	5	(	(	PUNCT
ejpam-3129	43	6	x	x	NOUN
ejpam-3129	43	7	,	,	PUNCT
ejpam-3129	43	8	λy	λy	PROPN
ejpam-3129	43	9	)	)	PUNCT
ejpam-3129	44	1	=	=	SYM
ejpam-3129	44	2	λf	λf	X
ejpam-3129	44	3	(	(	PUNCT
ejpam-3129	44	4	x	x	NOUN
ejpam-3129	44	5	,	,	PUNCT
ejpam-3129	44	6	y	y	PROPN
ejpam-3129	44	7	)	)	PUNCT
ejpam-3129	44	8	,	,	PUNCT
ejpam-3129	44	9	for	for	ADP
ejpam-3129	44	10	any	any	DET
ejpam-3129	44	11	x	x	SYM
ejpam-3129	44	12	∈m	∈m	NOUN
ejpam-3129	44	13	,	,	PUNCT
ejpam-3129	44	14	y	y	PROPN
ejpam-3129	44	15	∈	∈	PROPN
ejpam-3129	44	16	txm	txm	PROPN
ejpam-3129	44	17	and	and	CCONJ
ejpam-3129	44	18	λ	λ	X
ejpam-3129	44	19	>	>	X
ejpam-3129	44	20	0	0	NUM
ejpam-3129	44	21	.	.	PUNCT
ejpam-3129	45	1	(	(	PUNCT
ejpam-3129	45	2	iii	iii	X
ejpam-3129	45	3	)	)	PUNCT
ejpam-3129	45	4	f	f	NOUN
ejpam-3129	45	5	2	2	NUM
ejpam-3129	45	6	is	be	AUX
ejpam-3129	45	7	strongly	strongly	ADV
ejpam-3129	45	8	convex	convex	ADJ
ejpam-3129	45	9	,	,	PUNCT
ejpam-3129	45	10	i.e.	i.e.	X
ejpam-3129	45	11	,	,	PUNCT
ejpam-3129	45	12	gij(x	gij(x	PROPN
ejpam-3129	45	13	,	,	PUNCT
ejpam-3129	45	14	y	y	NOUN
ejpam-3129	45	15	)	)	PUNCT
ejpam-3129	45	16	:	:	PUNCT
ejpam-3129	46	1	=	=	SYM
ejpam-3129	46	2	1	1	NUM
ejpam-3129	46	3	2	2	NUM
ejpam-3129	46	4	∂2f	∂2f	VERB
ejpam-3129	46	5	2	2	NUM
ejpam-3129	46	6	∂yi∂yj	∂yi∂yj	NOUN
ejpam-3129	46	7	(	(	PUNCT
ejpam-3129	46	8	x	x	NOUN
ejpam-3129	46	9	,	,	PUNCT
ejpam-3129	46	10	y	y	NOUN
ejpam-3129	46	11	)	)	PUNCT
ejpam-3129	46	12	is	be	AUX
ejpam-3129	46	13	positive	positive	ADJ
ejpam-3129	46	14	definite	definite	ADJ
ejpam-3129	46	15	for	for	SCONJ
ejpam-3129	46	16	all	all	PRON
ejpam-3129	46	17	(	(	PUNCT
ejpam-3129	46	18	x	x	NOUN
ejpam-3129	46	19	,	,	PUNCT
ejpam-3129	46	20	y	y	NOUN
ejpam-3129	46	21	)	)	PUNCT
ejpam-3129	46	22	∈	∈	PROPN
ejpam-3129	46	23	t̃m	t̃m	NOUN
ejpam-3129	46	24	.	.	PUNCT
ejpam-3129	47	1	let	let	VERB
ejpam-3129	47	2	v	v	NOUN
ejpam-3129	47	3	=	=	PUNCT
ejpam-3129	47	4	vi∂/∂xi	vi∂/∂xi	NOUN
ejpam-3129	47	5	be	be	AUX
ejpam-3129	47	6	a	a	DET
ejpam-3129	47	7	non	non	ADJ
ejpam-3129	47	8	-	-	ADJ
ejpam-3129	47	9	vanishing	vanishing	ADJ
ejpam-3129	47	10	vector	vector	NOUN
ejpam-3129	47	11	field	field	NOUN
ejpam-3129	47	12	on	on	ADP
ejpam-3129	47	13	an	an	DET
ejpam-3129	47	14	open	open	ADJ
ejpam-3129	47	15	subset	subset	NOUN
ejpam-3129	47	16	u	u	NOUN
ejpam-3129	47	17	⊂	⊂	PROPN
ejpam-3129	47	18	m	m	PROPN
ejpam-3129	47	19	.	.	PUNCT
ejpam-3129	48	1	one	one	PRON
ejpam-3129	48	2	can	can	AUX
ejpam-3129	48	3	introduce	introduce	VERB
ejpam-3129	48	4	a	a	DET
ejpam-3129	48	5	riemannian	riemannian	ADJ
ejpam-3129	48	6	metric	metric	NOUN
ejpam-3129	48	7	gv	gv	ADP
ejpam-3129	48	8	and	and	CCONJ
ejpam-3129	48	9	a	a	DET
ejpam-3129	48	10	linear	linear	ADJ
ejpam-3129	48	11	connection	connection	NOUN
ejpam-3129	48	12	∇v	∇v	ADV
ejpam-3129	48	13	on	on	ADP
ejpam-3129	48	14	the	the	DET
ejpam-3129	48	15	tangent	tangent	NOUN
ejpam-3129	48	16	bundle	bundle	NOUN
ejpam-3129	48	17	over	over	ADP
ejpam-3129	48	18	u	u	NOUN
ejpam-3129	48	19	as	as	ADP
ejpam-3129	48	20	following	follow	VERB
ejpam-3129	48	21	[	[	X
ejpam-3129	48	22	1	1	NUM
ejpam-3129	48	23	]	]	PUNCT
ejpam-3129	48	24	:	:	PUNCT
ejpam-3129	48	25	gv	gv	ADP
ejpam-3129	48	26	(	(	PUNCT
ejpam-3129	48	27	x	x	X
ejpam-3129	48	28	,	,	PUNCT
ejpam-3129	48	29	y	y	PROPN
ejpam-3129	48	30	)	)	PUNCT
ejpam-3129	48	31	=	=	PUNCT
ejpam-3129	49	1	xiy	xiy	PROPN
ejpam-3129	49	2	jgij(x	jgij(x	PROPN
ejpam-3129	49	3	,	,	PUNCT
ejpam-3129	49	4	v	v	NOUN
ejpam-3129	49	5	)	)	PUNCT
ejpam-3129	49	6	,	,	PUNCT
ejpam-3129	49	7	∀x	∀x	X
ejpam-3129	49	8	=	=	SYM
ejpam-3129	49	9	xi	xi	X
ejpam-3129	49	10	∂	∂	NUM
ejpam-3129	49	11	∂xi	∂xi	PROPN
ejpam-3129	49	12	,	,	PUNCT
ejpam-3129	49	13	y	y	PROPN
ejpam-3129	49	14	=	=	SYM
ejpam-3129	49	15	y	y	PROPN
ejpam-3129	49	16	i	i	PROPN
ejpam-3129	49	17	∂	∂	NUM
ejpam-3129	49	18	∂xi	∂xi	NOUN
ejpam-3129	49	19	,	,	PUNCT
ejpam-3129	49	20	∇v∂	∇v∂	NOUN
ejpam-3129	49	21	∂xi	∂xi	PROPN
ejpam-3129	49	22	∂	∂	NUM
ejpam-3129	49	23	∂xj	∂xj	NOUN
ejpam-3129	49	24	=	=	SYM
ejpam-3129	49	25	γkij(x	γkij(x	PROPN
ejpam-3129	49	26	,	,	PUNCT
ejpam-3129	49	27	v	v	NOUN
ejpam-3129	49	28	)	)	PUNCT
ejpam-3129	49	29	∂	∂	NOUN
ejpam-3129	49	30	∂xk	∂xk	PROPN
ejpam-3129	49	31	.	.	PUNCT
ejpam-3129	50	1	from	from	ADP
ejpam-3129	50	2	the	the	DET
ejpam-3129	50	3	torsion	torsion	NOUN
ejpam-3129	50	4	freeness	freeness	NOUN
ejpam-3129	50	5	and	and	CCONJ
ejpam-3129	50	6	g−compatibility	g−compatibility	PROPN
ejpam-3129	50	7	of	of	ADP
ejpam-3129	50	8	chern	chern	PROPN
ejpam-3129	50	9	connection	connection	NOUN
ejpam-3129	50	10	we	we	PRON
ejpam-3129	50	11	have	have	VERB
ejpam-3129	50	12	∇vxy	∇vxy	NOUN
ejpam-3129	50	13	−∇vyx	−∇vyx	ADV
ejpam-3129	50	14	=	=	PUNCT
ejpam-3129	51	1	[	[	X
ejpam-3129	51	2	x	x	X
ejpam-3129	51	3	,	,	PUNCT
ejpam-3129	51	4	y	y	PROPN
ejpam-3129	51	5	]	]	PUNCT
ejpam-3129	51	6	,	,	PUNCT
ejpam-3129	51	7	p.	p.	PROPN
ejpam-3129	51	8	bahmandoust	bahmandoust	NOUN
ejpam-3129	51	9	,	,	PUNCT
ejpam-3129	51	10	d.	d.	PROPN
ejpam-3129	51	11	latifi	latifi	PROPN
ejpam-3129	51	12	/	/	SYM
ejpam-3129	51	13	eur	eur	PROPN
ejpam-3129	51	14	.	.	PUNCT
ejpam-3129	52	1	j.	j.	PROPN
ejpam-3129	52	2	pure	pure	PROPN
ejpam-3129	52	3	appl	appl	PROPN
ejpam-3129	52	4	.	.	PROPN
ejpam-3129	52	5	math	math	PROPN
ejpam-3129	52	6	,	,	PUNCT
ejpam-3129	52	7	10	10	NUM
ejpam-3129	52	8	(	(	PUNCT
ejpam-3129	52	9	5	5	NUM
ejpam-3129	52	10	)	)	PUNCT
ejpam-3129	52	11	(	(	PUNCT
ejpam-3129	52	12	2017	2017	NUM
ejpam-3129	52	13	)	)	PUNCT
ejpam-3129	52	14	,	,	PUNCT
ejpam-3129	52	15	1099	1099	NUM
ejpam-3129	52	16	-	-	SYM
ejpam-3129	52	17	1111	1111	NUM
ejpam-3129	52	18	1101	1101	NUM
ejpam-3129	52	19	xgv	xgv	NOUN
ejpam-3129	52	20	(	(	PUNCT
ejpam-3129	52	21	y	y	NOUN
ejpam-3129	52	22	,	,	PUNCT
ejpam-3129	52	23	z	z	NOUN
ejpam-3129	52	24	)	)	PUNCT
ejpam-3129	52	25	=	=	SYM
ejpam-3129	52	26	gv	gv	X
ejpam-3129	52	27	(	(	PUNCT
ejpam-3129	52	28	∇vxy	∇vxy	NOUN
ejpam-3129	52	29	,	,	PUNCT
ejpam-3129	52	30	z	z	NOUN
ejpam-3129	52	31	)	)	PUNCT
ejpam-3129	53	1	+	+	CCONJ
ejpam-3129	53	2	gv	gv	ADP
ejpam-3129	53	3	(	(	PUNCT
ejpam-3129	53	4	y,∇vxz	y,∇vxz	NOUN
ejpam-3129	53	5	)	)	PUNCT
ejpam-3129	53	6	+	+	CCONJ
ejpam-3129	53	7	2cv	2cv	ADJ
ejpam-3129	53	8	(	(	PUNCT
ejpam-3129	53	9	∇vxv	∇vxv	NOUN
ejpam-3129	53	10	,	,	PUNCT
ejpam-3129	53	11	y	y	PROPN
ejpam-3129	53	12	,	,	PUNCT
ejpam-3129	53	13	z	z	NOUN
ejpam-3129	53	14	)	)	PUNCT
ejpam-3129	53	15	,	,	PUNCT
ejpam-3129	53	16	where	where	SCONJ
ejpam-3129	53	17	cv	cv	PROPN
ejpam-3129	53	18	is	be	AUX
ejpam-3129	53	19	the	the	DET
ejpam-3129	53	20	cartan	cartan	PROPN
ejpam-3129	53	21	tensor	tensor	NOUN
ejpam-3129	53	22	defined	define	VERB
ejpam-3129	53	23	by	by	ADP
ejpam-3129	53	24	cv	cv	PROPN
ejpam-3129	53	25	(	(	PUNCT
ejpam-3129	53	26	x	x	PROPN
ejpam-3129	53	27	,	,	PUNCT
ejpam-3129	53	28	y	y	PROPN
ejpam-3129	53	29	,	,	PUNCT
ejpam-3129	53	30	z	z	NOUN
ejpam-3129	53	31	)	)	PUNCT
ejpam-3129	53	32	=	=	SYM
ejpam-3129	53	33	xiy	xiy	PROPN
ejpam-3129	53	34	jzkcijk(x	jzkcijk(x	PROPN
ejpam-3129	53	35	,	,	PUNCT
ejpam-3129	53	36	v	v	NOUN
ejpam-3129	53	37	)	)	PUNCT
ejpam-3129	53	38	,	,	PUNCT
ejpam-3129	53	39	cijk(x	cijk(x	PROPN
ejpam-3129	53	40	,	,	PUNCT
ejpam-3129	53	41	v	v	NOUN
ejpam-3129	53	42	)	)	PUNCT
ejpam-3129	53	43	=	=	SYM
ejpam-3129	53	44	1	1	NUM
ejpam-3129	53	45	4	4	NUM
ejpam-3129	53	46	∂3f	∂3f	NOUN
ejpam-3129	53	47	2(x	2(x	NUM
ejpam-3129	53	48	,	,	PUNCT
ejpam-3129	53	49	v	v	NOUN
ejpam-3129	53	50	)	)	PUNCT
ejpam-3129	54	1	∂yi∂yj∂yk	∂yi∂yj∂yk	NOUN
ejpam-3129	54	2	,	,	PUNCT
ejpam-3129	54	3	and	and	CCONJ
ejpam-3129	54	4	it	it	PRON
ejpam-3129	54	5	satisfies	satisfy	VERB
ejpam-3129	54	6	cv	cv	PROPN
ejpam-3129	54	7	(	(	PUNCT
ejpam-3129	54	8	v	v	NOUN
ejpam-3129	54	9	,	,	PUNCT
ejpam-3129	54	10	x	x	NOUN
ejpam-3129	54	11	,	,	PUNCT
ejpam-3129	54	12	y	y	PROPN
ejpam-3129	54	13	)	)	PUNCT
ejpam-3129	55	1	=	=	PUNCT
ejpam-3129	55	2	0	0	X
ejpam-3129	55	3	.	.	PUNCT
ejpam-3129	55	4	given	give	VERB
ejpam-3129	55	5	a	a	DET
ejpam-3129	55	6	nonzero	nonzero	ADJ
ejpam-3129	55	7	vector	vector	NOUN
ejpam-3129	55	8	field	field	NOUN
ejpam-3129	55	9	v	v	NOUN
ejpam-3129	55	10	on	on	ADP
ejpam-3129	55	11	a	a	DET
ejpam-3129	55	12	finsler	finsler	NOUN
ejpam-3129	55	13	manifold	manifold	NOUN
ejpam-3129	55	14	(	(	PUNCT
ejpam-3129	55	15	m	m	PROPN
ejpam-3129	55	16	,	,	PUNCT
ejpam-3129	55	17	f	f	PROPN
ejpam-3129	55	18	)	)	PUNCT
ejpam-3129	55	19	with	with	ADP
ejpam-3129	55	20	connection	connection	NOUN
ejpam-3129	55	21	∇v	∇v	PROPN
ejpam-3129	55	22	,	,	PUNCT
ejpam-3129	55	23	one	one	PRON
ejpam-3129	55	24	can	can	AUX
ejpam-3129	55	25	consider	consider	VERB
ejpam-3129	55	26	the	the	DET
ejpam-3129	55	27	curvature	curvature	NOUN
ejpam-3129	55	28	tensor	tensor	NOUN
ejpam-3129	55	29	rv	rv	NOUN
ejpam-3129	55	30	defined	define	VERB
ejpam-3129	55	31	by	by	ADP
ejpam-3129	55	32	rv	rv	PROPN
ejpam-3129	55	33	(	(	PUNCT
ejpam-3129	55	34	x	x	PROPN
ejpam-3129	55	35	,	,	PUNCT
ejpam-3129	55	36	y	y	NOUN
ejpam-3129	55	37	)	)	PUNCT
ejpam-3129	55	38	z	z	NOUN
ejpam-3129	56	1	=	=	PUNCT
ejpam-3129	56	2	∇vx∇vy	∇vx∇vy	PROPN
ejpam-3129	56	3	z	z	AUX
ejpam-3129	56	4	−∇vy∇vxz	−∇vy∇vxz	VERB
ejpam-3129	56	5	−∇v[x	−∇v[x	NOUN
ejpam-3129	56	6	,	,	PUNCT
ejpam-3129	56	7	y	y	PROPN
ejpam-3129	56	8	]	]	X
ejpam-3129	56	9	z.	z.	PROPN
ejpam-3129	56	10	for	for	ADP
ejpam-3129	56	11	a	a	DET
ejpam-3129	56	12	flag	flag	NOUN
ejpam-3129	56	13	(	(	PUNCT
ejpam-3129	56	14	v	v	NOUN
ejpam-3129	56	15	,	,	PUNCT
ejpam-3129	56	16	σ	σ	PROPN
ejpam-3129	56	17	)	)	PUNCT
ejpam-3129	56	18	consisting	consist	VERB
ejpam-3129	56	19	of	of	ADP
ejpam-3129	56	20	a	a	DET
ejpam-3129	56	21	nonzero	nonzero	ADJ
ejpam-3129	56	22	tangent	tangent	NOUN
ejpam-3129	56	23	vector	vector	NOUN
ejpam-3129	56	24	v	v	PROPN
ejpam-3129	56	25	∈	∈	PROPN
ejpam-3129	56	26	txm	txm	PROPN
ejpam-3129	56	27	and	and	CCONJ
ejpam-3129	56	28	a	a	DET
ejpam-3129	56	29	plane	plane	NOUN
ejpam-3129	56	30	σ	σ	PROPN
ejpam-3129	56	31	⊂	⊂	PROPN
ejpam-3129	56	32	txm	txm	PROPN
ejpam-3129	56	33	spanned	span	VERB
ejpam-3129	56	34	by	by	ADP
ejpam-3129	56	35	the	the	DET
ejpam-3129	56	36	tangent	tangent	NOUN
ejpam-3129	56	37	vectors	vector	NOUN
ejpam-3129	56	38	v	v	ADP
ejpam-3129	56	39	,	,	PUNCT
ejpam-3129	56	40	w	w	PROPN
ejpam-3129	56	41	,	,	PUNCT
ejpam-3129	56	42	the	the	DET
ejpam-3129	56	43	flag	flag	NOUN
ejpam-3129	56	44	curvature	curvature	NOUN
ejpam-3129	56	45	is	be	AUX
ejpam-3129	56	46	defined	define	VERB
ejpam-3129	56	47	as	as	ADP
ejpam-3129	56	48	k(v	k(v	PROPN
ejpam-3129	56	49	,	,	PUNCT
ejpam-3129	56	50	σ	σ	PROPN
ejpam-3129	56	51	)	)	PUNCT
ejpam-3129	56	52	=	=	SYM
ejpam-3129	57	1	k(v	k(v	PROPN
ejpam-3129	57	2	,	,	PUNCT
ejpam-3129	57	3	w	w	NOUN
ejpam-3129	57	4	)	)	PUNCT
ejpam-3129	57	5	=	=	SYM
ejpam-3129	58	1	gv	gv	X
ejpam-3129	58	2	(	(	PUNCT
ejpam-3129	58	3	rv	rv	PROPN
ejpam-3129	58	4	(	(	PUNCT
ejpam-3129	58	5	v	v	NOUN
ejpam-3129	58	6	,	,	PUNCT
ejpam-3129	58	7	w	w	NOUN
ejpam-3129	58	8	)	)	PUNCT
ejpam-3129	58	9	w	w	PROPN
ejpam-3129	58	10	,	,	PUNCT
ejpam-3129	58	11	v	v	NOUN
ejpam-3129	58	12	)	)	PUNCT
ejpam-3129	58	13	gv	gv	ADP
ejpam-3129	58	14	(	(	PUNCT
ejpam-3129	58	15	v	v	NOUN
ejpam-3129	58	16	,	,	PUNCT
ejpam-3129	58	17	v	v	NOUN
ejpam-3129	58	18	)	)	PUNCT
ejpam-3129	58	19	gv	gv	ADP
ejpam-3129	58	20	(	(	PUNCT
ejpam-3129	58	21	w	w	PROPN
ejpam-3129	58	22	,	,	PUNCT
ejpam-3129	58	23	w	w	NOUN
ejpam-3129	58	24	)	)	PUNCT
ejpam-3129	58	25	−	−	NOUN
ejpam-3129	58	26	gv	gv	ADP
ejpam-3129	58	27	(	(	PUNCT
ejpam-3129	58	28	v	v	NOUN
ejpam-3129	58	29	,	,	PUNCT
ejpam-3129	58	30	w	w	NOUN
ejpam-3129	58	31	)	)	PUNCT
ejpam-3129	58	32	2	2	NUM
ejpam-3129	58	33	.	.	PUNCT
ejpam-3129	59	1	in	in	ADP
ejpam-3129	59	2	the	the	DET
ejpam-3129	59	3	riemannian	riemannian	ADJ
ejpam-3129	59	4	case	case	NOUN
ejpam-3129	59	5	the	the	DET
ejpam-3129	59	6	flag	flag	NOUN
ejpam-3129	59	7	curvature	curvature	NOUN
ejpam-3129	59	8	is	be	AUX
ejpam-3129	59	9	the	the	DET
ejpam-3129	59	10	sectional	sectional	ADJ
ejpam-3129	59	11	curvature	curvature	NOUN
ejpam-3129	59	12	of	of	ADP
ejpam-3129	59	13	the	the	DET
ejpam-3129	59	14	plane	plane	NOUN
ejpam-3129	59	15	σ	σ	PROPN
ejpam-3129	59	16	and	and	CCONJ
ejpam-3129	59	17	does	do	AUX
ejpam-3129	59	18	not	not	PART
ejpam-3129	59	19	depend	depend	VERB
ejpam-3129	59	20	on	on	ADP
ejpam-3129	59	21	v	v	NOUN
ejpam-3129	59	22	.	.	PUNCT
ejpam-3129	60	1	a	a	DET
ejpam-3129	60	2	diffeomorphism	diffeomorphism	NOUN
ejpam-3129	60	3	,	,	PUNCT
ejpam-3129	60	4	ϕ	ϕ	NOUN
ejpam-3129	60	5	:	:	PUNCT
ejpam-3129	60	6	m	m	VERB
ejpam-3129	60	7	−→m	−→m	INTJ
ejpam-3129	60	8	,	,	PUNCT
ejpam-3129	60	9	is	be	AUX
ejpam-3129	60	10	an	an	DET
ejpam-3129	60	11	isometry	isometry	NOUN
ejpam-3129	60	12	on	on	ADP
ejpam-3129	60	13	a	a	DET
ejpam-3129	60	14	finsler	finsler	NOUN
ejpam-3129	60	15	manifold	manifold	NOUN
ejpam-3129	60	16	(	(	PUNCT
ejpam-3129	60	17	m	m	PROPN
ejpam-3129	60	18	,	,	PUNCT
ejpam-3129	60	19	f	f	PROPN
ejpam-3129	60	20	)	)	PUNCT
ejpam-3129	60	21	if	if	SCONJ
ejpam-3129	60	22	it	it	PRON
ejpam-3129	60	23	preserves	preserve	VERB
ejpam-3129	60	24	the	the	DET
ejpam-3129	60	25	finsler	finsler	NOUN
ejpam-3129	60	26	function	function	NOUN
ejpam-3129	60	27	:	:	PUNCT
ejpam-3129	60	28	f	f	PROPN
ejpam-3129	60	29	(	(	PUNCT
ejpam-3129	60	30	ϕ(x	ϕ(x	NOUN
ejpam-3129	60	31	)	)	PUNCT
ejpam-3129	60	32	,	,	PUNCT
ejpam-3129	60	33	dϕx(x	dϕx(x	PROPN
ejpam-3129	60	34	)	)	PUNCT
ejpam-3129	60	35	)	)	PUNCT
ejpam-3129	61	1	=	=	SYM
ejpam-3129	61	2	f	f	X
ejpam-3129	61	3	(	(	PUNCT
ejpam-3129	61	4	x	x	X
ejpam-3129	61	5	,	,	PUNCT
ejpam-3129	61	6	x	x	X
ejpam-3129	61	7	)	)	PUNCT
ejpam-3129	61	8	∀x	∀x	X
ejpam-3129	61	9	∈m	∈m	NOUN
ejpam-3129	61	10	,	,	PUNCT
ejpam-3129	61	11	x	x	PROPN
ejpam-3129	61	12	∈	∈	PROPN
ejpam-3129	61	13	txm	txm	PROPN
ejpam-3129	61	14	.	.	PUNCT
ejpam-3129	61	15	by	by	ADP
ejpam-3129	61	16	the	the	DET
ejpam-3129	61	17	classical	classical	ADJ
ejpam-3129	61	18	dantzing	dantzing	ADJ
ejpam-3129	61	19	-	-	PUNCT
ejpam-3129	61	20	van	van	PROPN
ejpam-3129	61	21	der	der	NOUN
ejpam-3129	61	22	waereden	waereden	PROPN
ejpam-3129	61	23	theorem	theorem	NOUN
ejpam-3129	61	24	(	(	PUNCT
ejpam-3129	61	25	[	[	X
ejpam-3129	61	26	10]vol	10]vol	NUM
ejpam-3129	61	27	i	i	NOUN
ejpam-3129	61	28	,	,	PUNCT
ejpam-3129	61	29	chapter	chapter	NOUN
ejpam-3129	61	30	i	i	PROPN
ejpam-3129	61	31	,	,	PUNCT
ejpam-3129	61	32	theorem	theorem	VERB
ejpam-3129	61	33	4.7	4.7	NUM
ejpam-3129	61	34	)	)	PUNCT
ejpam-3129	61	35	and	and	CCONJ
ejpam-3129	61	36	the	the	DET
ejpam-3129	61	37	montgomeryzippin	montgomeryzippin	NOUN
ejpam-3129	61	38	theorem	theorem	NOUN
ejpam-3129	61	39	(	(	PUNCT
ejpam-3129	61	40	[	[	X
ejpam-3129	61	41	10],vol	10],vol	NUM
ejpam-3129	61	42	i	i	NOUN
ejpam-3129	61	43	,	,	PUNCT
ejpam-3129	61	44	chapter	chapter	NOUN
ejpam-3129	61	45	i	i	PROPN
ejpam-3129	61	46	,	,	PUNCT
ejpam-3129	61	47	theorem	theorem	VERB
ejpam-3129	61	48	4.6	4.6	NUM
ejpam-3129	61	49	)	)	PUNCT
ejpam-3129	61	50	,	,	PUNCT
ejpam-3129	61	51	the	the	DET
ejpam-3129	61	52	group	group	NOUN
ejpam-3129	61	53	of	of	ADP
ejpam-3129	61	54	isometries	isometry	NOUN
ejpam-3129	61	55	on	on	ADP
ejpam-3129	61	56	a	a	DET
ejpam-3129	61	57	connected	connected	ADJ
ejpam-3129	61	58	finsler	finsler	NOUN
ejpam-3129	61	59	manifold	manifold	ADJ
ejpam-3129	61	60	form	form	NOUN
ejpam-3129	61	61	a	a	DET
ejpam-3129	61	62	lie	lie	NOUN
ejpam-3129	61	63	group	group	NOUN
ejpam-3129	61	64	.	.	PUNCT
ejpam-3129	62	1	strictly	strictly	ADV
ejpam-3129	62	2	speaking	speak	VERB
ejpam-3129	62	3	,	,	PUNCT
ejpam-3129	62	4	these	these	DET
ejpam-3129	62	5	theorems	theorem	NOUN
ejpam-3129	62	6	prove	prove	VERB
ejpam-3129	62	7	the	the	DET
ejpam-3129	62	8	statement	statement	NOUN
ejpam-3129	62	9	for	for	ADP
ejpam-3129	62	10	absolute	absolute	ADJ
ejpam-3129	62	11	homogeneous	homogeneous	ADJ
ejpam-3129	62	12	finsler	finsler	NOUN
ejpam-3129	62	13	functions	function	NOUN
ejpam-3129	62	14	.	.	PUNCT
ejpam-3129	63	1	for	for	ADP
ejpam-3129	63	2	positive	positive	ADJ
ejpam-3129	63	3	homogeneous	homogeneous	ADJ
ejpam-3129	63	4	finsler	finsler	NOUN
ejpam-3129	63	5	functions	function	NOUN
ejpam-3129	63	6	consider	consider	VERB
ejpam-3129	63	7	the	the	DET
ejpam-3129	63	8	metric	metric	ADJ
ejpam-3129	63	9	,	,	PUNCT
ejpam-3129	63	10	d∗	d∗	PROPN
ejpam-3129	63	11	,	,	PUNCT
ejpam-3129	63	12	defined	define	VERB
ejpam-3129	63	13	by	by	ADP
ejpam-3129	63	14	the	the	DET
ejpam-3129	63	15	function	function	NOUN
ejpam-3129	63	16	f	f	PROPN
ejpam-3129	63	17	∗(x	∗(x	PROPN
ejpam-3129	63	18	)	)	PUNCT
ejpam-3129	64	1	=	=	SYM
ejpam-3129	64	2	f	f	X
ejpam-3129	64	3	(	(	PUNCT
ejpam-3129	64	4	x	x	X
ejpam-3129	64	5	)	)	PUNCT
ejpam-3129	65	1	+	+	NUM
ejpam-3129	65	2	f	f	X
ejpam-3129	65	3	(	(	PUNCT
ejpam-3129	65	4	−x	−x	NOUN
ejpam-3129	65	5	)	)	PUNCT
ejpam-3129	65	6	then	then	ADV
ejpam-3129	65	7	the	the	DET
ejpam-3129	65	8	g	g	PROPN
ejpam-3129	65	9	is	be	AUX
ejpam-3129	65	10	a	a	DET
ejpam-3129	65	11	closed	closed	ADJ
ejpam-3129	65	12	subgroup	subgroup	NOUN
ejpam-3129	65	13	of	of	ADP
ejpam-3129	65	14	g∗	g∗	PROPN
ejpam-3129	65	15	defined	define	VERB
ejpam-3129	65	16	for	for	ADP
ejpam-3129	65	17	d∗.	d∗.	PROPN
ejpam-3129	65	18	thus	thus	ADV
ejpam-3129	65	19	both	both	DET
ejpam-3129	65	20	groups	group	NOUN
ejpam-3129	65	21	are	be	AUX
ejpam-3129	65	22	lie	lie	NOUN
ejpam-3129	65	23	groups	group	NOUN
ejpam-3129	65	24	[	[	X
ejpam-3129	65	25	22	22	NUM
ejpam-3129	65	26	]	]	PUNCT
ejpam-3129	65	27	.	.	PUNCT
ejpam-3129	66	1	3	3	X
ejpam-3129	66	2	.	.	X
ejpam-3129	66	3	finsler	finsler	NOUN
ejpam-3129	66	4	s	s	NOUN
ejpam-3129	66	5	-	-	PUNCT
ejpam-3129	66	6	manifolds	manifolds	ADJ
ejpam-3129	66	7	affine	affine	NOUN
ejpam-3129	66	8	and	and	CCONJ
ejpam-3129	66	9	riemmannian	riemmannian	ADJ
ejpam-3129	66	10	s−manifolds	s−manifolds	PROPN
ejpam-3129	66	11	were	be	AUX
ejpam-3129	66	12	first	first	ADV
ejpam-3129	66	13	defined	define	VERB
ejpam-3129	66	14	in	in	ADP
ejpam-3129	66	15	[	[	X
ejpam-3129	66	16	18	18	NUM
ejpam-3129	66	17	]	]	PUNCT
ejpam-3129	66	18	following	follow	VERB
ejpam-3129	66	19	the	the	DET
ejpam-3129	66	20	introduction	introduction	NOUN
ejpam-3129	66	21	of	of	ADP
ejpam-3129	66	22	generalized	generalized	ADJ
ejpam-3129	66	23	riemannian	riemannian	ADJ
ejpam-3129	66	24	spaces	space	NOUN
ejpam-3129	66	25	in	in	ADP
ejpam-3129	66	26	[	[	X
ejpam-3129	66	27	19	19	NUM
ejpam-3129	66	28	]	]	PUNCT
ejpam-3129	66	29	.	.	PUNCT
ejpam-3129	67	1	they	they	PRON
ejpam-3129	67	2	form	form	VERB
ejpam-3129	67	3	a	a	DET
ejpam-3129	67	4	more	more	ADV
ejpam-3129	67	5	general	general	ADJ
ejpam-3129	67	6	class	class	NOUN
ejpam-3129	67	7	than	than	ADP
ejpam-3129	67	8	the	the	DET
ejpam-3129	67	9	symmetric	symmetric	ADJ
ejpam-3129	67	10	spaces	space	NOUN
ejpam-3129	67	11	of	of	ADP
ejpam-3129	67	12	e.	e.	PROPN
ejpam-3129	67	13	cartan	cartan	PROPN
ejpam-3129	67	14	.	.	PUNCT
ejpam-3129	68	1	let	let	VERB
ejpam-3129	68	2	(	(	PUNCT
ejpam-3129	68	3	m	m	NOUN
ejpam-3129	68	4	,	,	PUNCT
ejpam-3129	68	5	g	g	NOUN
ejpam-3129	68	6	)	)	PUNCT
ejpam-3129	68	7	be	be	VERB
ejpam-3129	68	8	a	a	DET
ejpam-3129	68	9	connected	connect	VERB
ejpam-3129	68	10	riemannian	riemannian	ADJ
ejpam-3129	68	11	manifold	manifold	NOUN
ejpam-3129	68	12	.	.	PUNCT
ejpam-3129	69	1	a	a	DET
ejpam-3129	69	2	symmetry	symmetry	NOUN
ejpam-3129	69	3	at	at	ADP
ejpam-3129	69	4	x	x	PROPN
ejpam-3129	69	5	∈	∈	PROPN
ejpam-3129	69	6	m	m	NOUN
ejpam-3129	69	7	is	be	AUX
ejpam-3129	69	8	a	a	DET
ejpam-3129	69	9	isometry	isometry	NOUN
ejpam-3129	69	10	of	of	ADP
ejpam-3129	69	11	(	(	PUNCT
ejpam-3129	69	12	m	m	PROPN
ejpam-3129	69	13	,	,	PUNCT
ejpam-3129	69	14	g	g	NOUN
ejpam-3129	69	15	)	)	PUNCT
ejpam-3129	69	16	for	for	ADP
ejpam-3129	69	17	which	which	PRON
ejpam-3129	69	18	x	x	PRON
ejpam-3129	69	19	is	be	AUX
ejpam-3129	69	20	an	an	DET
ejpam-3129	69	21	isolated	isolated	ADJ
ejpam-3129	69	22	fixed	fix	VERB
ejpam-3129	69	23	point	point	NOUN
ejpam-3129	69	24	.	.	PUNCT
ejpam-3129	70	1	a	a	DET
ejpam-3129	70	2	s−structure	s−structure	NOUN
ejpam-3129	70	3	on	on	ADP
ejpam-3129	70	4	(	(	PUNCT
ejpam-3129	70	5	m	m	PROPN
ejpam-3129	70	6	,	,	PUNCT
ejpam-3129	70	7	g	g	NOUN
ejpam-3129	70	8	)	)	PUNCT
ejpam-3129	70	9	is	be	AUX
ejpam-3129	70	10	a	a	DET
ejpam-3129	70	11	family	family	NOUN
ejpam-3129	70	12	{	{	PUNCT
ejpam-3129	70	13	sx}x∈m	sx}x∈m	NOUN
ejpam-3129	70	14	p.	p.	PROPN
ejpam-3129	70	15	bahmandoust	bahmandoust	NOUN
ejpam-3129	70	16	,	,	PUNCT
ejpam-3129	70	17	d.	d.	PROPN
ejpam-3129	70	18	latifi	latifi	PROPN
ejpam-3129	70	19	/	/	SYM
ejpam-3129	70	20	eur	eur	PROPN
ejpam-3129	70	21	.	.	PUNCT
ejpam-3129	71	1	j.	j.	PROPN
ejpam-3129	71	2	pure	pure	PROPN
ejpam-3129	71	3	appl	appl	PROPN
ejpam-3129	71	4	.	.	PROPN
ejpam-3129	71	5	math	math	PROPN
ejpam-3129	71	6	,	,	PUNCT
ejpam-3129	71	7	10	10	NUM
ejpam-3129	71	8	(	(	PUNCT
ejpam-3129	71	9	5	5	NUM
ejpam-3129	71	10	)	)	PUNCT
ejpam-3129	71	11	(	(	PUNCT
ejpam-3129	71	12	2017	2017	NUM
ejpam-3129	71	13	)	)	PUNCT
ejpam-3129	71	14	,	,	PUNCT
ejpam-3129	71	15	1099	1099	NUM
ejpam-3129	71	16	-	-	SYM
ejpam-3129	71	17	1111	1111	NUM
ejpam-3129	71	18	1102	1102	NUM
ejpam-3129	71	19	such	such	ADJ
ejpam-3129	71	20	that	that	SCONJ
ejpam-3129	71	21	sx	sx	PROPN
ejpam-3129	71	22	is	be	AUX
ejpam-3129	71	23	a	a	DET
ejpam-3129	71	24	symmetry	symmetry	NOUN
ejpam-3129	71	25	at	at	ADP
ejpam-3129	71	26	x	x	PROPN
ejpam-3129	71	27	∈	∈	PROPN
ejpam-3129	71	28	m	m	VERB
ejpam-3129	71	29	,	,	PUNCT
ejpam-3129	71	30	for	for	ADP
ejpam-3129	71	31	each	each	DET
ejpam-3129	71	32	x	x	SYM
ejpam-3129	71	33	∈	∈	PROPN
ejpam-3129	71	34	m	m	VERB
ejpam-3129	71	35	.	.	PUNCT
ejpam-3129	72	1	an	an	DET
ejpam-3129	72	2	s−structure	s−structure	NOUN
ejpam-3129	72	3	is	be	AUX
ejpam-3129	72	4	called	call	VERB
ejpam-3129	72	5	regular	regular	ADV
ejpam-3129	72	6	if	if	SCONJ
ejpam-3129	72	7	for	for	ADP
ejpam-3129	72	8	any	any	DET
ejpam-3129	72	9	two	two	NUM
ejpam-3129	72	10	points	point	NOUN
ejpam-3129	72	11	x	x	X
ejpam-3129	72	12	,	,	PUNCT
ejpam-3129	72	13	y	y	PROPN
ejpam-3129	72	14	∈m	∈m	NOUN
ejpam-3129	72	15	sx	sx	PROPN
ejpam-3129	72	16	◦	◦	NOUN
ejpam-3129	72	17	sy	sy	NOUN
ejpam-3129	72	18	=	=	SYM
ejpam-3129	72	19	sz	sz	PROPN
ejpam-3129	72	20	◦	◦	PROPN
ejpam-3129	72	21	sx	sx	PROPN
ejpam-3129	72	22	,	,	PUNCT
ejpam-3129	72	23	z	z	NOUN
ejpam-3129	72	24	=	=	SYM
ejpam-3129	72	25	sx(y	sx(y	NOUN
ejpam-3129	72	26	)	)	PUNCT
ejpam-3129	72	27	.	.	PUNCT
ejpam-3129	73	1	if	if	SCONJ
ejpam-3129	73	2	{	{	PUNCT
ejpam-3129	73	3	sx}x∈m	sx}x∈m	INTJ
ejpam-3129	73	4	is	be	AUX
ejpam-3129	73	5	regular	regular	ADJ
ejpam-3129	73	6	,	,	PUNCT
ejpam-3129	73	7	then	then	ADV
ejpam-3129	73	8	the	the	DET
ejpam-3129	73	9	map	map	NOUN
ejpam-3129	73	10	s	s	VERB
ejpam-3129	73	11	:	:	PUNCT
ejpam-3129	73	12	m	m	VERB
ejpam-3129	73	13	−→	−→	NOUN
ejpam-3129	73	14	i(m	i(m	NOUN
ejpam-3129	73	15	,	,	PUNCT
ejpam-3129	73	16	g	g	NOUN
ejpam-3129	73	17	)	)	PUNCT
ejpam-3129	73	18	,	,	PUNCT
ejpam-3129	73	19	x	x	PUNCT
ejpam-3129	73	20	−→	−→	NOUN
ejpam-3129	73	21	sx	sx	PROPN
ejpam-3129	73	22	is	be	AUX
ejpam-3129	73	23	always	always	ADV
ejpam-3129	73	24	c∞	c∞	ADJ
ejpam-3129	73	25	,	,	PUNCT
ejpam-3129	73	26	here	here	ADV
ejpam-3129	73	27	i(m	i(m	NOUN
ejpam-3129	73	28	,	,	PUNCT
ejpam-3129	73	29	g	g	NOUN
ejpam-3129	73	30	)	)	PUNCT
ejpam-3129	73	31	denotes	denote	VERB
ejpam-3129	73	32	the	the	DET
ejpam-3129	73	33	group	group	NOUN
ejpam-3129	73	34	of	of	ADP
ejpam-3129	73	35	isometries	isometry	NOUN
ejpam-3129	73	36	of	of	ADP
ejpam-3129	73	37	(	(	PUNCT
ejpam-3129	73	38	m	m	PROPN
ejpam-3129	73	39	,	,	PUNCT
ejpam-3129	73	40	g	g	NOUN
ejpam-3129	73	41	)	)	PUNCT
ejpam-3129	73	42	.	.	PUNCT
ejpam-3129	74	1	an	an	DET
ejpam-3129	74	2	s−structure	s−structure	NOUN
ejpam-3129	74	3	{	{	PUNCT
ejpam-3129	74	4	sx}x∈m	sx}x∈m	PRON
ejpam-3129	74	5	is	be	AUX
ejpam-3129	74	6	called	call	VERB
ejpam-3129	74	7	of	of	ADP
ejpam-3129	74	8	order	order	NOUN
ejpam-3129	74	9	k	k	NOUN
ejpam-3129	75	1	if	if	SCONJ
ejpam-3129	75	2	(	(	PUNCT
ejpam-3129	75	3	sx)k	sx)k	NOUN
ejpam-3129	75	4	=	=	PUNCT
ejpam-3129	75	5	idm	idm	NOUN
ejpam-3129	75	6	for	for	ADP
ejpam-3129	75	7	all	all	DET
ejpam-3129	75	8	x	x	SYM
ejpam-3129	75	9	∈m	∈m	NOUN
ejpam-3129	75	10	and	and	CCONJ
ejpam-3129	75	11	k	k	PROPN
ejpam-3129	75	12	is	be	AUX
ejpam-3129	75	13	the	the	DET
ejpam-3129	75	14	minimal	minimal	ADJ
ejpam-3129	75	15	number	number	NOUN
ejpam-3129	75	16	with	with	ADP
ejpam-3129	75	17	this	this	DET
ejpam-3129	75	18	property	property	NOUN
ejpam-3129	75	19	.	.	PUNCT
ejpam-3129	76	1	it	it	PRON
ejpam-3129	76	2	is	be	AUX
ejpam-3129	76	3	well	well	ADV
ejpam-3129	76	4	known	know	VERB
ejpam-3129	76	5	that	that	SCONJ
ejpam-3129	76	6	if	if	SCONJ
ejpam-3129	76	7	(	(	PUNCT
ejpam-3129	76	8	m	m	NOUN
ejpam-3129	76	9	,	,	PUNCT
ejpam-3129	76	10	g	g	NOUN
ejpam-3129	76	11	)	)	PUNCT
ejpam-3129	76	12	admits	admit	VERB
ejpam-3129	76	13	an	an	DET
ejpam-3129	76	14	s−structure	s−structure	NOUN
ejpam-3129	76	15	,	,	PUNCT
ejpam-3129	76	16	then	then	ADV
ejpam-3129	76	17	it	it	PRON
ejpam-3129	76	18	always	always	ADV
ejpam-3129	76	19	admits	admit	VERB
ejpam-3129	76	20	an	an	DET
ejpam-3129	76	21	s−structure	s−structure	NOUN
ejpam-3129	76	22	of	of	ADP
ejpam-3129	76	23	finite	finite	ADJ
ejpam-3129	76	24	order	order	NOUN
ejpam-3129	76	25	.	.	PUNCT
ejpam-3129	77	1	further	far	ADV
ejpam-3129	77	2	if	if	SCONJ
ejpam-3129	77	3	(	(	PUNCT
ejpam-3129	77	4	m	m	NOUN
ejpam-3129	77	5	,	,	PUNCT
ejpam-3129	77	6	g	g	NOUN
ejpam-3129	77	7	)	)	PUNCT
ejpam-3129	77	8	admits	admit	VERB
ejpam-3129	77	9	a	a	DET
ejpam-3129	77	10	regular	regular	ADJ
ejpam-3129	77	11	s−structure	s−structure	NOUN
ejpam-3129	77	12	,	,	PUNCT
ejpam-3129	77	13	then	then	ADV
ejpam-3129	77	14	(	(	PUNCT
ejpam-3129	77	15	m	m	PROPN
ejpam-3129	77	16	,	,	PUNCT
ejpam-3129	77	17	g	g	NOUN
ejpam-3129	77	18	)	)	PUNCT
ejpam-3129	77	19	admits	admit	VERB
ejpam-3129	77	20	a	a	DET
ejpam-3129	77	21	regular	regular	ADJ
ejpam-3129	77	22	s−structure	s−structure	NOUN
ejpam-3129	77	23	of	of	ADP
ejpam-3129	77	24	finite	finite	ADJ
ejpam-3129	77	25	order	order	NOUN
ejpam-3129	78	1	[	[	X
ejpam-3129	78	2	11	11	NUM
ejpam-3129	78	3	]	]	PUNCT
ejpam-3129	78	4	.	.	PUNCT
ejpam-3129	79	1	in	in	ADP
ejpam-3129	79	2	particular	particular	ADJ
ejpam-3129	79	3	if	if	SCONJ
ejpam-3129	79	4	(	(	PUNCT
ejpam-3129	79	5	m	m	NOUN
ejpam-3129	79	6	,	,	PUNCT
ejpam-3129	79	7	g	g	NOUN
ejpam-3129	79	8	)	)	PUNCT
ejpam-3129	79	9	admits	admit	VERB
ejpam-3129	79	10	an	an	DET
ejpam-3129	79	11	s−structure	s−structure	NOUN
ejpam-3129	79	12	of	of	ADP
ejpam-3129	79	13	order	order	NOUN
ejpam-3129	80	1	two	two	NUM
ejpam-3129	80	2	then	then	ADV
ejpam-3129	80	3	it	it	PRON
ejpam-3129	80	4	is	be	AUX
ejpam-3129	80	5	a	a	DET
ejpam-3129	80	6	usual	usual	ADJ
ejpam-3129	80	7	riemannian	riemannian	ADJ
ejpam-3129	80	8	symmetric	symmetric	ADJ
ejpam-3129	80	9	space	space	NOUN
ejpam-3129	80	10	.	.	PUNCT
ejpam-3129	81	1	let	let	VERB
ejpam-3129	81	2	(	(	PUNCT
ejpam-3129	81	3	m	m	PROPN
ejpam-3129	81	4	,	,	PUNCT
ejpam-3129	81	5	f	f	PROPN
ejpam-3129	81	6	)	)	PUNCT
ejpam-3129	81	7	be	be	AUX
ejpam-3129	81	8	a	a	DET
ejpam-3129	81	9	finsler	finsler	NOUN
ejpam-3129	81	10	space	space	NOUN
ejpam-3129	81	11	,	,	PUNCT
ejpam-3129	81	12	where	where	SCONJ
ejpam-3129	81	13	f	f	PROPN
ejpam-3129	81	14	is	be	AUX
ejpam-3129	81	15	positively	positively	ADV
ejpam-3129	81	16	homogeneous	homogeneous	ADJ
ejpam-3129	81	17	but	but	CCONJ
ejpam-3129	81	18	not	not	PART
ejpam-3129	81	19	necessarily	necessarily	ADV
ejpam-3129	81	20	absolutely	absolutely	ADV
ejpam-3129	81	21	homogeneous	homogeneous	ADJ
ejpam-3129	81	22	.	.	PUNCT
ejpam-3129	82	1	we	we	PRON
ejpam-3129	82	2	introduce	introduce	VERB
ejpam-3129	82	3	isometries	isometry	NOUN
ejpam-3129	82	4	of	of	ADP
ejpam-3129	82	5	(	(	PUNCT
ejpam-3129	82	6	m	m	PROPN
ejpam-3129	82	7	,	,	PUNCT
ejpam-3129	82	8	f	f	PROPN
ejpam-3129	82	9	)	)	PUNCT
ejpam-3129	82	10	which	which	PRON
ejpam-3129	82	11	form	form	VERB
ejpam-3129	82	12	a	a	DET
ejpam-3129	82	13	lie	lie	NOUN
ejpam-3129	82	14	transformation	transformation	NOUN
ejpam-3129	82	15	group	group	NOUN
ejpam-3129	82	16	of	of	ADP
ejpam-3129	82	17	m	m	PRON
ejpam-3129	82	18	as	as	ADP
ejpam-3129	82	19	a	a	DET
ejpam-3129	82	20	result	result	NOUN
ejpam-3129	82	21	of	of	ADP
ejpam-3129	82	22	s.	s.	PROPN
ejpam-3129	82	23	deng	deng	PROPN
ejpam-3129	82	24	and	and	CCONJ
ejpam-3129	82	25	z.	z.	PROPN
ejpam-3129	82	26	hou	hou	PROPN
ejpam-3129	83	1	[	[	X
ejpam-3129	83	2	2	2	NUM
ejpam-3129	83	3	]	]	PUNCT
ejpam-3129	83	4	and	and	CCONJ
ejpam-3129	83	5	moreover	moreover	ADV
ejpam-3129	83	6	for	for	ADP
ejpam-3129	83	7	any	any	DET
ejpam-3129	83	8	point	point	NOUN
ejpam-3129	83	9	x	x	PUNCT
ejpam-3129	83	10	∈	∈	NOUN
ejpam-3129	83	11	m	m	NOUN
ejpam-3129	83	12	,	,	PUNCT
ejpam-3129	83	13	the	the	DET
ejpam-3129	83	14	isotropic	isotropic	NOUN
ejpam-3129	83	15	subgroup	subgroup	NOUN
ejpam-3129	83	16	ix(m	ix(m	NUM
ejpam-3129	83	17	,	,	PUNCT
ejpam-3129	83	18	f	f	PROPN
ejpam-3129	83	19	)	)	PUNCT
ejpam-3129	83	20	is	be	AUX
ejpam-3129	83	21	a	a	DET
ejpam-3129	83	22	compact	compact	ADJ
ejpam-3129	83	23	subgroup	subgroup	NOUN
ejpam-3129	83	24	of	of	ADP
ejpam-3129	83	25	i(m	i(m	NOUN
ejpam-3129	83	26	,	,	PUNCT
ejpam-3129	83	27	f	f	PROPN
ejpam-3129	83	28	)	)	PUNCT
ejpam-3129	83	29	,	,	PUNCT
ejpam-3129	83	30	the	the	DET
ejpam-3129	83	31	group	group	NOUN
ejpam-3129	83	32	of	of	ADP
ejpam-3129	83	33	isometries	isometry	NOUN
ejpam-3129	83	34	,	,	PUNCT
ejpam-3129	83	35	which	which	PRON
ejpam-3129	83	36	can	can	AUX
ejpam-3129	83	37	be	be	AUX
ejpam-3129	83	38	used	use	VERB
ejpam-3129	83	39	to	to	PART
ejpam-3129	83	40	study	study	VERB
ejpam-3129	83	41	homogeneous	homogeneous	ADJ
ejpam-3129	83	42	and	and	CCONJ
ejpam-3129	83	43	symmetric	symmetric	ADJ
ejpam-3129	83	44	finsler	finsler	NOUN
ejpam-3129	83	45	spaces	space	NOUN
ejpam-3129	83	46	.	.	PUNCT
ejpam-3129	84	1	the	the	DET
ejpam-3129	84	2	definition	definition	NOUN
ejpam-3129	84	3	of	of	ADP
ejpam-3129	84	4	symmetric	symmetric	ADJ
ejpam-3129	84	5	finsler	finsler	NOUN
ejpam-3129	84	6	space	space	NOUN
ejpam-3129	84	7	is	be	AUX
ejpam-3129	84	8	a	a	DET
ejpam-3129	84	9	natural	natural	ADJ
ejpam-3129	84	10	generalization	generalization	NOUN
ejpam-3129	84	11	of	of	ADP
ejpam-3129	84	12	e.	e.	PROPN
ejpam-3129	84	13	cartan	cartan	PROPN
ejpam-3129	84	14	’s	’s	PART
ejpam-3129	84	15	definition	definition	NOUN
ejpam-3129	84	16	of	of	ADP
ejpam-3129	84	17	riemannian	riemannian	ADJ
ejpam-3129	84	18	symmetric	symmetric	ADJ
ejpam-3129	84	19	space	space	NOUN
ejpam-3129	84	20	[	[	X
ejpam-3129	84	21	5	5	NUM
ejpam-3129	84	22	]	]	PUNCT
ejpam-3129	84	23	,	,	PUNCT
ejpam-3129	84	24	[	[	X
ejpam-3129	84	25	6	6	NUM
ejpam-3129	84	26	]	]	PUNCT
ejpam-3129	84	27	,	,	PUNCT
ejpam-3129	84	28	[	[	X
ejpam-3129	84	29	12	12	NUM
ejpam-3129	84	30	]	]	PUNCT
ejpam-3129	84	31	.	.	PUNCT
ejpam-3129	85	1	we	we	PRON
ejpam-3129	85	2	call	call	VERB
ejpam-3129	85	3	a	a	DET
ejpam-3129	85	4	finsler	finsler	NOUN
ejpam-3129	85	5	space	space	NOUN
ejpam-3129	85	6	(	(	PUNCT
ejpam-3129	85	7	m	m	PROPN
ejpam-3129	85	8	,	,	PUNCT
ejpam-3129	85	9	f	f	PROPN
ejpam-3129	85	10	)	)	PUNCT
ejpam-3129	85	11	a	a	DET
ejpam-3129	85	12	symmetric	symmetric	ADJ
ejpam-3129	85	13	finsler	finsler	NOUN
ejpam-3129	85	14	space	space	NOUN
ejpam-3129	85	15	if	if	SCONJ
ejpam-3129	85	16	for	for	ADP
ejpam-3129	85	17	any	any	DET
ejpam-3129	85	18	point	point	NOUN
ejpam-3129	85	19	p	p	NOUN
ejpam-3129	85	20	∈m	∈m	NOUN
ejpam-3129	85	21	there	there	ADV
ejpam-3129	85	22	exists	exist	VERB
ejpam-3129	85	23	an	an	DET
ejpam-3129	85	24	involutive	involutive	ADJ
ejpam-3129	85	25	isometry	isometry	NOUN
ejpam-3129	85	26	sp	sp	ADP
ejpam-3129	85	27	of	of	ADP
ejpam-3129	85	28	(	(	PUNCT
ejpam-3129	85	29	m	m	PROPN
ejpam-3129	85	30	,	,	PUNCT
ejpam-3129	85	31	f	f	PROPN
ejpam-3129	85	32	)	)	PUNCT
ejpam-3129	85	33	such	such	ADJ
ejpam-3129	85	34	that	that	SCONJ
ejpam-3129	85	35	p	p	NOUN
ejpam-3129	85	36	is	be	AUX
ejpam-3129	85	37	an	an	DET
ejpam-3129	85	38	isolated	isolated	ADJ
ejpam-3129	85	39	fixed	fix	VERB
ejpam-3129	85	40	point	point	NOUN
ejpam-3129	85	41	of	of	ADP
ejpam-3129	85	42	sp	sp	NOUN
ejpam-3129	85	43	.	.	PUNCT
ejpam-3129	86	1	if	if	SCONJ
ejpam-3129	86	2	we	we	PRON
ejpam-3129	86	3	drop	drop	VERB
ejpam-3129	86	4	the	the	DET
ejpam-3129	86	5	involution	involution	NOUN
ejpam-3129	86	6	property	property	NOUN
ejpam-3129	86	7	in	in	ADP
ejpam-3129	86	8	the	the	DET
ejpam-3129	86	9	definition	definition	NOUN
ejpam-3129	86	10	of	of	ADP
ejpam-3129	86	11	symmetric	symmetric	ADJ
ejpam-3129	86	12	finsler	finsler	NOUN
ejpam-3129	86	13	space	space	NOUN
ejpam-3129	86	14	keeping	keep	VERB
ejpam-3129	86	15	the	the	DET
ejpam-3129	86	16	property	property	NOUN
ejpam-3129	86	17	sx	sx	PROPN
ejpam-3129	86	18	◦	◦	NOUN
ejpam-3129	86	19	sy	sy	NOUN
ejpam-3129	86	20	=	=	SYM
ejpam-3129	86	21	sz	sz	PROPN
ejpam-3129	86	22	◦	◦	PROPN
ejpam-3129	86	23	sx	sx	PROPN
ejpam-3129	86	24	,	,	PUNCT
ejpam-3129	86	25	z	z	NOUN
ejpam-3129	86	26	=	=	SYM
ejpam-3129	86	27	sx(y	sx(y	PROPN
ejpam-3129	86	28	)	)	PUNCT
ejpam-3129	86	29	,	,	PUNCT
ejpam-3129	86	30	we	we	PRON
ejpam-3129	86	31	get	get	VERB
ejpam-3129	86	32	a	a	DET
ejpam-3129	86	33	bigger	big	ADJ
ejpam-3129	86	34	class	class	NOUN
ejpam-3129	86	35	of	of	ADP
ejpam-3129	86	36	finsler	finsler	NOUN
ejpam-3129	86	37	manifolds	manifold	NOUN
ejpam-3129	86	38	as	as	SCONJ
ejpam-3129	86	39	symmetric	symmetric	ADJ
ejpam-3129	86	40	finsler	finsler	NOUN
ejpam-3129	86	41	spaces	space	VERB
ejpam-3129	86	42	.	.	PUNCT
ejpam-3129	87	1	the	the	DET
ejpam-3129	87	2	definition	definition	NOUN
ejpam-3129	87	3	of	of	ADP
ejpam-3129	87	4	finsler	finsler	NOUN
ejpam-3129	87	5	s−manifolds	s−manifolds	PROPN
ejpam-3129	87	6	is	be	AUX
ejpam-3129	87	7	a	a	DET
ejpam-3129	87	8	natural	natural	ADJ
ejpam-3129	87	9	generalization	generalization	NOUN
ejpam-3129	87	10	of	of	ADP
ejpam-3129	87	11	definition	definition	NOUN
ejpam-3129	87	12	of	of	ADP
ejpam-3129	87	13	riemannian	riemannian	NOUN
ejpam-3129	87	14	s−manifolds	s−manifolds	X
ejpam-3129	88	1	[	[	X
ejpam-3129	88	2	7	7	NUM
ejpam-3129	88	3	,	,	PUNCT
ejpam-3129	88	4	16	16	NUM
ejpam-3129	88	5	]	]	PUNCT
ejpam-3129	88	6	.	.	PUNCT
ejpam-3129	89	1	definition	definition	NOUN
ejpam-3129	89	2	1	1	NUM
ejpam-3129	89	3	.	.	PUNCT
ejpam-3129	90	1	let	let	VERB
ejpam-3129	90	2	(	(	PUNCT
ejpam-3129	90	3	m	m	PROPN
ejpam-3129	90	4	,	,	PUNCT
ejpam-3129	90	5	f	f	PROPN
ejpam-3129	90	6	)	)	PUNCT
ejpam-3129	90	7	be	be	AUX
ejpam-3129	90	8	a	a	DET
ejpam-3129	90	9	connected	connected	ADJ
ejpam-3129	90	10	finsler	finsler	NOUN
ejpam-3129	90	11	space	space	NOUN
ejpam-3129	90	12	.	.	PUNCT
ejpam-3129	91	1	an	an	DET
ejpam-3129	91	2	isometry	isometry	NOUN
ejpam-3129	91	3	on	on	ADP
ejpam-3129	91	4	(	(	PUNCT
ejpam-3129	91	5	m	m	PROPN
ejpam-3129	91	6	,	,	PUNCT
ejpam-3129	91	7	f	f	PROPN
ejpam-3129	91	8	)	)	PUNCT
ejpam-3129	91	9	with	with	ADP
ejpam-3129	91	10	an	an	DET
ejpam-3129	91	11	isolated	isolated	ADJ
ejpam-3129	91	12	fixed	fix	VERB
ejpam-3129	91	13	point	point	NOUN
ejpam-3129	91	14	x	x	PUNCT
ejpam-3129	91	15	will	will	AUX
ejpam-3129	91	16	be	be	AUX
ejpam-3129	91	17	called	call	VERB
ejpam-3129	91	18	a	a	DET
ejpam-3129	91	19	symmetry	symmetry	NOUN
ejpam-3129	91	20	at	at	ADP
ejpam-3129	91	21	x	x	X
ejpam-3129	91	22	,	,	PUNCT
ejpam-3129	91	23	and	and	CCONJ
ejpam-3129	91	24	will	will	AUX
ejpam-3129	91	25	usually	usually	ADV
ejpam-3129	91	26	be	be	AUX
ejpam-3129	91	27	written	write	VERB
ejpam-3129	91	28	as	as	ADP
ejpam-3129	91	29	sx	sx	PROPN
ejpam-3129	91	30	.	.	PROPN
ejpam-3129	91	31	definition	definition	NOUN
ejpam-3129	91	32	2	2	NUM
ejpam-3129	91	33	.	.	PUNCT
ejpam-3129	91	34	a	a	PRON
ejpam-3129	91	35	family	family	NOUN
ejpam-3129	91	36	{	{	PUNCT
ejpam-3129	91	37	sx|x	sx|x	PROPN
ejpam-3129	91	38	∈m	∈m	PROPN
ejpam-3129	91	39	}	}	PUNCT
ejpam-3129	91	40	of	of	ADP
ejpam-3129	91	41	symmetries	symmetry	NOUN
ejpam-3129	91	42	on	on	ADP
ejpam-3129	91	43	a	a	DET
ejpam-3129	91	44	connected	connected	ADJ
ejpam-3129	91	45	finsler	finsler	NOUN
ejpam-3129	91	46	manifold	manifold	NOUN
ejpam-3129	91	47	(	(	PUNCT
ejpam-3129	91	48	m	m	PROPN
ejpam-3129	91	49	,	,	PUNCT
ejpam-3129	91	50	f	f	PROPN
ejpam-3129	91	51	)	)	PUNCT
ejpam-3129	91	52	is	be	AUX
ejpam-3129	91	53	called	call	VERB
ejpam-3129	91	54	an	an	DET
ejpam-3129	91	55	s−structure	s−structure	NOUN
ejpam-3129	91	56	on	on	ADP
ejpam-3129	91	57	(	(	PUNCT
ejpam-3129	91	58	m	m	PROPN
ejpam-3129	91	59	,	,	PUNCT
ejpam-3129	91	60	f	f	PROPN
ejpam-3129	91	61	)	)	PUNCT
ejpam-3129	91	62	an	an	DET
ejpam-3129	91	63	s−structure	s−structure	NOUN
ejpam-3129	91	64	{	{	PUNCT
ejpam-3129	91	65	sx|x	sx|x	NOUN
ejpam-3129	91	66	∈m	∈m	NOUN
ejpam-3129	91	67	}	}	PUNCT
ejpam-3129	91	68	is	be	AUX
ejpam-3129	91	69	called	call	VERB
ejpam-3129	91	70	of	of	ADP
ejpam-3129	91	71	order	order	NOUN
ejpam-3129	92	1	k	k	PROPN
ejpam-3129	93	1	(	(	PUNCT
ejpam-3129	93	2	k	k	X
ejpam-3129	93	3	≥	≥	NUM
ejpam-3129	93	4	2	2	NUM
ejpam-3129	93	5	)	)	PUNCT
ejpam-3129	93	6	if	if	SCONJ
ejpam-3129	93	7	(	(	PUNCT
ejpam-3129	93	8	sx)k	sx)k	NOUN
ejpam-3129	93	9	=	=	NOUN
ejpam-3129	93	10	i	i	PROPN
ejpam-3129	93	11	d	d	PROPN
ejpam-3129	93	12	for	for	ADP
ejpam-3129	93	13	all	all	DET
ejpam-3129	93	14	x	x	SYM
ejpam-3129	93	15	∈m	∈m	NOUN
ejpam-3129	93	16	and	and	CCONJ
ejpam-3129	93	17	k	k	PROPN
ejpam-3129	93	18	is	be	AUX
ejpam-3129	93	19	the	the	DET
ejpam-3129	93	20	least	least	ADJ
ejpam-3129	93	21	integer	integer	NOUN
ejpam-3129	93	22	of	of	ADP
ejpam-3129	93	23	this	this	DET
ejpam-3129	93	24	property	property	NOUN
ejpam-3129	93	25	.	.	PUNCT
ejpam-3129	94	1	obviously	obviously	ADV
ejpam-3129	94	2	a	a	DET
ejpam-3129	94	3	finsler	finsler	NOUN
ejpam-3129	94	4	space	space	NOUN
ejpam-3129	94	5	is	be	AUX
ejpam-3129	94	6	symmetric	symmetric	ADJ
ejpam-3129	94	7	if	if	SCONJ
ejpam-3129	95	1	and	and	CCONJ
ejpam-3129	95	2	only	only	ADV
ejpam-3129	95	3	if	if	SCONJ
ejpam-3129	95	4	it	it	PRON
ejpam-3129	95	5	admits	admit	VERB
ejpam-3129	95	6	an	an	DET
ejpam-3129	95	7	s−structure	s−structure	NOUN
ejpam-3129	95	8	of	of	ADP
ejpam-3129	95	9	order	order	NOUN
ejpam-3129	95	10	2	2	NUM
ejpam-3129	95	11	.	.	PUNCT
ejpam-3129	95	12	an	an	DET
ejpam-3129	95	13	s−structure	s−structure	NOUN
ejpam-3129	95	14	{	{	PUNCT
ejpam-3129	95	15	sx|x	sx|x	PROPN
ejpam-3129	95	16	∈	∈	PROPN
ejpam-3129	95	17	m	m	NOUN
ejpam-3129	95	18	}	}	PUNCT
ejpam-3129	95	19	on	on	ADP
ejpam-3129	95	20	(	(	PUNCT
ejpam-3129	95	21	m	m	PROPN
ejpam-3129	95	22	,	,	PUNCT
ejpam-3129	95	23	f	f	PROPN
ejpam-3129	95	24	)	)	PUNCT
ejpam-3129	95	25	is	be	AUX
ejpam-3129	95	26	called	call	VERB
ejpam-3129	95	27	regular	regular	ADV
ejpam-3129	95	28	if	if	SCONJ
ejpam-3129	95	29	for	for	ADP
ejpam-3129	95	30	every	every	DET
ejpam-3129	95	31	pair	pair	NOUN
ejpam-3129	95	32	of	of	ADP
ejpam-3129	95	33	points	point	NOUN
ejpam-3129	95	34	x	x	X
ejpam-3129	95	35	,	,	PUNCT
ejpam-3129	95	36	y	y	PROPN
ejpam-3129	95	37	∈m	∈m	NOUN
ejpam-3129	95	38	sx	sx	PROPN
ejpam-3129	95	39	◦	◦	NOUN
ejpam-3129	95	40	sy	sy	NOUN
ejpam-3129	95	41	=	=	SYM
ejpam-3129	95	42	sz	sz	PROPN
ejpam-3129	95	43	◦	◦	PROPN
ejpam-3129	95	44	sx	sx	PROPN
ejpam-3129	95	45	,	,	PUNCT
ejpam-3129	95	46	z	z	NOUN
ejpam-3129	95	47	=	=	SYM
ejpam-3129	95	48	sx(y	sx(y	PROPN
ejpam-3129	95	49	)	)	PUNCT
ejpam-3129	95	50	.	.	PUNCT
ejpam-3129	96	1	definition	definition	NOUN
ejpam-3129	96	2	3	3	NUM
ejpam-3129	96	3	.	.	PUNCT
ejpam-3129	97	1	a	a	DET
ejpam-3129	97	2	finsler	finsler	NOUN
ejpam-3129	97	3	s−manifold	s−manifold	NOUN
ejpam-3129	97	4	is	be	AUX
ejpam-3129	97	5	a	a	DET
ejpam-3129	97	6	connected	connected	ADJ
ejpam-3129	97	7	finsler	finsler	NOUN
ejpam-3129	97	8	manifold	manifold	NOUN
ejpam-3129	97	9	(	(	PUNCT
ejpam-3129	97	10	m	m	PROPN
ejpam-3129	97	11	,	,	PUNCT
ejpam-3129	97	12	f	f	PROPN
ejpam-3129	97	13	)	)	PUNCT
ejpam-3129	97	14	admitting	admit	VERB
ejpam-3129	97	15	a	a	DET
ejpam-3129	97	16	regular	regular	ADJ
ejpam-3129	97	17	s−structure	s−structure	NOUN
ejpam-3129	97	18	and	and	CCONJ
ejpam-3129	97	19	a	a	DET
ejpam-3129	97	20	finsler	finsler	NOUN
ejpam-3129	97	21	space	space	NOUN
ejpam-3129	97	22	(	(	PUNCT
ejpam-3129	97	23	m	m	PROPN
ejpam-3129	97	24	,	,	PUNCT
ejpam-3129	97	25	f	f	PROPN
ejpam-3129	97	26	)	)	PUNCT
ejpam-3129	97	27	is	be	AUX
ejpam-3129	97	28	said	say	VERB
ejpam-3129	97	29	to	to	PART
ejpam-3129	97	30	be	be	AUX
ejpam-3129	97	31	k−symmetric	k−symmetric	PROPN
ejpam-3129	97	32	(	(	PUNCT
ejpam-3129	97	33	k	k	X
ejpam-3129	97	34	≥	≥	NUM
ejpam-3129	97	35	2	2	NUM
ejpam-3129	97	36	)	)	PUNCT
ejpam-3129	97	37	if	if	SCONJ
ejpam-3129	97	38	it	it	PRON
ejpam-3129	97	39	admits	admit	VERB
ejpam-3129	97	40	a	a	DET
ejpam-3129	97	41	regular	regular	ADJ
ejpam-3129	97	42	s−structure	s−structure	NOUN
ejpam-3129	97	43	of	of	ADP
ejpam-3129	97	44	order	order	NOUN
ejpam-3129	97	45	k.	k.	PROPN
ejpam-3129	97	46	p.	p.	NOUN
ejpam-3129	97	47	bahmandoust	bahmandoust	PROPN
ejpam-3129	97	48	,	,	PUNCT
ejpam-3129	97	49	d.	d.	PROPN
ejpam-3129	97	50	latifi	latifi	PROPN
ejpam-3129	97	51	/	/	SYM
ejpam-3129	97	52	eur	eur	PROPN
ejpam-3129	97	53	.	.	PUNCT
ejpam-3129	98	1	j.	j.	PROPN
ejpam-3129	98	2	pure	pure	PROPN
ejpam-3129	98	3	appl	appl	PROPN
ejpam-3129	98	4	.	.	PROPN
ejpam-3129	98	5	math	math	PROPN
ejpam-3129	98	6	,	,	PUNCT
ejpam-3129	98	7	10	10	NUM
ejpam-3129	98	8	(	(	PUNCT
ejpam-3129	98	9	5	5	NUM
ejpam-3129	98	10	)	)	PUNCT
ejpam-3129	98	11	(	(	PUNCT
ejpam-3129	98	12	2017	2017	NUM
ejpam-3129	98	13	)	)	PUNCT
ejpam-3129	98	14	,	,	PUNCT
ejpam-3129	98	15	1099	1099	NUM
ejpam-3129	98	16	-	-	SYM
ejpam-3129	98	17	1111	1111	NUM
ejpam-3129	98	18	1103	1103	NUM
ejpam-3129	98	19	here	here	ADV
ejpam-3129	98	20	we	we	PRON
ejpam-3129	98	21	construct	construct	VERB
ejpam-3129	98	22	some	some	DET
ejpam-3129	98	23	finsler	finsler	NOUN
ejpam-3129	98	24	s−manifolds	s−manifolds	ADP
ejpam-3129	98	25	which	which	PRON
ejpam-3129	98	26	are	be	AUX
ejpam-3129	98	27	non	non	ADJ
ejpam-3129	98	28	-	-	ADJ
ejpam-3129	98	29	riemannian	riemannian	ADJ
ejpam-3129	98	30	and	and	CCONJ
ejpam-3129	98	31	nonsymmetric	nonsymmetric	NOUN
ejpam-3129	98	32	.	.	PUNCT
ejpam-3129	98	33	example	example	NOUN
ejpam-3129	99	1	1	1	NUM
ejpam-3129	99	2	.	.	PUNCT
ejpam-3129	99	3	let	let	VERB
ejpam-3129	99	4	k	k	PRON
ejpam-3129	99	5	be	be	AUX
ejpam-3129	99	6	a	a	DET
ejpam-3129	99	7	constant	constant	ADJ
ejpam-3129	99	8	|k|	|k|	NOUN
ejpam-3129	99	9	<	<	X
ejpam-3129	99	10	1√	1√	PROPN
ejpam-3129	99	11	3	3	NUM
ejpam-3129	99	12	.	.	PUNCT
ejpam-3129	100	1	consider	consider	VERB
ejpam-3129	100	2	the	the	DET
ejpam-3129	100	3	following	follow	VERB
ejpam-3129	100	4	randers	rander	NOUN
ejpam-3129	100	5	metric	metric	ADJ
ejpam-3129	100	6	on	on	ADP
ejpam-3129	100	7	r3	r3	PROPN
ejpam-3129	100	8	,	,	PUNCT
ejpam-3129	100	9	f	f	PROPN
ejpam-3129	100	10	(	(	PUNCT
ejpam-3129	100	11	p1	p1	PROPN
ejpam-3129	100	12	,	,	PUNCT
ejpam-3129	100	13	p2	p2	NOUN
ejpam-3129	100	14	,	,	PUNCT
ejpam-3129	100	15	p3	p3	PROPN
ejpam-3129	100	16	,	,	PUNCT
ejpam-3129	100	17	y1	y1	NOUN
ejpam-3129	100	18	,	,	PUNCT
ejpam-3129	100	19	y2	y2	PROPN
ejpam-3129	100	20	,	,	PUNCT
ejpam-3129	100	21	y3	y3	NOUN
ejpam-3129	100	22	)	)	PUNCT
ejpam-3129	100	23	=	=	SYM
ejpam-3129	101	1	√	√	NUM
ejpam-3129	101	2	y21	y21	NOUN
ejpam-3129	101	3	+	+	CCONJ
ejpam-3129	101	4	y22	y22	PROPN
ejpam-3129	101	5	+	+	CCONJ
ejpam-3129	101	6	y23	y23	NOUN
ejpam-3129	101	7	+	+	CCONJ
ejpam-3129	101	8	k(y1	k(y1	NOUN
ejpam-3129	101	9	+	+	CCONJ
ejpam-3129	101	10	y2	y2	PROPN
ejpam-3129	101	11	+	+	CCONJ
ejpam-3129	101	12	y3	y3	NOUN
ejpam-3129	101	13	)	)	PUNCT
ejpam-3129	101	14	where	where	SCONJ
ejpam-3129	101	15	p	p	NOUN
ejpam-3129	101	16	=	=	SYM
ejpam-3129	101	17	(	(	PUNCT
ejpam-3129	101	18	p1	p1	PROPN
ejpam-3129	101	19	,	,	PUNCT
ejpam-3129	101	20	p2	p2	NOUN
ejpam-3129	101	21	,	,	PUNCT
ejpam-3129	101	22	p3	p3	NOUN
ejpam-3129	101	23	)	)	PUNCT
ejpam-3129	101	24	∈	∈	PROPN
ejpam-3129	101	25	r3	r3	PROPN
ejpam-3129	101	26	and	and	CCONJ
ejpam-3129	101	27	(	(	PUNCT
ejpam-3129	101	28	y1	y1	PROPN
ejpam-3129	101	29	,	,	PUNCT
ejpam-3129	101	30	y2	y2	PROPN
ejpam-3129	101	31	,	,	PUNCT
ejpam-3129	101	32	y3	y3	PROPN
ejpam-3129	101	33	)	)	PUNCT
ejpam-3129	101	34	∈	∈	PROPN
ejpam-3129	101	35	tpr3	tpr3	PROPN
ejpam-3129	101	36	.	.	PUNCT
ejpam-3129	102	1	define	define	VERB
ejpam-3129	102	2	sp(x1	sp(x1	PROPN
ejpam-3129	102	3	,	,	PUNCT
ejpam-3129	102	4	x2	x2	PROPN
ejpam-3129	102	5	,	,	PUNCT
ejpam-3129	102	6	x3	x3	ADJ
ejpam-3129	102	7	)	)	PUNCT
ejpam-3129	103	1	=	=	SYM
ejpam-3129	103	2	(	(	PUNCT
ejpam-3129	103	3	x3	x3	ADJ
ejpam-3129	103	4	−	−	PROPN
ejpam-3129	103	5	p3	p3	PROPN
ejpam-3129	103	6	+	+	CCONJ
ejpam-3129	103	7	p1	p1	PROPN
ejpam-3129	103	8	,	,	PUNCT
ejpam-3129	103	9	x1	x1	PROPN
ejpam-3129	103	10	−	−	PROPN
ejpam-3129	103	11	p1	p1	NOUN
ejpam-3129	103	12	+	+	CCONJ
ejpam-3129	103	13	p2	p2	NOUN
ejpam-3129	103	14	,	,	PUNCT
ejpam-3129	103	15	x2	x2	PROPN
ejpam-3129	103	16	−	−	PROPN
ejpam-3129	103	17	p2	p2	PROPN
ejpam-3129	103	18	+	+	CCONJ
ejpam-3129	103	19	p3	p3	PROPN
ejpam-3129	103	20	)	)	PUNCT
ejpam-3129	103	21	,	,	PUNCT
ejpam-3129	103	22	for	for	ADP
ejpam-3129	103	23	any	any	DET
ejpam-3129	103	24	p	p	PROPN
ejpam-3129	103	25	∈	∈	PROPN
ejpam-3129	103	26	r3	r3	NOUN
ejpam-3129	103	27	we	we	PRON
ejpam-3129	103	28	clearly	clearly	ADV
ejpam-3129	103	29	see	see	VERB
ejpam-3129	103	30	that	that	DET
ejpam-3129	103	31	sp	sp	NOUN
ejpam-3129	103	32	is	be	AUX
ejpam-3129	103	33	an	an	DET
ejpam-3129	103	34	isometry	isometry	NOUN
ejpam-3129	103	35	of	of	ADP
ejpam-3129	103	36	f	f	PROPN
ejpam-3129	103	37	such	such	ADJ
ejpam-3129	103	38	that	that	SCONJ
ejpam-3129	103	39	p	p	NOUN
ejpam-3129	103	40	is	be	AUX
ejpam-3129	103	41	an	an	DET
ejpam-3129	103	42	isolated	isolated	ADJ
ejpam-3129	103	43	fixed	fix	VERB
ejpam-3129	103	44	point	point	NOUN
ejpam-3129	103	45	of	of	ADP
ejpam-3129	103	46	sp	sp	NOUN
ejpam-3129	103	47	.	.	PUNCT
ejpam-3129	104	1	it	it	PRON
ejpam-3129	104	2	is	be	AUX
ejpam-3129	104	3	evident	evident	ADJ
ejpam-3129	104	4	that	that	SCONJ
ejpam-3129	104	5	s3p	s3p	X
ejpam-3129	104	6	=	=	PUNCT
ejpam-3129	104	7	i	i	PROPN
ejpam-3129	104	8	d	d	PROPN
ejpam-3129	104	9	and	and	CCONJ
ejpam-3129	104	10	s2p	s2p	PROPN
ejpam-3129	104	11	6=	6=	PUNCT
ejpam-3129	104	12	i	i	PROPN
ejpam-3129	104	13	d	d	PROPN
ejpam-3129	104	14	and	and	CCONJ
ejpam-3129	104	15	sp	sp	ADP
ejpam-3129	104	16	6=	6=	PROPN
ejpam-3129	104	17	i	i	PROPN
ejpam-3129	104	18	d	d	PROPN
ejpam-3129	104	19	and	and	CCONJ
ejpam-3129	104	20	sp	sp	ADP
ejpam-3129	104	21	◦	◦	NOUN
ejpam-3129	104	22	sq(x	sq(x	NUM
ejpam-3129	104	23	)	)	PUNCT
ejpam-3129	105	1	=	=	SYM
ejpam-3129	105	2	sz	sz	NOUN
ejpam-3129	105	3	◦	◦	NOUN
ejpam-3129	105	4	sp(x	sp(x	NUM
ejpam-3129	105	5	)	)	PUNCT
ejpam-3129	105	6	,	,	PUNCT
ejpam-3129	105	7	z	z	NOUN
ejpam-3129	105	8	=	=	PUNCT
ejpam-3129	105	9	sp(q	sp(q	NOUN
ejpam-3129	105	10	)	)	PUNCT
ejpam-3129	105	11	.	.	PUNCT
ejpam-3129	106	1	so	so	ADV
ejpam-3129	106	2	{	{	PUNCT
ejpam-3129	106	3	sp	sp	NOUN
ejpam-3129	106	4	}	}	PUNCT
ejpam-3129	106	5	is	be	AUX
ejpam-3129	106	6	a	a	DET
ejpam-3129	106	7	regular	regular	ADJ
ejpam-3129	106	8	3	3	NUM
ejpam-3129	106	9	-	-	PUNCT
ejpam-3129	106	10	structure	structure	NOUN
ejpam-3129	106	11	on	on	ADP
ejpam-3129	106	12	(	(	PUNCT
ejpam-3129	106	13	r3	r3	PROPN
ejpam-3129	106	14	,	,	PUNCT
ejpam-3129	106	15	f	f	PROPN
ejpam-3129	106	16	)	)	PUNCT
ejpam-3129	106	17	�	�	PROPN
ejpam-3129	106	18	example	example	NOUN
ejpam-3129	107	1	2	2	X
ejpam-3129	107	2	.	.	PUNCT
ejpam-3129	108	1	let	let	VERB
ejpam-3129	108	2	g	g	PRON
ejpam-3129	108	3	be	be	AUX
ejpam-3129	108	4	a	a	DET
ejpam-3129	108	5	compact	compact	ADJ
ejpam-3129	108	6	connected	connect	VERB
ejpam-3129	108	7	lie	lie	NOUN
ejpam-3129	108	8	group	group	NOUN
ejpam-3129	108	9	.	.	PUNCT
ejpam-3129	109	1	consider	consider	VERB
ejpam-3129	109	2	the	the	DET
ejpam-3129	109	3	coset	coset	NOUN
ejpam-3129	109	4	space	space	NOUN
ejpam-3129	109	5	(	(	PUNCT
ejpam-3129	109	6	g	g	PROPN
ejpam-3129	109	7	×	×	PROPN
ejpam-3129	109	8	g)/g∗	g)/g∗	PROPN
ejpam-3129	109	9	,	,	PUNCT
ejpam-3129	109	10	where	where	SCONJ
ejpam-3129	109	11	g∗	g∗	PROPN
ejpam-3129	109	12	is	be	AUX
ejpam-3129	109	13	the	the	DET
ejpam-3129	109	14	diagonal	diagonal	ADJ
ejpam-3129	109	15	of	of	ADP
ejpam-3129	109	16	g×g	g×g	PROPN
ejpam-3129	109	17	.	.	PUNCT
ejpam-3129	110	1	(	(	PUNCT
ejpam-3129	110	2	g×g)/g∗	g×g)/g∗	NOUN
ejpam-3129	110	3	is	be	AUX
ejpam-3129	110	4	diffeomorphic	diffeomorphic	ADJ
ejpam-3129	110	5	to	to	ADP
ejpam-3129	110	6	g	g	NOUN
ejpam-3129	110	7	via	via	ADP
ejpam-3129	110	8	the	the	DET
ejpam-3129	110	9	map	map	NOUN
ejpam-3129	110	10	(	(	PUNCT
ejpam-3129	110	11	g1	g1	NOUN
ejpam-3129	110	12	,	,	PUNCT
ejpam-3129	110	13	gg)g	gg)g	NOUN
ejpam-3129	110	14	∗	∗	NOUN
ejpam-3129	110	15	−→	−→	NOUN
ejpam-3129	110	16	g1	g1	PROPN
ejpam-3129	110	17	g	g	ADP
ejpam-3129	110	18	−1	−1	NOUN
ejpam-3129	110	19	2	2	NUM
ejpam-3129	110	20	g×g	g×g	PROPN
ejpam-3129	110	21	acts	act	VERB
ejpam-3129	110	22	on	on	ADP
ejpam-3129	110	23	g	g	PROPN
ejpam-3129	110	24	by	by	ADP
ejpam-3129	110	25	(	(	PUNCT
ejpam-3129	110	26	g1	g1	PROPN
ejpam-3129	110	27	,	,	PUNCT
ejpam-3129	110	28	g2)y	g2)y	NOUN
ejpam-3129	110	29	=	=	PUNCT
ejpam-3129	110	30	g1yg	g1yg	PROPN
ejpam-3129	110	31	−1	−1	NOUN
ejpam-3129	110	32	2	2	NUM
ejpam-3129	110	33	.	.	PUNCT
ejpam-3129	111	1	the	the	DET
ejpam-3129	111	2	isotropy	isotropy	ADJ
ejpam-3129	111	3	group	group	NOUN
ejpam-3129	111	4	at	at	ADP
ejpam-3129	111	5	the	the	DET
ejpam-3129	111	6	origin	origin	NOUN
ejpam-3129	111	7	e	e	PROPN
ejpam-3129	111	8	∈	∈	PROPN
ejpam-3129	111	9	g	g	PROPN
ejpam-3129	111	10	is	be	AUX
ejpam-3129	111	11	g∗.	g∗.	ADV
ejpam-3129	111	12	now	now	ADV
ejpam-3129	111	13	define	define	VERB
ejpam-3129	111	14	σ	σ	NOUN
ejpam-3129	111	15	:	:	PUNCT
ejpam-3129	111	16	g×g	g×g	ADJ
ejpam-3129	111	17	−→	−→	NOUN
ejpam-3129	111	18	g×g	g×g	PROPN
ejpam-3129	111	19	by	by	ADP
ejpam-3129	111	20	σ(g1	σ(g1	NOUN
ejpam-3129	111	21	,	,	PUNCT
ejpam-3129	111	22	g2	g2	PROPN
ejpam-3129	111	23	)	)	PUNCT
ejpam-3129	112	1	=	=	PRON
ejpam-3129	112	2	(	(	PUNCT
ejpam-3129	112	3	g2	g2	PROPN
ejpam-3129	112	4	,	,	PUNCT
ejpam-3129	112	5	g1	g1	PROPN
ejpam-3129	112	6	)	)	PUNCT
ejpam-3129	112	7	,	,	PUNCT
ejpam-3129	112	8	which	which	PRON
ejpam-3129	112	9	is	be	AUX
ejpam-3129	112	10	an	an	DET
ejpam-3129	112	11	involute	involute	ADJ
ejpam-3129	112	12	automorphism	automorphism	NOUN
ejpam-3129	112	13	.	.	PUNCT
ejpam-3129	113	1	the	the	DET
ejpam-3129	113	2	fixed	fix	VERB
ejpam-3129	113	3	point	point	NOUN
ejpam-3129	113	4	set	set	NOUN
ejpam-3129	113	5	is	be	AUX
ejpam-3129	113	6	(	(	PUNCT
ejpam-3129	113	7	g×g)σ	g×g)σ	PROPN
ejpam-3129	113	8	=	=	SYM
ejpam-3129	113	9	g∗	g∗	PROPN
ejpam-3129	113	10	and	and	CCONJ
ejpam-3129	113	11	σ	σ	NOUN
ejpam-3129	113	12	induces	induce	VERB
ejpam-3129	113	13	the	the	DET
ejpam-3129	113	14	map	map	NOUN
ejpam-3129	113	15	s	s	VERB
ejpam-3129	113	16	:	:	PUNCT
ejpam-3129	113	17	g	g	PROPN
ejpam-3129	113	18	−→	−→	NOUN
ejpam-3129	113	19	g	g	PROPN
ejpam-3129	113	20	,	,	PUNCT
ejpam-3129	113	21	s(g	s(g	PROPN
ejpam-3129	113	22	)	)	PUNCT
ejpam-3129	113	23	=	=	SYM
ejpam-3129	114	1	g−1	g−1	PROPN
ejpam-3129	114	2	.	.	PUNCT
ejpam-3129	114	3	take	take	VERB
ejpam-3129	114	4	a	a	DET
ejpam-3129	114	5	bi	bi	ADJ
ejpam-3129	114	6	-	-	ADJ
ejpam-3129	114	7	invariant	invariant	ADJ
ejpam-3129	114	8	absolutely	absolutely	ADV
ejpam-3129	114	9	homogeneous	homogeneous	ADJ
ejpam-3129	114	10	finsler	finsler	NOUN
ejpam-3129	114	11	metric	metric	ADJ
ejpam-3129	114	12	f	f	PROPN
ejpam-3129	114	13	on	on	ADP
ejpam-3129	114	14	g.	g.	PROPN
ejpam-3129	115	1	then	then	ADV
ejpam-3129	115	2	f	f	PROPN
ejpam-3129	115	3	is	be	AUX
ejpam-3129	115	4	invariant	invariant	ADJ
ejpam-3129	115	5	with	with	ADP
ejpam-3129	115	6	respect	respect	NOUN
ejpam-3129	115	7	to	to	ADP
ejpam-3129	115	8	the	the	DET
ejpam-3129	115	9	action	action	NOUN
ejpam-3129	115	10	of	of	ADP
ejpam-3129	115	11	g	g	PROPN
ejpam-3129	115	12	×	×	PROPN
ejpam-3129	115	13	g	g	PROPN
ejpam-3129	115	14	on	on	ADP
ejpam-3129	115	15	g.	g.	PROPN
ejpam-3129	115	16	it	it	PRON
ejpam-3129	115	17	is	be	AUX
ejpam-3129	115	18	also	also	ADV
ejpam-3129	115	19	invariant	invariant	ADJ
ejpam-3129	115	20	with	with	ADP
ejpam-3129	115	21	respect	respect	NOUN
ejpam-3129	115	22	to	to	ADP
ejpam-3129	115	23	s.	s.	PROPN
ejpam-3129	115	24	then	then	ADV
ejpam-3129	115	25	(	(	PUNCT
ejpam-3129	115	26	g	g	PROPN
ejpam-3129	115	27	,	,	PUNCT
ejpam-3129	115	28	f	f	PROPN
ejpam-3129	115	29	)	)	PUNCT
ejpam-3129	115	30	is	be	AUX
ejpam-3129	115	31	a	a	DET
ejpam-3129	115	32	symmetric	symmetric	ADJ
ejpam-3129	115	33	finsler	finsler	NOUN
ejpam-3129	115	34	space	space	NOUN
ejpam-3129	115	35	[	[	X
ejpam-3129	115	36	17	17	NUM
ejpam-3129	115	37	]	]	PUNCT
ejpam-3129	115	38	.	.	PUNCT
ejpam-3129	116	1	we	we	PRON
ejpam-3129	116	2	now	now	ADV
ejpam-3129	116	3	consider	consider	VERB
ejpam-3129	116	4	the	the	DET
ejpam-3129	116	5	more	more	ADV
ejpam-3129	116	6	general	general	ADJ
ejpam-3129	116	7	case	case	NOUN
ejpam-3129	116	8	of	of	ADP
ejpam-3129	116	9	gk+1	gk+1	NOUN
ejpam-3129	116	10	/	/	SYM
ejpam-3129	116	11	g∗	g∗	NOUN
ejpam-3129	116	12	where	where	SCONJ
ejpam-3129	116	13	gk+1	gk+1	NOUN
ejpam-3129	116	14	is	be	AUX
ejpam-3129	116	15	the	the	DET
ejpam-3129	116	16	direct	direct	ADJ
ejpam-3129	116	17	product	product	NOUN
ejpam-3129	116	18	of	of	ADP
ejpam-3129	116	19	g	g	NOUN
ejpam-3129	116	20	with	with	ADP
ejpam-3129	116	21	itself	itself	PRON
ejpam-3129	116	22	(	(	PUNCT
ejpam-3129	116	23	k+1	k+1	NOUN
ejpam-3129	116	24	)	)	PUNCT
ejpam-3129	116	25	times	time	NOUN
ejpam-3129	116	26	,	,	PUNCT
ejpam-3129	116	27	and	and	CCONJ
ejpam-3129	116	28	g∗	g∗	PROPN
ejpam-3129	116	29	is	be	AUX
ejpam-3129	116	30	the	the	DET
ejpam-3129	116	31	diagonal	diagonal	NOUN
ejpam-3129	116	32	of	of	ADP
ejpam-3129	116	33	gk+1	gk+1	NOUN
ejpam-3129	116	34	.	.	PUNCT
ejpam-3129	117	1	we	we	PRON
ejpam-3129	117	2	have	have	VERB
ejpam-3129	117	3	gk+1	gk+1	NOUN
ejpam-3129	117	4	/	/	SYM
ejpam-3129	117	5	g∗	g∗	PROPN
ejpam-3129	117	6	∼=	∼=	PROPN
ejpam-3129	117	7	gk	gk	NOUN
ejpam-3129	117	8	via	via	ADP
ejpam-3129	117	9	π	π	PROPN
ejpam-3129	117	10	:	:	PUNCT
ejpam-3129	117	11	gk+1	gk+1	X
ejpam-3129	117	12	−→	−→	NOUN
ejpam-3129	117	13	gk	gk	PROPN
ejpam-3129	117	14	,	,	PUNCT
ejpam-3129	117	15	where	where	SCONJ
ejpam-3129	117	16	π(g1	π(g1	NUM
ejpam-3129	117	17	,	,	PUNCT
ejpam-3129	117	18	...	...	PUNCT
ejpam-3129	117	19	,	,	PUNCT
ejpam-3129	117	20	gk+1	gk+1	X
ejpam-3129	117	21	)	)	PUNCT
ejpam-3129	117	22	=	=	SYM
ejpam-3129	117	23	(	(	PUNCT
ejpam-3129	117	24	g1	g1	PROPN
ejpam-3129	117	25	g	g	PROPN
ejpam-3129	117	26	−1	−1	NOUN
ejpam-3129	117	27	k+1	k+1	NOUN
ejpam-3129	117	28	,	,	PUNCT
ejpam-3129	117	29	...	...	PUNCT
ejpam-3129	117	30	,	,	PUNCT
ejpam-3129	117	31	gkg	gkg	PROPN
ejpam-3129	117	32	−1	−1	NOUN
ejpam-3129	117	33	k+1	k+1	NOUN
ejpam-3129	117	34	)	)	PUNCT
ejpam-3129	117	35	.	.	PUNCT
ejpam-3129	118	1	further	far	ADV
ejpam-3129	118	2	define	define	VERB
ejpam-3129	118	3	σ	σ	NOUN
ejpam-3129	118	4	:	:	PUNCT
ejpam-3129	118	5	gk+1	gk+1	NOUN
ejpam-3129	118	6	−→	−→	NOUN
ejpam-3129	118	7	gk+1	gk+1	NOUN
ejpam-3129	118	8	by	by	ADP
ejpam-3129	118	9	σ(g1	σ(g1	NOUN
ejpam-3129	118	10	,	,	PUNCT
ejpam-3129	118	11	...	...	PUNCT
ejpam-3129	118	12	,	,	PUNCT
ejpam-3129	118	13	gk+1	gk+1	X
ejpam-3129	118	14	)	)	PUNCT
ejpam-3129	118	15	=	=	SYM
ejpam-3129	118	16	(	(	PUNCT
ejpam-3129	118	17	gk+1	gk+1	NOUN
ejpam-3129	118	18	,	,	PUNCT
ejpam-3129	118	19	g1	g1	NOUN
ejpam-3129	118	20	,	,	PUNCT
ejpam-3129	118	21	...	...	PUNCT
ejpam-3129	118	22	,	,	PUNCT
ejpam-3129	118	23	gk	gk	PROPN
ejpam-3129	118	24	)	)	PUNCT
ejpam-3129	118	25	.	.	PUNCT
ejpam-3129	119	1	p.	p.	NOUN
ejpam-3129	119	2	bahmandoust	bahmandoust	NOUN
ejpam-3129	119	3	,	,	PUNCT
ejpam-3129	119	4	d.	d.	PROPN
ejpam-3129	119	5	latifi	latifi	PROPN
ejpam-3129	119	6	/	/	SYM
ejpam-3129	119	7	eur	eur	PROPN
ejpam-3129	119	8	.	.	PUNCT
ejpam-3129	120	1	j.	j.	PROPN
ejpam-3129	120	2	pure	pure	PROPN
ejpam-3129	120	3	appl	appl	PROPN
ejpam-3129	120	4	.	.	PROPN
ejpam-3129	120	5	math	math	PROPN
ejpam-3129	120	6	,	,	PUNCT
ejpam-3129	120	7	10	10	NUM
ejpam-3129	120	8	(	(	PUNCT
ejpam-3129	120	9	5	5	NUM
ejpam-3129	120	10	)	)	PUNCT
ejpam-3129	120	11	(	(	PUNCT
ejpam-3129	120	12	2017	2017	NUM
ejpam-3129	120	13	)	)	PUNCT
ejpam-3129	120	14	,	,	PUNCT
ejpam-3129	120	15	1099	1099	NUM
ejpam-3129	120	16	-	-	SYM
ejpam-3129	120	17	1111	1111	NUM
ejpam-3129	120	18	1104	1104	NUM
ejpam-3129	120	19	then	then	ADV
ejpam-3129	120	20	σ	σ	PROPN
ejpam-3129	120	21	is	be	AUX
ejpam-3129	120	22	an	an	DET
ejpam-3129	120	23	automorphism	automorphism	NOUN
ejpam-3129	120	24	of	of	ADP
ejpam-3129	120	25	order	order	NOUN
ejpam-3129	120	26	k	k	PROPN
ejpam-3129	121	1	+	+	NOUN
ejpam-3129	121	2	1	1	X
ejpam-3129	121	3	.	.	PUNCT
ejpam-3129	121	4	it	it	PRON
ejpam-3129	121	5	induces	induce	VERB
ejpam-3129	121	6	a	a	DET
ejpam-3129	121	7	map	map	NOUN
ejpam-3129	121	8	s	s	VERB
ejpam-3129	121	9	:	:	PUNCT
ejpam-3129	121	10	gk	gk	PROPN
ejpam-3129	121	11	−→	−→	PROPN
ejpam-3129	121	12	gk	gk	PROPN
ejpam-3129	121	13	defined	define	VERB
ejpam-3129	121	14	by	by	ADP
ejpam-3129	121	15	s(g1	s(g1	NOUN
ejpam-3129	121	16	,	,	PUNCT
ejpam-3129	121	17	...	...	PUNCT
ejpam-3129	121	18	,	,	PUNCT
ejpam-3129	121	19	gk	gk	PROPN
ejpam-3129	121	20	)	)	PUNCT
ejpam-3129	121	21	=	=	PUNCT
ejpam-3129	122	1	(	(	PUNCT
ejpam-3129	122	2	g−1k	g−1k	NOUN
ejpam-3129	122	3	,	,	PUNCT
ejpam-3129	122	4	g1	g1	VERB
ejpam-3129	122	5	g	g	PROPN
ejpam-3129	122	6	−1	−1	NOUN
ejpam-3129	122	7	k	k	PROPN
ejpam-3129	122	8	,	,	PUNCT
ejpam-3129	122	9	...	...	PUNCT
ejpam-3129	122	10	,	,	PUNCT
ejpam-3129	122	11	gk−1	gk−1	VERB
ejpam-3129	122	12	g	g	NOUN
ejpam-3129	122	13	−1	−1	NOUN
ejpam-3129	122	14	k	k	PROPN
ejpam-3129	122	15	)	)	PUNCT
ejpam-3129	122	16	.	.	PUNCT
ejpam-3129	123	1	let	let	VERB
ejpam-3129	123	2	f	f	PRON
ejpam-3129	123	3	be	be	AUX
ejpam-3129	123	4	a	a	DET
ejpam-3129	123	5	bi	bi	ADJ
ejpam-3129	123	6	-	-	ADJ
ejpam-3129	123	7	invariant	invariant	ADJ
ejpam-3129	123	8	finsler	finsler	NOUN
ejpam-3129	123	9	metric	metric	NOUN
ejpam-3129	123	10	on	on	ADP
ejpam-3129	123	11	g.	g.	PROPN
ejpam-3129	123	12	then	then	ADV
ejpam-3129	123	13	f	f	PROPN
ejpam-3129	123	14	generates	generate	VERB
ejpam-3129	123	15	a	a	DET
ejpam-3129	123	16	bi	bi	ADJ
ejpam-3129	123	17	-	-	ADJ
ejpam-3129	123	18	invariant	invariant	ADJ
ejpam-3129	123	19	finsler	finsler	NOUN
ejpam-3129	123	20	metric	metric	NOUN
ejpam-3129	123	21	f	f	PROPN
ejpam-3129	123	22	k+1	k+1	X
ejpam-3129	123	23	on	on	ADP
ejpam-3129	123	24	gk+1	gk+1	NOUN
ejpam-3129	123	25	such	such	ADJ
ejpam-3129	123	26	that	that	PRON
ejpam-3129	123	27	(	(	PUNCT
ejpam-3129	123	28	gk+1	gk+1	NOUN
ejpam-3129	123	29	,	,	PUNCT
ejpam-3129	123	30	f	f	PROPN
ejpam-3129	123	31	k+1	k+1	NOUN
ejpam-3129	123	32	)	)	PUNCT
ejpam-3129	123	33	∼=	∼=	PROPN
ejpam-3129	123	34	(	(	PUNCT
ejpam-3129	123	35	g	g	PROPN
ejpam-3129	123	36	,	,	PUNCT
ejpam-3129	123	37	f	f	PROPN
ejpam-3129	123	38	)	)	PUNCT
ejpam-3129	123	39	×	×	NOUN
ejpam-3129	123	40	...	...	PUNCT
ejpam-3129	123	41	×	×	NOUN
ejpam-3129	123	42	(	(	PUNCT
ejpam-3129	123	43	g	g	PROPN
ejpam-3129	123	44	,	,	PUNCT
ejpam-3129	123	45	f	f	PROPN
ejpam-3129	123	46	)	)	PUNCT
ejpam-3129	124	1	then	then	ADV
ejpam-3129	124	2	f	f	PROPN
ejpam-3129	124	3	k+1	k+1	PROPN
ejpam-3129	124	4	induces	induce	VERB
ejpam-3129	124	5	a	a	DET
ejpam-3129	124	6	gk+1−invariant	gk+1−invariant	NOUN
ejpam-3129	124	7	finsler	finsler	NOUN
ejpam-3129	124	8	metric	metric	NOUN
ejpam-3129	124	9	f	f	PROPN
ejpam-3129	125	1	[	[	X
ejpam-3129	125	2	k	k	X
ejpam-3129	125	3	]	]	X
ejpam-3129	125	4	on	on	ADP
ejpam-3129	125	5	gk	gk	PROPN
ejpam-3129	125	6	.	.	PUNCT
ejpam-3129	126	1	the	the	DET
ejpam-3129	126	2	finsler	finsler	NOUN
ejpam-3129	126	3	space	space	NOUN
ejpam-3129	126	4	(	(	PUNCT
ejpam-3129	126	5	gk	gk	PROPN
ejpam-3129	126	6	,	,	PUNCT
ejpam-3129	126	7	f	f	PROPN
ejpam-3129	127	1	[	[	X
ejpam-3129	127	2	k	k	X
ejpam-3129	127	3	]	]	X
ejpam-3129	127	4	)	)	PUNCT
ejpam-3129	127	5	is	be	AUX
ejpam-3129	127	6	a	a	DET
ejpam-3129	127	7	(	(	PUNCT
ejpam-3129	127	8	k+1)-symmetric	k+1)-symmetric	X
ejpam-3129	127	9	finsler	finsler	NOUN
ejpam-3129	127	10	space	space	NOUN
ejpam-3129	127	11	.	.	PUNCT
ejpam-3129	128	1	similar	similar	ADJ
ejpam-3129	128	2	to	to	ADP
ejpam-3129	128	3	the	the	DET
ejpam-3129	128	4	riemannian	riemannian	ADJ
ejpam-3129	128	5	case	case	NOUN
ejpam-3129	128	6	(	(	PUNCT
ejpam-3129	128	7	gk	gk	PROPN
ejpam-3129	128	8	,	,	PUNCT
ejpam-3129	128	9	f	f	PROPN
ejpam-3129	129	1	[	[	X
ejpam-3129	129	2	k	k	X
ejpam-3129	129	3	]	]	X
ejpam-3129	129	4	)	)	PUNCT
ejpam-3129	129	5	is	be	AUX
ejpam-3129	129	6	not	not	PART
ejpam-3129	129	7	a	a	DET
ejpam-3129	129	8	symmetric	symmetric	ADJ
ejpam-3129	129	9	space	space	NOUN
ejpam-3129	129	10	.	.	PUNCT
ejpam-3129	130	1	�	�	PROPN
ejpam-3129	130	2	example	example	NOUN
ejpam-3129	130	3	3	3	X
ejpam-3129	130	4	.	.	PUNCT
ejpam-3129	131	1	let	let	VERB
ejpam-3129	131	2	(	(	PUNCT
ejpam-3129	131	3	g1	g1	VERB
ejpam-3129	131	4	/	/	SYM
ejpam-3129	131	5	h1	h1	PROPN
ejpam-3129	131	6	,	,	PUNCT
ejpam-3129	131	7	g1	g1	PROPN
ejpam-3129	131	8	)	)	PUNCT
ejpam-3129	131	9	,	,	PUNCT
ejpam-3129	131	10	(	(	PUNCT
ejpam-3129	131	11	g2	g2	PROPN
ejpam-3129	131	12	/	/	SYM
ejpam-3129	131	13	h2	h2	PROPN
ejpam-3129	131	14	,	,	PUNCT
ejpam-3129	131	15	g2	g2	PROPN
ejpam-3129	131	16	)	)	PUNCT
ejpam-3129	131	17	be	be	VERB
ejpam-3129	131	18	two	two	NUM
ejpam-3129	131	19	riemannian	riemannian	ADJ
ejpam-3129	131	20	s−manifolds	s−manifolds	ADP
ejpam-3129	131	21	with	with	ADP
ejpam-3129	131	22	h1	h1	NOUN
ejpam-3129	131	23	and	and	CCONJ
ejpam-3129	131	24	h2	h2	NOUN
ejpam-3129	131	25	compact	compact	ADJ
ejpam-3129	131	26	and	and	CCONJ
ejpam-3129	131	27	{	{	PUNCT
ejpam-3129	131	28	τp	τp	NOUN
ejpam-3129	131	29	}	}	PUNCT
ejpam-3129	131	30	,	,	PUNCT
ejpam-3129	131	31	{	{	PUNCT
ejpam-3129	131	32	σq	σq	AUX
ejpam-3129	131	33	}	}	PUNCT
ejpam-3129	131	34	be	be	AUX
ejpam-3129	131	35	s−structures	s−structure	NOUN
ejpam-3129	131	36	on	on	ADP
ejpam-3129	131	37	g1	g1	NOUN
ejpam-3129	131	38	/	/	SYM
ejpam-3129	131	39	h1	h1	NOUN
ejpam-3129	131	40	,	,	PUNCT
ejpam-3129	131	41	g2	g2	PROPN
ejpam-3129	131	42	/	/	SYM
ejpam-3129	131	43	h2	h2	PROPN
ejpam-3129	131	44	,	,	PUNCT
ejpam-3129	131	45	respectively	respectively	ADV
ejpam-3129	131	46	of	of	ADP
ejpam-3129	131	47	order	order	NOUN
ejpam-3129	131	48	k.	k.	PROPN
ejpam-3129	131	49	let	let	VERB
ejpam-3129	131	50	m	m	NOUN
ejpam-3129	131	51	=	=	PUNCT
ejpam-3129	131	52	g1	g1	X
ejpam-3129	131	53	/	/	SYM
ejpam-3129	131	54	h1	h1	PROPN
ejpam-3129	131	55	×	×	PROPN
ejpam-3129	131	56	g2	g2	PROPN
ejpam-3129	131	57	/	/	SYM
ejpam-3129	131	58	h2	h2	PROPN
ejpam-3129	131	59	and	and	CCONJ
ejpam-3129	131	60	o1	o1	NOUN
ejpam-3129	131	61	,	,	PUNCT
ejpam-3129	131	62	o2	o2	PROPN
ejpam-3129	131	63	be	be	VERB
ejpam-3129	131	64	the	the	DET
ejpam-3129	131	65	origins	origin	NOUN
ejpam-3129	131	66	of	of	ADP
ejpam-3129	131	67	g1	g1	PROPN
ejpam-3129	131	68	/	/	SYM
ejpam-3129	131	69	h1	h1	PROPN
ejpam-3129	131	70	,	,	PUNCT
ejpam-3129	131	71	g2	g2	PROPN
ejpam-3129	131	72	/	/	SYM
ejpam-3129	131	73	h2	h2	PROPN
ejpam-3129	131	74	respectively	respectively	ADV
ejpam-3129	131	75	,	,	PUNCT
ejpam-3129	131	76	and	and	CCONJ
ejpam-3129	131	77	denote	denote	VERB
ejpam-3129	131	78	the	the	DET
ejpam-3129	131	79	origin	origin	NOUN
ejpam-3129	131	80	of	of	ADP
ejpam-3129	131	81	m	m	PRON
ejpam-3129	131	82	by	by	ADP
ejpam-3129	131	83	o	o	PROPN
ejpam-3129	131	84	=	=	SYM
ejpam-3129	131	85	(	(	PUNCT
ejpam-3129	131	86	o1	o1	PROPN
ejpam-3129	131	87	,	,	PUNCT
ejpam-3129	131	88	o2	o2	PROPN
ejpam-3129	131	89	)	)	PUNCT
ejpam-3129	131	90	.	.	PUNCT
ejpam-3129	132	1	now	now	ADV
ejpam-3129	132	2	for	for	ADP
ejpam-3129	132	3	y	y	PROPN
ejpam-3129	132	4	=	=	SYM
ejpam-3129	132	5	y1	y1	PROPN
ejpam-3129	133	1	+	+	CCONJ
ejpam-3129	133	2	y2	y2	NOUN
ejpam-3129	133	3	∈	∈	PROPN
ejpam-3129	133	4	tom	tom	PROPN
ejpam-3129	133	5	=	=	SYM
ejpam-3129	133	6	to1(g1	to1(g1	PROPN
ejpam-3129	133	7	/	/	SYM
ejpam-3129	133	8	h1	h1	NOUN
ejpam-3129	133	9	)	)	PUNCT
ejpam-3129	133	10	+	+	CCONJ
ejpam-3129	133	11	to2(g2	to2(g2	PROPN
ejpam-3129	133	12	/	/	SYM
ejpam-3129	133	13	h2	h2	NOUN
ejpam-3129	133	14	)	)	PUNCT
ejpam-3129	133	15	,	,	PUNCT
ejpam-3129	133	16	we	we	PRON
ejpam-3129	133	17	define	define	VERB
ejpam-3129	133	18	f	f	PROPN
ejpam-3129	133	19	(	(	PUNCT
ejpam-3129	133	20	y	y	NOUN
ejpam-3129	133	21	)	)	PUNCT
ejpam-3129	133	22	=	=	NOUN
ejpam-3129	133	23	√	√	NUM
ejpam-3129	133	24	g1(y1	g1(y1	NOUN
ejpam-3129	133	25	,	,	PUNCT
ejpam-3129	133	26	y1	y1	NOUN
ejpam-3129	133	27	)	)	PUNCT
ejpam-3129	133	28	+	+	CCONJ
ejpam-3129	134	1	g2(y2	g2(y2	ADJ
ejpam-3129	134	2	,	,	PUNCT
ejpam-3129	134	3	y2	y2	NOUN
ejpam-3129	134	4	)	)	PUNCT
ejpam-3129	135	1	+	+	PRON
ejpam-3129	135	2	s	s	VERB
ejpam-3129	135	3	√	√	NUM
ejpam-3129	135	4	g1(y1	g1(y1	NOUN
ejpam-3129	135	5	,	,	PUNCT
ejpam-3129	135	6	y1)s	y1)s	PROPN
ejpam-3129	135	7	+	+	CCONJ
ejpam-3129	135	8	g2(y2	g2(y2	ADJ
ejpam-3129	135	9	,	,	PUNCT
ejpam-3129	135	10	y2)s	y2)s	ADJ
ejpam-3129	135	11	where	where	SCONJ
ejpam-3129	135	12	s	s	NOUN
ejpam-3129	135	13	is	be	AUX
ejpam-3129	135	14	any	any	DET
ejpam-3129	135	15	integer	integer	NOUN
ejpam-3129	135	16	≥	≥	NOUN
ejpam-3129	135	17	2	2	NUM
ejpam-3129	135	18	.	.	PUNCT
ejpam-3129	136	1	then	then	ADV
ejpam-3129	136	2	f	f	PROPN
ejpam-3129	136	3	(	(	PUNCT
ejpam-3129	136	4	y	y	NOUN
ejpam-3129	136	5	)	)	PUNCT
ejpam-3129	136	6	is	be	AUX
ejpam-3129	136	7	a	a	DET
ejpam-3129	136	8	minkowski	minkowski	ADJ
ejpam-3129	136	9	norm	norm	NOUN
ejpam-3129	136	10	on	on	ADP
ejpam-3129	136	11	tom	tom	PROPN
ejpam-3129	136	12	which	which	PRON
ejpam-3129	136	13	is	be	AUX
ejpam-3129	136	14	invariant	invariant	ADJ
ejpam-3129	136	15	under	under	ADP
ejpam-3129	136	16	h1	h1	PROPN
ejpam-3129	136	17	×	×	PROPN
ejpam-3129	136	18	h2	h2	NOUN
ejpam-3129	136	19	.	.	PUNCT
ejpam-3129	137	1	hence	hence	ADV
ejpam-3129	137	2	it	it	PRON
ejpam-3129	137	3	defines	define	VERB
ejpam-3129	137	4	a	a	DET
ejpam-3129	137	5	g−invariant	g−invariant	NOUN
ejpam-3129	137	6	finsler	finsler	NOUN
ejpam-3129	137	7	metric	metric	ADJ
ejpam-3129	137	8	on	on	ADP
ejpam-3129	137	9	m	m	PROPN
ejpam-3129	137	10	.	.	PUNCT
ejpam-3129	138	1	it	it	PRON
ejpam-3129	138	2	is	be	AUX
ejpam-3129	138	3	easy	easy	ADJ
ejpam-3129	138	4	to	to	PART
ejpam-3129	138	5	see	see	VERB
ejpam-3129	138	6	that	that	DET
ejpam-3129	138	7	finsler	finsler	NOUN
ejpam-3129	138	8	manifold	manifold	ADJ
ejpam-3129	138	9	(	(	PUNCT
ejpam-3129	138	10	m	m	PROPN
ejpam-3129	138	11	,	,	PUNCT
ejpam-3129	138	12	f	f	PROPN
ejpam-3129	138	13	)	)	PUNCT
ejpam-3129	138	14	is	be	AUX
ejpam-3129	138	15	non	non	ADJ
ejpam-3129	138	16	-	-	ADJ
ejpam-3129	138	17	riemannian	riemannian	ADJ
ejpam-3129	138	18	s−manifold	s−manifold	NOUN
ejpam-3129	138	19	with	with	ADP
ejpam-3129	138	20	regular	regular	ADJ
ejpam-3129	138	21	s−structure	s−structure	NOUN
ejpam-3129	138	22	{	{	PUNCT
ejpam-3129	138	23	τp	τp	PRON
ejpam-3129	138	24	×	×	PROPN
ejpam-3129	138	25	σq	σq	NOUN
ejpam-3129	138	26	}	}	PUNCT
ejpam-3129	138	27	.	.	PUNCT
ejpam-3129	139	1	�	�	PROPN
ejpam-3129	139	2	given	give	VERB
ejpam-3129	139	3	an	an	DET
ejpam-3129	139	4	s−structure	s−structure	NOUN
ejpam-3129	139	5	{	{	PUNCT
ejpam-3129	139	6	sx|x	sx|x	PROPN
ejpam-3129	139	7	∈	∈	PROPN
ejpam-3129	139	8	m	m	NOUN
ejpam-3129	139	9	}	}	PUNCT
ejpam-3129	139	10	on	on	ADP
ejpam-3129	139	11	(	(	PUNCT
ejpam-3129	139	12	m	m	PROPN
ejpam-3129	139	13	,	,	PUNCT
ejpam-3129	139	14	f	f	PROPN
ejpam-3129	139	15	)	)	PUNCT
ejpam-3129	139	16	we	we	PRON
ejpam-3129	139	17	shall	shall	AUX
ejpam-3129	139	18	always	always	ADV
ejpam-3129	139	19	denote	denote	VERB
ejpam-3129	139	20	by	by	ADP
ejpam-3129	139	21	s	s	PRON
ejpam-3129	139	22	the	the	DET
ejpam-3129	139	23	tensor	tensor	NOUN
ejpam-3129	139	24	field	field	NOUN
ejpam-3129	139	25	of	of	ADP
ejpam-3129	139	26	type	type	NOUN
ejpam-3129	139	27	(	(	PUNCT
ejpam-3129	139	28	1	1	NUM
ejpam-3129	139	29	,	,	PUNCT
ejpam-3129	139	30	1	1	NUM
ejpam-3129	139	31	)	)	PUNCT
ejpam-3129	139	32	defined	define	VERB
ejpam-3129	139	33	by	by	ADP
ejpam-3129	139	34	sx	sx	PROPN
ejpam-3129	139	35	=	=	PUNCT
ejpam-3129	139	36	(	(	PUNCT
ejpam-3129	139	37	sx)∗	sx)∗	PROPN
ejpam-3129	139	38	for	for	ADP
ejpam-3129	139	39	all	all	DET
ejpam-3129	139	40	x	x	SYM
ejpam-3129	139	41	∈	∈	PROPN
ejpam-3129	139	42	m	m	VERB
ejpam-3129	139	43	.	.	PUNCT
ejpam-3129	140	1	suppose	suppose	VERB
ejpam-3129	140	2	there	there	PRON
ejpam-3129	140	3	exists	exist	VERB
ejpam-3129	140	4	a	a	DET
ejpam-3129	140	5	nonzero	nonzero	PROPN
ejpam-3129	140	6	vector	vector	NOUN
ejpam-3129	140	7	x	x	PROPN
ejpam-3129	140	8	∈	∈	PROPN
ejpam-3129	140	9	txm	txm	PROPN
ejpam-3129	140	10	such	such	ADJ
ejpam-3129	140	11	that	that	DET
ejpam-3129	140	12	sxx	sxx	NOUN
ejpam-3129	141	1	=	=	PUNCT
ejpam-3129	141	2	x.	x.	NOUN
ejpam-3129	141	3	since	since	SCONJ
ejpam-3129	141	4	sx	sx	PROPN
ejpam-3129	141	5	is	be	AUX
ejpam-3129	141	6	isometry	isometry	NOUN
ejpam-3129	141	7	,	,	PUNCT
ejpam-3129	141	8	sx(expx(tx	sx(expx(tx	NOUN
ejpam-3129	141	9	)	)	PUNCT
ejpam-3129	141	10	)	)	PUNCT
ejpam-3129	141	11	,	,	PUNCT
ejpam-3129	141	12	|t|	|t|	VERB
ejpam-3129	141	13	<	<	X
ejpam-3129	141	14	ε	ε	PROPN
ejpam-3129	141	15	is	be	AUX
ejpam-3129	141	16	a	a	DET
ejpam-3129	141	17	geodesic	geodesic	NOUN
ejpam-3129	141	18	.	.	PUNCT
ejpam-3129	142	1	now	now	ADV
ejpam-3129	142	2	expx(tx	expx(tx	VERB
ejpam-3129	142	3	)	)	PUNCT
ejpam-3129	142	4	and	and	CCONJ
ejpam-3129	142	5	sx(expx(tx	sx(expx(tx	NOUN
ejpam-3129	142	6	)	)	PUNCT
ejpam-3129	142	7	)	)	PUNCT
ejpam-3129	142	8	are	be	AUX
ejpam-3129	142	9	two	two	NUM
ejpam-3129	142	10	geodesics	geodesic	NOUN
ejpam-3129	142	11	through	through	ADP
ejpam-3129	142	12	x	x	PUNCT
ejpam-3129	142	13	with	with	ADP
ejpam-3129	142	14	the	the	DET
ejpam-3129	142	15	same	same	ADJ
ejpam-3129	142	16	initial	initial	ADJ
ejpam-3129	142	17	vector	vector	NOUN
ejpam-3129	142	18	x.	x.	NOUN
ejpam-3129	142	19	therefore	therefore	ADV
ejpam-3129	142	20	,	,	PUNCT
ejpam-3129	142	21	for	for	ADP
ejpam-3129	142	22	any	any	DET
ejpam-3129	142	23	|t|	|t|	NOUN
ejpam-3129	142	24	<	<	X
ejpam-3129	142	25	ε	ε	X
ejpam-3129	142	26	we	we	PRON
ejpam-3129	142	27	have	have	AUX
ejpam-3129	142	28	sx(expx(tx	sx(expx(tx	NOUN
ejpam-3129	142	29	)	)	PUNCT
ejpam-3129	142	30	)	)	PUNCT
ejpam-3129	143	1	=	=	PUNCT
ejpam-3129	143	2	expx(tx	expx(tx	NOUN
ejpam-3129	143	3	)	)	PUNCT
ejpam-3129	143	4	.	.	PUNCT
ejpam-3129	144	1	but	but	CCONJ
ejpam-3129	144	2	this	this	PRON
ejpam-3129	144	3	contradicts	contradict	VERB
ejpam-3129	144	4	to	to	ADP
ejpam-3129	144	5	assumption	assumption	NOUN
ejpam-3129	144	6	that	that	SCONJ
ejpam-3129	144	7	x	x	PRON
ejpam-3129	144	8	is	be	AUX
ejpam-3129	144	9	an	an	DET
ejpam-3129	144	10	isolated	isolated	ADJ
ejpam-3129	144	11	fixed	fix	VERB
ejpam-3129	144	12	point	point	NOUN
ejpam-3129	144	13	of	of	ADP
ejpam-3129	144	14	sx	sx	PROPN
ejpam-3129	144	15	.	.	PUNCT
ejpam-3129	145	1	therefore	therefore	ADV
ejpam-3129	145	2	sx	sx	PROPN
ejpam-3129	145	3	has	have	VERB
ejpam-3129	145	4	no	no	DET
ejpam-3129	145	5	non	non	ADJ
ejpam-3129	145	6	-	-	ADJ
ejpam-3129	145	7	zero	zero	NUM
ejpam-3129	145	8	invariant	invariant	ADJ
ejpam-3129	145	9	vector	vector	NOUN
ejpam-3129	145	10	.	.	PUNCT
ejpam-3129	146	1	theorem	theorem	NOUN
ejpam-3129	146	2	1	1	NUM
ejpam-3129	146	3	.	.	PUNCT
ejpam-3129	147	1	let	let	VERB
ejpam-3129	147	2	(	(	PUNCT
ejpam-3129	147	3	m	m	PROPN
ejpam-3129	147	4	,	,	PUNCT
ejpam-3129	147	5	f	f	PROPN
ejpam-3129	147	6	)	)	PUNCT
ejpam-3129	147	7	be	be	AUX
ejpam-3129	147	8	a	a	DET
ejpam-3129	147	9	finsler	finsler	NOUN
ejpam-3129	147	10	s−manifold	s−manifold	NOUN
ejpam-3129	147	11	.	.	PUNCT
ejpam-3129	148	1	then	then	ADV
ejpam-3129	148	2	we	we	PRON
ejpam-3129	148	3	have	have	VERB
ejpam-3129	148	4	(	(	PUNCT
ejpam-3129	148	5	a	a	X
ejpam-3129	148	6	)	)	PUNCT
ejpam-3129	148	7	for	for	ADP
ejpam-3129	148	8	any	any	DET
ejpam-3129	148	9	x	x	SYM
ejpam-3129	148	10	∈m	∈m	NOUN
ejpam-3129	148	11	,	,	PUNCT
ejpam-3129	148	12	sx	sx	PROPN
ejpam-3129	148	13	=	=	PUNCT
ejpam-3129	148	14	(	(	PUNCT
ejpam-3129	148	15	dsx)x	dsx)x	PROPN
ejpam-3129	148	16	has	have	VERB
ejpam-3129	148	17	no	no	DET
ejpam-3129	148	18	invariant	invariant	ADJ
ejpam-3129	148	19	vector	vector	NOUN
ejpam-3129	148	20	,	,	PUNCT
ejpam-3129	148	21	(	(	PUNCT
ejpam-3129	148	22	b	b	NOUN
ejpam-3129	148	23	)	)	PUNCT
ejpam-3129	148	24	(	(	PUNCT
ejpam-3129	148	25	m	m	PROPN
ejpam-3129	148	26	,	,	PUNCT
ejpam-3129	148	27	f	f	PROPN
ejpam-3129	148	28	)	)	PUNCT
ejpam-3129	148	29	is	be	AUX
ejpam-3129	148	30	homogeneous	homogeneous	ADJ
ejpam-3129	148	31	.	.	PUNCT
ejpam-3129	149	1	that	that	PRON
ejpam-3129	149	2	is	is	ADV
ejpam-3129	149	3	,	,	PUNCT
ejpam-3129	149	4	the	the	DET
ejpam-3129	149	5	group	group	NOUN
ejpam-3129	149	6	of	of	ADP
ejpam-3129	149	7	isometries	isometry	NOUN
ejpam-3129	149	8	of	of	ADP
ejpam-3129	149	9	(	(	PUNCT
ejpam-3129	149	10	m	m	PROPN
ejpam-3129	149	11	,	,	PUNCT
ejpam-3129	149	12	f	f	PROPN
ejpam-3129	149	13	)	)	PUNCT
ejpam-3129	149	14	,	,	PUNCT
ejpam-3129	149	15	i(m	i(m	NOUN
ejpam-3129	149	16	,	,	PUNCT
ejpam-3129	149	17	f	f	PROPN
ejpam-3129	149	18	)	)	PUNCT
ejpam-3129	149	19	,	,	PUNCT
ejpam-3129	149	20	acts	act	VERB
ejpam-3129	149	21	transitively	transitively	PROPN
ejpam-3129	149	22	on	on	ADP
ejpam-3129	149	23	m	m	PROPN
ejpam-3129	149	24	.	.	PUNCT
ejpam-3129	150	1	p.	p.	NOUN
ejpam-3129	150	2	bahmandoust	bahmandoust	NOUN
ejpam-3129	150	3	,	,	PUNCT
ejpam-3129	150	4	d.	d.	PROPN
ejpam-3129	150	5	latifi	latifi	PROPN
ejpam-3129	150	6	/	/	SYM
ejpam-3129	150	7	eur	eur	PROPN
ejpam-3129	150	8	.	.	PUNCT
ejpam-3129	151	1	j.	j.	PROPN
ejpam-3129	151	2	pure	pure	PROPN
ejpam-3129	151	3	appl	appl	PROPN
ejpam-3129	151	4	.	.	PROPN
ejpam-3129	151	5	math	math	PROPN
ejpam-3129	151	6	,	,	PUNCT
ejpam-3129	151	7	10	10	NUM
ejpam-3129	151	8	(	(	PUNCT
ejpam-3129	151	9	5	5	NUM
ejpam-3129	151	10	)	)	PUNCT
ejpam-3129	151	11	(	(	PUNCT
ejpam-3129	151	12	2017	2017	NUM
ejpam-3129	151	13	)	)	PUNCT
ejpam-3129	151	14	,	,	PUNCT
ejpam-3129	151	15	1099	1099	NUM
ejpam-3129	151	16	-	-	SYM
ejpam-3129	151	17	1111	1111	NUM
ejpam-3129	151	18	1105	1105	NUM
ejpam-3129	151	19	(	(	PUNCT
ejpam-3129	151	20	c	c	NOUN
ejpam-3129	151	21	)	)	PUNCT
ejpam-3129	151	22	(	(	PUNCT
ejpam-3129	151	23	m	m	PROPN
ejpam-3129	151	24	,	,	PUNCT
ejpam-3129	151	25	f	f	PROPN
ejpam-3129	151	26	)	)	PUNCT
ejpam-3129	151	27	is	be	AUX
ejpam-3129	151	28	forward	forward	ADV
ejpam-3129	151	29	complete	complete	ADJ
ejpam-3129	151	30	.	.	PUNCT
ejpam-3129	152	1	proof	proof	NOUN
ejpam-3129	152	2	:	:	PUNCT
ejpam-3129	152	3	see	see	VERB
ejpam-3129	152	4	[	[	X
ejpam-3129	152	5	7	7	NUM
ejpam-3129	152	6	]	]	SYM
ejpam-3129	152	7	.	.	PUNCT
ejpam-3129	153	1	�	�	PROPN
ejpam-3129	153	2	theorem	theorem	VERB
ejpam-3129	153	3	2	2	NUM
ejpam-3129	153	4	.	.	PUNCT
ejpam-3129	154	1	let	let	VERB
ejpam-3129	154	2	(	(	PUNCT
ejpam-3129	154	3	m	m	PROPN
ejpam-3129	154	4	,	,	PUNCT
ejpam-3129	154	5	f	f	PROPN
ejpam-3129	154	6	)	)	PUNCT
ejpam-3129	154	7	be	be	AUX
ejpam-3129	154	8	a	a	DET
ejpam-3129	154	9	finsler	finsler	NOUN
ejpam-3129	154	10	s−manifol	s−manifol	VERB
ejpam-3129	154	11	with	with	ADP
ejpam-3129	154	12	regular	regular	ADJ
ejpam-3129	154	13	s−structure	s−structure	NOUN
ejpam-3129	154	14	{	{	PUNCT
ejpam-3129	154	15	sx	sx	NOUN
ejpam-3129	154	16	}	}	PUNCT
ejpam-3129	154	17	.	.	PUNCT
ejpam-3129	155	1	then	then	ADV
ejpam-3129	155	2	there	there	PRON
ejpam-3129	155	3	is	be	VERB
ejpam-3129	155	4	a	a	DET
ejpam-3129	155	5	unique	unique	ADJ
ejpam-3129	155	6	connection	connection	NOUN
ejpam-3129	155	7	∇̃	∇̃	NUM
ejpam-3129	156	1	on	on	ADP
ejpam-3129	156	2	m	m	PRON
ejpam-3129	156	3	such	such	ADJ
ejpam-3129	156	4	that	that	SCONJ
ejpam-3129	156	5	(	(	PUNCT
ejpam-3129	156	6	i	i	NOUN
ejpam-3129	156	7	)	)	PUNCT
ejpam-3129	156	8	∇̃	∇̃	PRON
ejpam-3129	156	9	is	be	AUX
ejpam-3129	156	10	invariant	invariant	ADJ
ejpam-3129	156	11	under	under	ADP
ejpam-3129	156	12	all	all	DET
ejpam-3129	156	13	sx	sx	PROPN
ejpam-3129	156	14	(	(	PUNCT
ejpam-3129	156	15	ii	ii	NOUN
ejpam-3129	156	16	)	)	PUNCT
ejpam-3129	156	17	∇̃s	∇̃s	X
ejpam-3129	157	1	=	=	SYM
ejpam-3129	157	2	0	0	NUM
ejpam-3129	157	3	proof	proof	NOUN
ejpam-3129	157	4	:	:	PUNCT
ejpam-3129	157	5	the	the	DET
ejpam-3129	157	6	proof	proof	NOUN
ejpam-3129	157	7	is	be	AUX
ejpam-3129	157	8	similar	similar	ADJ
ejpam-3129	157	9	to	to	ADP
ejpam-3129	157	10	the	the	DET
ejpam-3129	157	11	riemannian	riemannian	ADJ
ejpam-3129	157	12	case	case	NOUN
ejpam-3129	158	1	[	[	X
ejpam-3129	158	2	11	11	NUM
ejpam-3129	158	3	]	]	PUNCT
ejpam-3129	158	4	.	.	PUNCT
ejpam-3129	158	5	�	�	PROPN
ejpam-3129	158	6	if	if	SCONJ
ejpam-3129	158	7	the	the	DET
ejpam-3129	158	8	finsler	finsler	NOUN
ejpam-3129	158	9	space	space	NOUN
ejpam-3129	158	10	(	(	PUNCT
ejpam-3129	158	11	m	m	PROPN
ejpam-3129	158	12	,	,	PUNCT
ejpam-3129	158	13	f	f	PROPN
ejpam-3129	158	14	)	)	PUNCT
ejpam-3129	158	15	is	be	AUX
ejpam-3129	158	16	of	of	ADP
ejpam-3129	158	17	berwald	berwald	NOUN
ejpam-3129	158	18	type	type	NOUN
ejpam-3129	158	19	,	,	PUNCT
ejpam-3129	158	20	then	then	ADV
ejpam-3129	158	21	∇̃	∇̃	PRON
ejpam-3129	158	22	is	be	AUX
ejpam-3129	158	23	given	give	VERB
ejpam-3129	158	24	by	by	ADP
ejpam-3129	158	25	the	the	DET
ejpam-3129	158	26	formula	formula	NOUN
ejpam-3129	158	27	∇̃xy	∇̃xy	NOUN
ejpam-3129	158	28	=	=	SYM
ejpam-3129	158	29	∇xy	∇xy	ADP
ejpam-3129	158	30	−	−	PROPN
ejpam-3129	158	31	(	(	PUNCT
ejpam-3129	158	32	∇(i−s)−1xs)(s−1y	∇(i−s)−1xs)(s−1y	NOUN
ejpam-3129	158	33	)	)	PUNCT
ejpam-3129	158	34	where	where	SCONJ
ejpam-3129	158	35	∇	∇	PROPN
ejpam-3129	158	36	is	be	AUX
ejpam-3129	158	37	the	the	DET
ejpam-3129	158	38	chern	chern	PROPN
ejpam-3129	158	39	connection	connection	NOUN
ejpam-3129	158	40	of	of	ADP
ejpam-3129	158	41	(	(	PUNCT
ejpam-3129	158	42	m	m	PROPN
ejpam-3129	158	43	,	,	PUNCT
ejpam-3129	158	44	f	f	PROPN
ejpam-3129	158	45	)	)	PUNCT
ejpam-3129	158	46	.	.	PUNCT
ejpam-3129	159	1	definition	definition	NOUN
ejpam-3129	159	2	4	4	NUM
ejpam-3129	159	3	.	.	PUNCT
ejpam-3129	160	1	let	let	VERB
ejpam-3129	160	2	(	(	PUNCT
ejpam-3129	160	3	m	m	PROPN
ejpam-3129	160	4	,	,	PUNCT
ejpam-3129	160	5	f	f	PROPN
ejpam-3129	160	6	)	)	PUNCT
ejpam-3129	160	7	be	be	AUX
ejpam-3129	160	8	a	a	DET
ejpam-3129	160	9	generalized	generalized	ADJ
ejpam-3129	160	10	symmetric	symmetric	ADJ
ejpam-3129	160	11	finsler	finsler	NOUN
ejpam-3129	160	12	space	space	NOUN
ejpam-3129	160	13	,	,	PUNCT
ejpam-3129	160	14	and	and	CCONJ
ejpam-3129	160	15	let	let	VERB
ejpam-3129	160	16	{	{	PUNCT
ejpam-3129	160	17	sx	sx	NOUN
ejpam-3129	160	18	}	}	PUNCT
ejpam-3129	160	19	be	be	AUX
ejpam-3129	160	20	the	the	DET
ejpam-3129	160	21	regular	regular	ADJ
ejpam-3129	160	22	s−structure	s−structure	NOUN
ejpam-3129	160	23	of	of	ADP
ejpam-3129	160	24	(	(	PUNCT
ejpam-3129	160	25	m	m	PROPN
ejpam-3129	160	26	,	,	PUNCT
ejpam-3129	160	27	f	f	PROPN
ejpam-3129	160	28	)	)	PUNCT
ejpam-3129	160	29	.	.	PUNCT
ejpam-3129	161	1	then	then	ADV
ejpam-3129	161	2	a	a	DET
ejpam-3129	161	3	diffeomorphism	diffeomorphism	NOUN
ejpam-3129	161	4	φ	φ	NOUN
ejpam-3129	161	5	:	:	PUNCT
ejpam-3129	161	6	m	m	VERB
ejpam-3129	161	7	−→	−→	ADJ
ejpam-3129	161	8	m	m	VERB
ejpam-3129	161	9	is	be	AUX
ejpam-3129	161	10	called	call	VERB
ejpam-3129	161	11	symmetry	symmetry	NOUN
ejpam-3129	161	12	preserving	preserve	VERB
ejpam-3129	161	13	if	if	SCONJ
ejpam-3129	161	14	φ(sx(y	φ(sx(y	NOUN
ejpam-3129	161	15	)	)	PUNCT
ejpam-3129	161	16	)	)	PUNCT
ejpam-3129	162	1	=	=	SYM
ejpam-3129	162	2	sφ(x)φ(y	sφ(x)φ(y	NOUN
ejpam-3129	162	3	)	)	PUNCT
ejpam-3129	162	4	for	for	ADP
ejpam-3129	162	5	all	all	DET
ejpam-3129	162	6	x	x	NOUN
ejpam-3129	162	7	,	,	PUNCT
ejpam-3129	162	8	y	y	PROPN
ejpam-3129	162	9	∈m	∈m	NOUN
ejpam-3129	162	10	.	.	PUNCT
ejpam-3129	163	1	obviously	obviously	ADV
ejpam-3129	163	2	,	,	PUNCT
ejpam-3129	163	3	all	all	DET
ejpam-3129	163	4	symmetries	symmetry	NOUN
ejpam-3129	163	5	sx	sx	PROPN
ejpam-3129	163	6	are	be	AUX
ejpam-3129	163	7	symmetry	symmetry	NOUN
ejpam-3129	163	8	preserving	preserve	VERB
ejpam-3129	163	9	due	due	ADP
ejpam-3129	163	10	to	to	ADP
ejpam-3129	163	11	sx	sx	PROPN
ejpam-3129	163	12	◦	◦	NOUN
ejpam-3129	163	13	sy	sy	NOUN
ejpam-3129	163	14	=	=	SYM
ejpam-3129	163	15	sz	sz	PROPN
ejpam-3129	163	16	◦	◦	NOUN
ejpam-3129	163	17	sx	sx	NOUN
ejpam-3129	163	18	,	,	PUNCT
ejpam-3129	163	19	z	z	NOUN
ejpam-3129	163	20	=	=	SYM
ejpam-3129	163	21	sx(y	sx(y	PROPN
ejpam-3129	163	22	)	)	PUNCT
ejpam-3129	163	23	.	.	PUNCT
ejpam-3129	164	1	we	we	PRON
ejpam-3129	164	2	denote	denote	VERB
ejpam-3129	164	3	the	the	DET
ejpam-3129	164	4	group	group	NOUN
ejpam-3129	164	5	of	of	ADP
ejpam-3129	164	6	symmetry	symmetry	NOUN
ejpam-3129	164	7	preserving	preserve	VERB
ejpam-3129	164	8	diffeomorphism	diffeomorphism	NOUN
ejpam-3129	164	9	by	by	ADP
ejpam-3129	164	10	aut({sx	aut({sx	ADJ
ejpam-3129	164	11	}	}	PUNCT
ejpam-3129	164	12	)	)	PUNCT
ejpam-3129	164	13	.	.	PUNCT
ejpam-3129	165	1	let	let	VERB
ejpam-3129	165	2	us	we	PRON
ejpam-3129	165	3	denote	denote	VERB
ejpam-3129	165	4	by	by	ADP
ejpam-3129	165	5	a(m	a(m	NOUN
ejpam-3129	165	6	)	)	PUNCT
ejpam-3129	165	7	the	the	DET
ejpam-3129	165	8	lie	lie	NOUN
ejpam-3129	165	9	group	group	NOUN
ejpam-3129	165	10	of	of	ADP
ejpam-3129	165	11	all	all	DET
ejpam-3129	165	12	affine	affine	ADJ
ejpam-3129	165	13	transformations	transformation	NOUN
ejpam-3129	165	14	of	of	ADP
ejpam-3129	165	15	m	m	VERB
ejpam-3129	165	16	with	with	ADP
ejpam-3129	165	17	respect	respect	NOUN
ejpam-3129	165	18	to	to	ADP
ejpam-3129	165	19	the	the	DET
ejpam-3129	165	20	connection	connection	NOUN
ejpam-3129	165	21	∇̃.	∇̃.	PRON
ejpam-3129	165	22	each	each	DET
ejpam-3129	165	23	symmetry	symmetry	NOUN
ejpam-3129	165	24	preserving	preserve	VERB
ejpam-3129	165	25	diffeomorphism	diffeomorphism	NOUN
ejpam-3129	165	26	is	be	AUX
ejpam-3129	165	27	an	an	DET
ejpam-3129	165	28	affine	affine	ADJ
ejpam-3129	165	29	transformation	transformation	NOUN
ejpam-3129	165	30	of	of	ADP
ejpam-3129	165	31	(	(	PUNCT
ejpam-3129	165	32	m	m	PROPN
ejpam-3129	165	33	,	,	PUNCT
ejpam-3129	165	34	∇̃	∇̃	NUM
ejpam-3129	165	35	)	)	PUNCT
ejpam-3129	165	36	,	,	PUNCT
ejpam-3129	165	37	i.e.	i.e.	X
ejpam-3129	165	38	aut(m	aut(m	PROPN
ejpam-3129	165	39	,	,	PUNCT
ejpam-3129	165	40	{	{	PUNCT
ejpam-3129	165	41	sx	sx	NOUN
ejpam-3129	165	42	}	}	PUNCT
ejpam-3129	165	43	)	)	PUNCT
ejpam-3129	166	1	⊂	⊂	PROPN
ejpam-3129	166	2	a(m	a(m	NOUN
ejpam-3129	166	3	)	)	PUNCT
ejpam-3129	166	4	.	.	PUNCT
ejpam-3129	167	1	lemma	lemma	PROPN
ejpam-3129	167	2	1	1	NUM
ejpam-3129	167	3	.	.	PUNCT
ejpam-3129	168	1	an	an	DET
ejpam-3129	168	2	affine	affine	NOUN
ejpam-3129	168	3	transformation	transformation	NOUN
ejpam-3129	168	4	φ	φ	PROPN
ejpam-3129	168	5	∈	∈	PROPN
ejpam-3129	168	6	a(m	a(m	NOUN
ejpam-3129	168	7	)	)	PUNCT
ejpam-3129	168	8	is	be	AUX
ejpam-3129	168	9	symmetry	symmetry	NOUN
ejpam-3129	168	10	preserving	preserve	VERB
ejpam-3129	168	11	if	if	SCONJ
ejpam-3129	168	12	and	and	CCONJ
ejpam-3129	168	13	only	only	ADV
ejpam-3129	168	14	if	if	SCONJ
ejpam-3129	168	15	it	it	PRON
ejpam-3129	168	16	preserves	preserve	VERB
ejpam-3129	168	17	the	the	DET
ejpam-3129	168	18	tensor	tensor	NOUN
ejpam-3129	168	19	field	field	NOUN
ejpam-3129	168	20	s.	s.	PROPN
ejpam-3129	168	21	consequently	consequently	ADV
ejpam-3129	168	22	,	,	PUNCT
ejpam-3129	168	23	aut({sx	aut({sx	ADJ
ejpam-3129	168	24	}	}	PUNCT
ejpam-3129	168	25	)	)	PUNCT
ejpam-3129	168	26	is	be	AUX
ejpam-3129	168	27	a	a	DET
ejpam-3129	168	28	closed	closed	ADJ
ejpam-3129	168	29	subgroup	subgroup	NOUN
ejpam-3129	168	30	of	of	ADP
ejpam-3129	168	31	a(m	a(m	PROPN
ejpam-3129	168	32	)	)	PUNCT
ejpam-3129	168	33	and	and	CCONJ
ejpam-3129	168	34	hence	hence	ADV
ejpam-3129	168	35	a	a	DET
ejpam-3129	168	36	lie	lie	NOUN
ejpam-3129	168	37	transformation	transformation	NOUN
ejpam-3129	168	38	group	group	NOUN
ejpam-3129	168	39	of	of	ADP
ejpam-3129	168	40	m	m	PROPN
ejpam-3129	168	41	.	.	PUNCT
ejpam-3129	169	1	proof	proof	NOUN
ejpam-3129	169	2	:	:	PUNCT
ejpam-3129	169	3	let	let	VERB
ejpam-3129	169	4	φ	φ	PROPN
ejpam-3129	169	5	∈	∈	PROPN
ejpam-3129	169	6	a(m	a(m	PROPN
ejpam-3129	169	7	)	)	PUNCT
ejpam-3129	169	8	be	be	VERB
ejpam-3129	169	9	symmetry	symmetry	NOUN
ejpam-3129	169	10	preserving	preserve	VERB
ejpam-3129	169	11	transformation	transformation	NOUN
ejpam-3129	169	12	then	then	ADV
ejpam-3129	169	13	for	for	ADP
ejpam-3129	169	14	each	each	DET
ejpam-3129	169	15	x	x	SYM
ejpam-3129	169	16	∈	∈	PROPN
ejpam-3129	169	17	m	m	PROPN
ejpam-3129	169	18	,	,	PUNCT
ejpam-3129	169	19	maps	map	VERB
ejpam-3129	169	20	φ	φ	NOUN
ejpam-3129	169	21	◦	◦	PROPN
ejpam-3129	169	22	sx	sx	PROPN
ejpam-3129	169	23	,	,	PUNCT
ejpam-3129	169	24	sφ(x	sφ(x	NUM
ejpam-3129	169	25	)	)	PUNCT
ejpam-3129	169	26	◦	◦	NOUN
ejpam-3129	169	27	φ	φ	NUM
ejpam-3129	169	28	coincide	coincide	NOUN
ejpam-3129	169	29	,	,	PUNCT
ejpam-3129	169	30	so	so	CCONJ
ejpam-3129	169	31	(	(	PUNCT
ejpam-3129	169	32	φ	φ	NUM
ejpam-3129	169	33	◦	◦	NOUN
ejpam-3129	169	34	sx)∗x	sx)∗x	NUM
ejpam-3129	169	35	=	=	SYM
ejpam-3129	169	36	(	(	PUNCT
ejpam-3129	169	37	sφ(x	sφ(x	NOUN
ejpam-3129	169	38	)	)	PUNCT
ejpam-3129	169	39	◦	◦	NOUN
ejpam-3129	169	40	φ)∗x	φ)∗x	NOUN
ejpam-3129	169	41	.	.	PUNCT
ejpam-3129	170	1	then	then	ADV
ejpam-3129	170	2	φ	φ	PROPN
ejpam-3129	170	3	preserves	preserve	VERB
ejpam-3129	170	4	the	the	DET
ejpam-3129	170	5	tensor	tensor	NOUN
ejpam-3129	170	6	field	field	NOUN
ejpam-3129	170	7	s.	s.	PROPN
ejpam-3129	170	8	on	on	ADP
ejpam-3129	170	9	the	the	DET
ejpam-3129	170	10	other	other	ADJ
ejpam-3129	170	11	hand	hand	NOUN
ejpam-3129	170	12	if	if	SCONJ
ejpam-3129	170	13	φ	φ	PROPN
ejpam-3129	170	14	∈	∈	PROPN
ejpam-3129	170	15	a(m	a(m	NOUN
ejpam-3129	170	16	)	)	PUNCT
ejpam-3129	170	17	preserves	preserve	VERB
ejpam-3129	170	18	the	the	DET
ejpam-3129	170	19	tensor	tensor	NOUN
ejpam-3129	170	20	field	field	NOUN
ejpam-3129	170	21	s	s	VERB
ejpam-3129	170	22	then	then	ADV
ejpam-3129	170	23	for	for	ADP
ejpam-3129	170	24	each	each	DET
ejpam-3129	170	25	x	x	SYM
ejpam-3129	170	26	∈m	∈m	NOUN
ejpam-3129	170	27	,	,	PUNCT
ejpam-3129	170	28	(	(	PUNCT
ejpam-3129	170	29	φ	φ	NUM
ejpam-3129	170	30	◦	◦	NOUN
ejpam-3129	170	31	sx)∗x	sx)∗x	NUM
ejpam-3129	170	32	=	=	SYM
ejpam-3129	170	33	(	(	PUNCT
ejpam-3129	170	34	sφ(x	sφ(x	NOUN
ejpam-3129	170	35	)	)	PUNCT
ejpam-3129	170	36	◦	◦	NOUN
ejpam-3129	170	37	φ)∗x	φ)∗x	NOUN
ejpam-3129	170	38	.	.	PUNCT
ejpam-3129	171	1	because	because	SCONJ
ejpam-3129	171	2	φ	φ	PROPN
ejpam-3129	171	3	◦	◦	PROPN
ejpam-3129	171	4	sx	sx	PROPN
ejpam-3129	171	5	and	and	CCONJ
ejpam-3129	171	6	sφ(x	sφ(x	NUM
ejpam-3129	171	7	)	)	PUNCT
ejpam-3129	171	8	◦	◦	NOUN
ejpam-3129	171	9	φ	φ	PROPN
ejpam-3129	171	10	are	be	AUX
ejpam-3129	171	11	affine	affine	ADJ
ejpam-3129	171	12	transformations	transformation	NOUN
ejpam-3129	171	13	,	,	PUNCT
ejpam-3129	171	14	so	so	SCONJ
ejpam-3129	171	15	φ	φ	NUM
ejpam-3129	171	16	◦	◦	PROPN
ejpam-3129	171	17	sx	sx	NOUN
ejpam-3129	171	18	=	=	PUNCT
ejpam-3129	171	19	sφ(x	sφ(x	X
ejpam-3129	171	20	)	)	PUNCT
ejpam-3129	171	21	◦	◦	NOUN
ejpam-3129	171	22	φ	φ	NUM
ejpam-3129	171	23	that	that	PRON
ejpam-3129	171	24	is	be	AUX
ejpam-3129	171	25	φ	φ	PROPN
ejpam-3129	171	26	is	be	AUX
ejpam-3129	171	27	symmetry	symmetry	NOUN
ejpam-3129	171	28	preserving	preserve	VERB
ejpam-3129	171	29	map	map	NOUN
ejpam-3129	171	30	.	.	PUNCT
ejpam-3129	171	31	�	�	PROPN
ejpam-3129	171	32	in	in	ADP
ejpam-3129	171	33	the	the	DET
ejpam-3129	171	34	following	following	NOUN
ejpam-3129	171	35	we	we	PRON
ejpam-3129	171	36	show	show	VERB
ejpam-3129	171	37	that	that	SCONJ
ejpam-3129	171	38	the	the	DET
ejpam-3129	171	39	group	group	NOUN
ejpam-3129	171	40	aut({sx	aut({sx	NOUN
ejpam-3129	171	41	}	}	PUNCT
ejpam-3129	171	42	)	)	PUNCT
ejpam-3129	171	43	of	of	ADP
ejpam-3129	171	44	all	all	DET
ejpam-3129	171	45	symmetry	symmetry	NOUN
ejpam-3129	171	46	preserving	preserve	VERB
ejpam-3129	171	47	diffeomorphisms	diffeomorphism	NOUN
ejpam-3129	171	48	of	of	ADP
ejpam-3129	171	49	(	(	PUNCT
ejpam-3129	171	50	m	m	PROPN
ejpam-3129	171	51	,	,	PUNCT
ejpam-3129	171	52	f	f	PROPN
ejpam-3129	171	53	)	)	PUNCT
ejpam-3129	171	54	is	be	AUX
ejpam-3129	171	55	a	a	DET
ejpam-3129	171	56	transitive	transitive	ADJ
ejpam-3129	171	57	lie	lie	NOUN
ejpam-3129	171	58	transformation	transformation	NOUN
ejpam-3129	171	59	group	group	NOUN
ejpam-3129	171	60	.	.	PUNCT
ejpam-3129	172	1	theorem	theorem	VERB
ejpam-3129	172	2	3	3	NUM
ejpam-3129	172	3	.	.	PUNCT
ejpam-3129	173	1	the	the	DET
ejpam-3129	173	2	lie	lie	NOUN
ejpam-3129	173	3	transformation	transformation	NOUN
ejpam-3129	173	4	group	group	NOUN
ejpam-3129	173	5	aut({sx	aut({sx	ADJ
ejpam-3129	173	6	}	}	PUNCT
ejpam-3129	173	7	)	)	PUNCT
ejpam-3129	173	8	act	act	NOUN
ejpam-3129	173	9	transitively	transitively	PROPN
ejpam-3129	173	10	on	on	ADP
ejpam-3129	173	11	m	m	PROPN
ejpam-3129	173	12	.	.	PUNCT
ejpam-3129	174	1	proof	proof	NOUN
ejpam-3129	174	2	:	:	PUNCT
ejpam-3129	174	3	let	let	VERB
ejpam-3129	174	4	k	k	PROPN
ejpam-3129	174	5	⊂	⊂	PROPN
ejpam-3129	174	6	aut({sx	aut({sx	ADJ
ejpam-3129	174	7	}	}	PUNCT
ejpam-3129	174	8	)	)	PUNCT
ejpam-3129	174	9	be	be	VERB
ejpam-3129	174	10	the	the	DET
ejpam-3129	174	11	transformation	transformation	NOUN
ejpam-3129	174	12	group	group	NOUN
ejpam-3129	174	13	of	of	ADP
ejpam-3129	174	14	m	m	AUX
ejpam-3129	174	15	generated	generate	VERB
ejpam-3129	174	16	algebraicaly	algebraicaly	NOUN
ejpam-3129	174	17	by	by	ADP
ejpam-3129	174	18	all	all	DET
ejpam-3129	174	19	the	the	DET
ejpam-3129	174	20	symmetries	symmetry	NOUN
ejpam-3129	174	21	sx	sx	PROPN
ejpam-3129	174	22	,	,	PUNCT
ejpam-3129	174	23	x	x	PROPN
ejpam-3129	174	24	∈	∈	PROPN
ejpam-3129	174	25	m	m	VERB
ejpam-3129	174	26	.	.	PUNCT
ejpam-3129	175	1	choose	choose	VERB
ejpam-3129	175	2	an	an	DET
ejpam-3129	175	3	origin	origin	NOUN
ejpam-3129	175	4	o	o	NOUN
ejpam-3129	175	5	∈	∈	PROPN
ejpam-3129	175	6	m	m	VERB
ejpam-3129	175	7	.	.	PUNCT
ejpam-3129	176	1	let	let	VERB
ejpam-3129	176	2	k(o	k(o	PRON
ejpam-3129	176	3	)	)	PUNCT
ejpam-3129	176	4	be	be	VERB
ejpam-3129	176	5	the	the	DET
ejpam-3129	176	6	orbit	orbit	NOUN
ejpam-3129	176	7	of	of	ADP
ejpam-3129	176	8	o	o	NOUN
ejpam-3129	176	9	with	with	ADP
ejpam-3129	176	10	respect	respect	NOUN
ejpam-3129	176	11	to	to	ADP
ejpam-3129	176	12	k.	k.	PROPN
ejpam-3129	176	13	consider	consider	VERB
ejpam-3129	176	14	the	the	DET
ejpam-3129	176	15	map	map	NOUN
ejpam-3129	176	16	f(x	f(x	PROPN
ejpam-3129	176	17	)	)	PUNCT
ejpam-3129	176	18	=	=	PUNCT
ejpam-3129	176	19	sx(p	sx(p	X
ejpam-3129	176	20	)	)	PUNCT
ejpam-3129	176	21	where	where	SCONJ
ejpam-3129	176	22	p	p	PROPN
ejpam-3129	176	23	∈	∈	PROPN
ejpam-3129	176	24	k(o	k(o	PROPN
ejpam-3129	176	25	)	)	PUNCT
ejpam-3129	176	26	and	and	CCONJ
ejpam-3129	176	27	x	x	PUNCT
ejpam-3129	176	28	∈	∈	PROPN
ejpam-3129	176	29	m	m	VERB
ejpam-3129	176	30	.	.	PUNCT
ejpam-3129	177	1	clearly	clearly	ADV
ejpam-3129	177	2	f(p	f(p	NOUN
ejpam-3129	177	3	)	)	PUNCT
ejpam-3129	178	1	=	=	PUNCT
ejpam-3129	179	1	p.	p.	NOUN
ejpam-3129	179	2	for	for	ADP
ejpam-3129	179	3	v	v	NOUN
ejpam-3129	179	4	∈	∈	NOUN
ejpam-3129	179	5	tpm	tpm	NOUN
ejpam-3129	179	6	we	we	PRON
ejpam-3129	179	7	have	have	VERB
ejpam-3129	179	8	f∗p(v	f∗p(v	NOUN
ejpam-3129	179	9	)	)	PUNCT
ejpam-3129	179	10	=	=	PRON
ejpam-3129	180	1	(	(	PUNCT
ejpam-3129	180	2	ip	ip	NOUN
ejpam-3129	180	3	−	−	NOUN
ejpam-3129	180	4	sp)v	sp)v	NOUN
ejpam-3129	180	5	.	.	PUNCT
ejpam-3129	181	1	hence	hence	ADV
ejpam-3129	181	2	f∗p	f∗p	NUM
ejpam-3129	181	3	=	=	SYM
ejpam-3129	181	4	(	(	PUNCT
ejpam-3129	181	5	ip	ip	NOUN
ejpam-3129	181	6	−	−	PROPN
ejpam-3129	181	7	sp	sp	NOUN
ejpam-3129	181	8	)	)	PUNCT
ejpam-3129	181	9	is	be	AUX
ejpam-3129	181	10	a	a	DET
ejpam-3129	181	11	non	non	ADJ
ejpam-3129	181	12	-	-	ADJ
ejpam-3129	181	13	singular	singular	ADJ
ejpam-3129	181	14	transformation	transformation	NOUN
ejpam-3129	181	15	and	and	CCONJ
ejpam-3129	181	16	f	f	PROPN
ejpam-3129	181	17	maps	map	VERB
ejpam-3129	181	18	a	a	DET
ejpam-3129	181	19	neighborhood	neighborhood	NOUN
ejpam-3129	181	20	u	u	NOUN
ejpam-3129	181	21	of	of	ADP
ejpam-3129	181	22	p	p	NOUN
ejpam-3129	181	23	diffeomorphically	diffeomorphically	ADV
ejpam-3129	181	24	onto	onto	ADP
ejpam-3129	181	25	p.	p.	NOUN
ejpam-3129	181	26	bahmandoust	bahmandoust	NOUN
ejpam-3129	181	27	,	,	PUNCT
ejpam-3129	181	28	d.	d.	PROPN
ejpam-3129	181	29	latifi	latifi	PROPN
ejpam-3129	181	30	/	/	SYM
ejpam-3129	181	31	eur	eur	PROPN
ejpam-3129	181	32	.	.	PUNCT
ejpam-3129	182	1	j.	j.	PROPN
ejpam-3129	182	2	pure	pure	PROPN
ejpam-3129	182	3	appl	appl	PROPN
ejpam-3129	182	4	.	.	PROPN
ejpam-3129	182	5	math	math	PROPN
ejpam-3129	182	6	,	,	PUNCT
ejpam-3129	182	7	10	10	NUM
ejpam-3129	182	8	(	(	PUNCT
ejpam-3129	182	9	5	5	NUM
ejpam-3129	182	10	)	)	PUNCT
ejpam-3129	182	11	(	(	PUNCT
ejpam-3129	182	12	2017	2017	NUM
ejpam-3129	182	13	)	)	PUNCT
ejpam-3129	182	14	,	,	PUNCT
ejpam-3129	182	15	1099	1099	NUM
ejpam-3129	182	16	-	-	SYM
ejpam-3129	182	17	1111	1111	NUM
ejpam-3129	182	18	1106	1106	NUM
ejpam-3129	182	19	a	a	DET
ejpam-3129	182	20	neighborhood	neighborhood	NOUN
ejpam-3129	182	21	v	v	NOUN
ejpam-3129	182	22	of	of	ADP
ejpam-3129	182	23	p.	p.	NOUN
ejpam-3129	182	24	we	we	PRON
ejpam-3129	182	25	get	get	VERB
ejpam-3129	182	26	v	v	ADP
ejpam-3129	182	27	⊂	⊂	PRON
ejpam-3129	182	28	k(o	k(o	PROPN
ejpam-3129	182	29	)	)	PUNCT
ejpam-3129	182	30	and	and	CCONJ
ejpam-3129	182	31	the	the	DET
ejpam-3129	182	32	orbit	orbit	NOUN
ejpam-3129	182	33	k(o	k(o	PROPN
ejpam-3129	182	34	)	)	PUNCT
ejpam-3129	182	35	is	be	AUX
ejpam-3129	182	36	open	open	ADJ
ejpam-3129	182	37	.	.	PUNCT
ejpam-3129	183	1	the	the	DET
ejpam-3129	183	2	union	union	NOUN
ejpam-3129	183	3	of	of	ADP
ejpam-3129	183	4	all	all	DET
ejpam-3129	183	5	other	other	ADJ
ejpam-3129	183	6	orbits	orbit	NOUN
ejpam-3129	183	7	of	of	ADP
ejpam-3129	183	8	k	k	PROPN
ejpam-3129	183	9	must	must	AUX
ejpam-3129	183	10	be	be	AUX
ejpam-3129	183	11	also	also	ADV
ejpam-3129	183	12	open	open	ADJ
ejpam-3129	183	13	and	and	CCONJ
ejpam-3129	183	14	hence	hence	ADV
ejpam-3129	183	15	k(o	k(o	PROPN
ejpam-3129	183	16	)	)	PUNCT
ejpam-3129	183	17	is	be	AUX
ejpam-3129	183	18	closed	close	VERB
ejpam-3129	183	19	.	.	PUNCT
ejpam-3129	184	1	consequently	consequently	ADV
ejpam-3129	184	2	k(o	k(o	PRON
ejpam-3129	184	3	)	)	PUNCT
ejpam-3129	185	1	=	=	SYM
ejpam-3129	185	2	m	m	NOUN
ejpam-3129	185	3	.	.	PUNCT
ejpam-3129	186	1	�	�	PROPN
ejpam-3129	186	2	let	let	VERB
ejpam-3129	186	3	v	v	PART
ejpam-3129	186	4	be	be	AUX
ejpam-3129	186	5	a	a	DET
ejpam-3129	186	6	finite	finite	ADJ
ejpam-3129	186	7	dimensional	dimensional	ADJ
ejpam-3129	186	8	vector	vector	NOUN
ejpam-3129	186	9	space	space	NOUN
ejpam-3129	186	10	and	and	CCONJ
ejpam-3129	186	11	t	t	NOUN
ejpam-3129	186	12	:	:	PUNCT
ejpam-3129	186	13	v	v	X
ejpam-3129	186	14	−→	−→	NOUN
ejpam-3129	186	15	v	v	ADP
ejpam-3129	186	16	an	an	DET
ejpam-3129	186	17	endomorphism	endomorphism	NOUN
ejpam-3129	186	18	.	.	PUNCT
ejpam-3129	187	1	then	then	ADV
ejpam-3129	187	2	there	there	PRON
ejpam-3129	187	3	is	be	VERB
ejpam-3129	187	4	a	a	DET
ejpam-3129	187	5	unique	unique	ADJ
ejpam-3129	187	6	decomposition	decomposition	NOUN
ejpam-3129	187	7	v	v	ADP
ejpam-3129	187	8	=	=	SYM
ejpam-3129	187	9	v0	v0	PROPN
ejpam-3129	187	10	t	t	NOUN
ejpam-3129	187	11	+	+	PROPN
ejpam-3129	187	12	v1	v1	PROPN
ejpam-3129	187	13	t	t	NOUN
ejpam-3129	187	14	of	of	ADP
ejpam-3129	187	15	v	v	NOUN
ejpam-3129	187	16	into	into	ADP
ejpam-3129	187	17	t−invariant	t−invariant	NOUN
ejpam-3129	187	18	subspaces	subspace	NOUN
ejpam-3129	187	19	such	such	ADJ
ejpam-3129	187	20	that	that	SCONJ
ejpam-3129	187	21	the	the	DET
ejpam-3129	187	22	restriction	restriction	NOUN
ejpam-3129	187	23	of	of	ADP
ejpam-3129	187	24	t	t	PROPN
ejpam-3129	187	25	to	to	ADP
ejpam-3129	187	26	v0	v0	PROPN
ejpam-3129	187	27	t	t	PROPN
ejpam-3129	187	28	is	be	AUX
ejpam-3129	187	29	nilpotent	nilpotent	ADJ
ejpam-3129	187	30	and	and	CCONJ
ejpam-3129	187	31	the	the	DET
ejpam-3129	187	32	restriction	restriction	NOUN
ejpam-3129	187	33	of	of	ADP
ejpam-3129	187	34	t	t	PROPN
ejpam-3129	187	35	to	to	PART
ejpam-3129	187	36	v1	v1	VERB
ejpam-3129	187	37	t	t	PROPN
ejpam-3129	187	38	is	be	AUX
ejpam-3129	187	39	an	an	DET
ejpam-3129	187	40	automorphism	automorphism	NOUN
ejpam-3129	187	41	.	.	PUNCT
ejpam-3129	188	1	definition	definition	NOUN
ejpam-3129	188	2	5	5	NUM
ejpam-3129	188	3	.	.	PUNCT
ejpam-3129	189	1	a	a	DET
ejpam-3129	189	2	regular	regular	ADJ
ejpam-3129	189	3	homogeneous	homogeneous	ADJ
ejpam-3129	189	4	s−manifold	s−manifold	NOUN
ejpam-3129	189	5	is	be	AUX
ejpam-3129	189	6	a	a	DET
ejpam-3129	189	7	triplet	triplet	NOUN
ejpam-3129	189	8	(	(	PUNCT
ejpam-3129	189	9	g	g	NOUN
ejpam-3129	189	10	,	,	PUNCT
ejpam-3129	189	11	h	h	NOUN
ejpam-3129	189	12	,	,	PUNCT
ejpam-3129	189	13	σ	σ	PROPN
ejpam-3129	189	14	)	)	PUNCT
ejpam-3129	189	15	,	,	PUNCT
ejpam-3129	189	16	where	where	SCONJ
ejpam-3129	189	17	g	g	PROPN
ejpam-3129	189	18	is	be	AUX
ejpam-3129	189	19	a	a	DET
ejpam-3129	189	20	connected	connected	ADJ
ejpam-3129	189	21	lie	lie	NOUN
ejpam-3129	189	22	group	group	NOUN
ejpam-3129	189	23	,	,	PUNCT
ejpam-3129	189	24	h	h	PRON
ejpam-3129	189	25	its	its	PRON
ejpam-3129	189	26	closed	closed	ADJ
ejpam-3129	189	27	subgroup	subgroup	NOUN
ejpam-3129	189	28	and	and	CCONJ
ejpam-3129	189	29	σ	σ	NOUN
ejpam-3129	189	30	an	an	DET
ejpam-3129	189	31	automorphism	automorphism	NOUN
ejpam-3129	189	32	of	of	ADP
ejpam-3129	189	33	g	g	NOUN
ejpam-3129	189	34	such	such	ADJ
ejpam-3129	189	35	that	that	SCONJ
ejpam-3129	189	36	(	(	PUNCT
ejpam-3129	189	37	i	i	NOUN
ejpam-3129	189	38	)	)	PUNCT
ejpam-3129	189	39	g	g	ADP
ejpam-3129	189	40	◦	◦	NOUN
ejpam-3129	189	41	σ	σ	NOUN
ejpam-3129	189	42	⊂	⊂	PROPN
ejpam-3129	189	43	h	h	PROPN
ejpam-3129	190	1	⊂	⊂	NOUN
ejpam-3129	190	2	gσ	gσ	VERB
ejpam-3129	190	3	where	where	SCONJ
ejpam-3129	190	4	gσ	gσ	NOUN
ejpam-3129	190	5	is	be	AUX
ejpam-3129	190	6	the	the	DET
ejpam-3129	190	7	subgroup	subgroup	NOUN
ejpam-3129	190	8	consisting	consist	VERB
ejpam-3129	190	9	of	of	ADP
ejpam-3129	190	10	the	the	DET
ejpam-3129	190	11	fixed	fix	VERB
ejpam-3129	190	12	points	point	NOUN
ejpam-3129	190	13	of	of	ADP
ejpam-3129	190	14	σ	σ	PROPN
ejpam-3129	190	15	in	in	ADP
ejpam-3129	190	16	g	g	PROPN
ejpam-3129	190	17	and	and	CCONJ
ejpam-3129	190	18	g	g	ADP
ejpam-3129	190	19	◦	◦	NOUN
ejpam-3129	190	20	σ	σ	NOUN
ejpam-3129	190	21	denotes	denote	VERB
ejpam-3129	190	22	the	the	DET
ejpam-3129	190	23	identity	identity	NOUN
ejpam-3129	190	24	component	component	NOUN
ejpam-3129	190	25	of	of	ADP
ejpam-3129	190	26	gσ	gσ	NOUN
ejpam-3129	190	27	.	.	PUNCT
ejpam-3129	191	1	(	(	PUNCT
ejpam-3129	191	2	ii	ii	NOUN
ejpam-3129	191	3	)	)	PUNCT
ejpam-3129	191	4	if	if	SCONJ
ejpam-3129	191	5	t	t	PROPN
ejpam-3129	191	6	denotes	denote	VERB
ejpam-3129	191	7	the	the	DET
ejpam-3129	191	8	linear	linear	ADJ
ejpam-3129	191	9	endomorphism	endomorphism	PROPN
ejpam-3129	191	10	id−	id−	NUM
ejpam-3129	191	11	σ∗	σ∗	PROPN
ejpam-3129	191	12	,	,	PUNCT
ejpam-3129	191	13	then	then	ADV
ejpam-3129	191	14	g0	g0	PROPN
ejpam-3129	191	15	t	t	PROPN
ejpam-3129	191	16	=	=	SYM
ejpam-3129	191	17	h.	h.	PROPN
ejpam-3129	191	18	clearly	clearly	ADV
ejpam-3129	191	19	if	if	SCONJ
ejpam-3129	191	20	(	(	PUNCT
ejpam-3129	191	21	g	g	NOUN
ejpam-3129	191	22	,	,	PUNCT
ejpam-3129	191	23	h	h	NOUN
ejpam-3129	191	24	,	,	PUNCT
ejpam-3129	191	25	σ	σ	PROPN
ejpam-3129	191	26	)	)	PUNCT
ejpam-3129	191	27	is	be	AUX
ejpam-3129	191	28	a	a	DET
ejpam-3129	191	29	regular	regular	ADJ
ejpam-3129	191	30	homogeneous	homogeneous	ADJ
ejpam-3129	191	31	s−manifold	s−manifold	NOUN
ejpam-3129	191	32	,	,	PUNCT
ejpam-3129	191	33	then	then	ADV
ejpam-3129	191	34	g0	g0	PROPN
ejpam-3129	191	35	t	t	PROPN
ejpam-3129	191	36	=	=	SYM
ejpam-3129	191	37	h	h	PROPN
ejpam-3129	191	38	=	=	PUNCT
ejpam-3129	191	39	ker	ker	PROPN
ejpam-3129	191	40	t	t	PROPN
ejpam-3129	191	41	and	and	CCONJ
ejpam-3129	191	42	g1	g1	PROPN
ejpam-3129	191	43	t	t	PROPN
ejpam-3129	191	44	=	=	SYM
ejpam-3129	191	45	im(t	im(t	X
ejpam-3129	191	46	)	)	PUNCT
ejpam-3129	191	47	.	.	PUNCT
ejpam-3129	192	1	let	let	VERB
ejpam-3129	192	2	g	g	PRON
ejpam-3129	192	3	be	be	AUX
ejpam-3129	192	4	a	a	DET
ejpam-3129	192	5	connected	connected	ADJ
ejpam-3129	192	6	lie	lie	NOUN
ejpam-3129	192	7	group	group	NOUN
ejpam-3129	192	8	and	and	CCONJ
ejpam-3129	192	9	h	h	PRON
ejpam-3129	192	10	its	its	PRON
ejpam-3129	192	11	closed	closed	ADJ
ejpam-3129	192	12	subgroup	subgroup	NOUN
ejpam-3129	192	13	.	.	PUNCT
ejpam-3129	193	1	consider	consider	VERB
ejpam-3129	193	2	the	the	DET
ejpam-3129	193	3	homogeneous	homogeneous	ADJ
ejpam-3129	193	4	manifold	manifold	ADJ
ejpam-3129	193	5	g	g	PROPN
ejpam-3129	193	6	/	/	SYM
ejpam-3129	193	7	h.	h.	PROPN
ejpam-3129	193	8	here	here	ADV
ejpam-3129	194	1	π	π	X
ejpam-3129	194	2	:	:	PUNCT
ejpam-3129	194	3	g	g	ADP
ejpam-3129	194	4	−→	−→	NOUN
ejpam-3129	194	5	g	g	PROPN
ejpam-3129	194	6	/	/	SYM
ejpam-3129	194	7	h	h	NOUN
ejpam-3129	194	8	will	will	AUX
ejpam-3129	194	9	denote	denote	VERB
ejpam-3129	194	10	the	the	DET
ejpam-3129	194	11	canonical	canonical	ADJ
ejpam-3129	194	12	projection	projection	NOUN
ejpam-3129	194	13	,	,	PUNCT
ejpam-3129	194	14	and	and	CCONJ
ejpam-3129	194	15	o	o	X
ejpam-3129	194	16	=	=	PUNCT
ejpam-3129	194	17	π(h	π(h	NOUN
ejpam-3129	194	18	)	)	PUNCT
ejpam-3129	194	19	the	the	DET
ejpam-3129	194	20	origin	origin	NOUN
ejpam-3129	194	21	of	of	ADP
ejpam-3129	194	22	g	g	PROPN
ejpam-3129	194	23	/	/	SYM
ejpam-3129	194	24	h.	h.	PROPN
ejpam-3129	194	25	let	let	VERB
ejpam-3129	194	26	g	g	NOUN
ejpam-3129	194	27	and	and	CCONJ
ejpam-3129	194	28	h	h	NOUN
ejpam-3129	194	29	be	be	VERB
ejpam-3129	194	30	the	the	DET
ejpam-3129	194	31	lie	lie	NOUN
ejpam-3129	194	32	algebras	algebra	NOUN
ejpam-3129	194	33	of	of	ADP
ejpam-3129	194	34	g	g	PROPN
ejpam-3129	194	35	and	and	CCONJ
ejpam-3129	194	36	h	h	NOUN
ejpam-3129	194	37	respectively	respectively	ADV
ejpam-3129	194	38	.	.	PUNCT
ejpam-3129	195	1	suppose	suppose	VERB
ejpam-3129	195	2	that	that	SCONJ
ejpam-3129	195	3	there	there	PRON
ejpam-3129	195	4	is	be	VERB
ejpam-3129	195	5	a	a	DET
ejpam-3129	195	6	subspace	subspace	NOUN
ejpam-3129	195	7	m	m	VERB
ejpam-3129	195	8	⊂	⊂	PROPN
ejpam-3129	195	9	g	g	PROPN
ejpam-3129	195	10	such	such	ADJ
ejpam-3129	195	11	that	that	DET
ejpam-3129	195	12	g	g	NOUN
ejpam-3129	195	13	=	=	NOUN
ejpam-3129	195	14	h	h	PROPN
ejpam-3129	196	1	+	+	NOUN
ejpam-3129	196	2	m	m	VERB
ejpam-3129	196	3	(	(	PUNCT
ejpam-3129	196	4	direct	direct	ADJ
ejpam-3129	196	5	sum	sum	NOUN
ejpam-3129	196	6	of	of	ADP
ejpam-3129	196	7	vector	vector	NOUN
ejpam-3129	196	8	spaces	space	NOUN
ejpam-3129	196	9	)	)	PUNCT
ejpam-3129	196	10	and	and	CCONJ
ejpam-3129	196	11	ad(h)m	ad(h)m	PROPN
ejpam-3129	196	12	=	=	SYM
ejpam-3129	196	13	m	m	VERB
ejpam-3129	196	14	for	for	ADP
ejpam-3129	196	15	every	every	DET
ejpam-3129	196	16	h	h	NOUN
ejpam-3129	196	17	∈	∈	PROPN
ejpam-3129	196	18	h.	h.	NOUN
ejpam-3129	197	1	then	then	ADV
ejpam-3129	197	2	the	the	DET
ejpam-3129	197	3	homogeneous	homogeneous	ADJ
ejpam-3129	197	4	space	space	NOUN
ejpam-3129	197	5	g	g	NOUN
ejpam-3129	197	6	/	/	SYM
ejpam-3129	197	7	h	h	NOUN
ejpam-3129	197	8	is	be	AUX
ejpam-3129	197	9	said	say	VERB
ejpam-3129	197	10	to	to	PART
ejpam-3129	197	11	be	be	AUX
ejpam-3129	197	12	reductive	reductive	ADJ
ejpam-3129	197	13	with	with	ADP
ejpam-3129	197	14	respect	respect	NOUN
ejpam-3129	197	15	to	to	ADP
ejpam-3129	197	16	the	the	DET
ejpam-3129	197	17	decomposition	decomposition	NOUN
ejpam-3129	197	18	g	g	NOUN
ejpam-3129	197	19	=	=	SYM
ejpam-3129	197	20	h	h	PROPN
ejpam-3129	197	21	+	+	NUM
ejpam-3129	197	22	m.	m.	NOUN
ejpam-3129	197	23	lemma	lemma	PROPN
ejpam-3129	197	24	2	2	X
ejpam-3129	197	25	.	.	PUNCT
ejpam-3129	198	1	let	let	AUX
ejpam-3129	198	2	(	(	PUNCT
ejpam-3129	198	3	g	g	NOUN
ejpam-3129	198	4	,	,	PUNCT
ejpam-3129	198	5	h	h	NOUN
ejpam-3129	198	6	,	,	PUNCT
ejpam-3129	198	7	σ	σ	PROPN
ejpam-3129	198	8	)	)	PUNCT
ejpam-3129	198	9	be	be	AUX
ejpam-3129	198	10	a	a	DET
ejpam-3129	198	11	regular	regular	ADJ
ejpam-3129	198	12	homogeneous	homogeneous	ADJ
ejpam-3129	198	13	s−manifold	s−manifold	NOUN
ejpam-3129	198	14	,	,	PUNCT
ejpam-3129	198	15	then	then	ADV
ejpam-3129	198	16	the	the	DET
ejpam-3129	198	17	homogeneous	homogeneous	ADJ
ejpam-3129	198	18	space	space	NOUN
ejpam-3129	198	19	g	g	NOUN
ejpam-3129	198	20	/	/	SYM
ejpam-3129	198	21	h	h	NOUN
ejpam-3129	198	22	is	be	AUX
ejpam-3129	198	23	reductive	reductive	ADJ
ejpam-3129	198	24	with	with	ADP
ejpam-3129	198	25	respect	respect	NOUN
ejpam-3129	198	26	to	to	ADP
ejpam-3129	198	27	the	the	DET
ejpam-3129	198	28	decomposition	decomposition	NOUN
ejpam-3129	198	29	g	g	NOUN
ejpam-3129	198	30	=	=	SYM
ejpam-3129	198	31	h	h	PROPN
ejpam-3129	199	1	+	+	NUM
ejpam-3129	199	2	g1	g1	PROPN
ejpam-3129	199	3	t	t	NOUN
ejpam-3129	199	4	proof	proof	NOUN
ejpam-3129	199	5	:	:	PUNCT
ejpam-3129	199	6	let	let	VERB
ejpam-3129	199	7	(	(	PUNCT
ejpam-3129	199	8	g	g	NOUN
ejpam-3129	199	9	,	,	PUNCT
ejpam-3129	199	10	h	h	NOUN
ejpam-3129	199	11	,	,	PUNCT
ejpam-3129	199	12	σ	σ	PROPN
ejpam-3129	199	13	)	)	PUNCT
ejpam-3129	199	14	be	be	AUX
ejpam-3129	199	15	a	a	DET
ejpam-3129	199	16	regular	regular	ADJ
ejpam-3129	199	17	homogeneous	homogeneous	ADJ
ejpam-3129	199	18	s−manifold	s−manifold	NOUN
ejpam-3129	199	19	,	,	PUNCT
ejpam-3129	199	20	since	since	SCONJ
ejpam-3129	199	21	h	h	PROPN
ejpam-3129	199	22	⊂	⊂	PROPN
ejpam-3129	199	23	gσ	gσ	VERB
ejpam-3129	199	24	we	we	PRON
ejpam-3129	199	25	obtain	obtain	VERB
ejpam-3129	199	26	ad(h	ad(h	PUNCT
ejpam-3129	199	27	)	)	PUNCT
ejpam-3129	200	1	◦	◦	NOUN
ejpam-3129	200	2	σ∗	σ∗	NOUN
ejpam-3129	200	3	=	=	SYM
ejpam-3129	200	4	σ∗	σ∗	X
ejpam-3129	200	5	◦	◦	NOUN
ejpam-3129	200	6	ad(h	ad(h	PUNCT
ejpam-3129	200	7	)	)	PUNCT
ejpam-3129	200	8	for	for	ADP
ejpam-3129	200	9	each	each	DET
ejpam-3129	200	10	h	h	NOUN
ejpam-3129	200	11	∈	∈	PROPN
ejpam-3129	200	12	h.	h.	NOUN
ejpam-3129	200	13	hence	hence	ADV
ejpam-3129	200	14	ad(h	ad(h	PUNCT
ejpam-3129	200	15	)	)	PUNCT
ejpam-3129	200	16	commutes	commute	NOUN
ejpam-3129	200	17	with	with	ADP
ejpam-3129	200	18	t	t	PROPN
ejpam-3129	200	19	on	on	ADP
ejpam-3129	200	20	g	g	PROPN
ejpam-3129	200	21	and	and	CCONJ
ejpam-3129	200	22	ad(h)(g1	ad(h)(g1	NUM
ejpam-3129	200	23	t	t	NOUN
ejpam-3129	200	24	)	)	PUNCT
ejpam-3129	200	25	=	=	SYM
ejpam-3129	200	26	(	(	PUNCT
ejpam-3129	200	27	ad(h	ad(h	NOUN
ejpam-3129	200	28	)	)	PUNCT
ejpam-3129	200	29	◦	◦	NOUN
ejpam-3129	200	30	t	t	PROPN
ejpam-3129	200	31	)	)	PUNCT
ejpam-3129	200	32	(	(	PUNCT
ejpam-3129	200	33	g	g	NOUN
ejpam-3129	200	34	)	)	PUNCT
ejpam-3129	200	35	=	=	SYM
ejpam-3129	200	36	t	t	PROPN
ejpam-3129	200	37	(	(	PUNCT
ejpam-3129	200	38	ad(h)g	ad(h)g	X
ejpam-3129	200	39	)	)	PUNCT
ejpam-3129	201	1	=	=	SYM
ejpam-3129	201	2	t	t	PROPN
ejpam-3129	201	3	(	(	PUNCT
ejpam-3129	201	4	g	g	NOUN
ejpam-3129	201	5	)	)	PUNCT
ejpam-3129	201	6	=	=	SYM
ejpam-3129	201	7	g1	g1	PROPN
ejpam-3129	201	8	t	t	PROPN
ejpam-3129	201	9	.	.	PUNCT
ejpam-3129	202	1	�	�	PROPN
ejpam-3129	202	2	theorem	theorem	VERB
ejpam-3129	202	3	4	4	NUM
ejpam-3129	202	4	.	.	PUNCT
ejpam-3129	203	1	let	let	VERB
ejpam-3129	203	2	g	g	PRON
ejpam-3129	203	3	be	be	AUX
ejpam-3129	203	4	a	a	DET
ejpam-3129	203	5	connected	connected	ADJ
ejpam-3129	203	6	lie	lie	NOUN
ejpam-3129	203	7	group	group	NOUN
ejpam-3129	203	8	,	,	PUNCT
ejpam-3129	203	9	h	h	PRON
ejpam-3129	203	10	its	its	PRON
ejpam-3129	203	11	closed	closed	ADJ
ejpam-3129	203	12	subgroup	subgroup	NOUN
ejpam-3129	203	13	and	and	CCONJ
ejpam-3129	203	14	σ	σ	NOUN
ejpam-3129	203	15	an	an	DET
ejpam-3129	203	16	automorphism	automorphism	NOUN
ejpam-3129	203	17	of	of	ADP
ejpam-3129	203	18	g	g	NOUN
ejpam-3129	203	19	such	such	ADJ
ejpam-3129	203	20	that	that	SCONJ
ejpam-3129	203	21	(	(	PUNCT
ejpam-3129	203	22	i	i	NOUN
ejpam-3129	203	23	)	)	PUNCT
ejpam-3129	203	24	(	(	PUNCT
ejpam-3129	203	25	gσ	gσ	NOUN
ejpam-3129	203	26	)	)	PUNCT
ejpam-3129	203	27	◦	◦	NOUN
ejpam-3129	203	28	⊂	⊂	PROPN
ejpam-3129	203	29	h	h	X
ejpam-3129	203	30	⊂	⊂	PROPN
ejpam-3129	203	31	gσ	gσ	PROPN
ejpam-3129	203	32	,	,	PUNCT
ejpam-3129	203	33	(	(	PUNCT
ejpam-3129	203	34	ii	ii	NOUN
ejpam-3129	203	35	)	)	PUNCT
ejpam-3129	204	1	σk	σk	ADV
ejpam-3129	204	2	=	=	PUNCT
ejpam-3129	204	3	i	i	PROPN
ejpam-3129	204	4	d	d	PROPN
ejpam-3129	204	5	,	,	PUNCT
ejpam-3129	204	6	where	where	SCONJ
ejpam-3129	204	7	k	k	PROPN
ejpam-3129	204	8	is	be	AUX
ejpam-3129	204	9	the	the	DET
ejpam-3129	204	10	minimum	minimum	ADJ
ejpam-3129	204	11	number	number	NOUN
ejpam-3129	204	12	with	with	ADP
ejpam-3129	204	13	this	this	DET
ejpam-3129	204	14	property	property	NOUN
ejpam-3129	204	15	,	,	PUNCT
ejpam-3129	204	16	then	then	ADV
ejpam-3129	204	17	the	the	DET
ejpam-3129	204	18	triple	triple	ADJ
ejpam-3129	204	19	(	(	PUNCT
ejpam-3129	204	20	g	g	NOUN
ejpam-3129	204	21	,	,	PUNCT
ejpam-3129	204	22	h	h	NOUN
ejpam-3129	204	23	,	,	PUNCT
ejpam-3129	204	24	σ	σ	PROPN
ejpam-3129	204	25	)	)	PUNCT
ejpam-3129	204	26	is	be	AUX
ejpam-3129	204	27	a	a	DET
ejpam-3129	204	28	regular	regular	ADJ
ejpam-3129	204	29	homogeneous	homogeneous	ADJ
ejpam-3129	204	30	s−manifold	s−manifold	NOUN
ejpam-3129	204	31	of	of	ADP
ejpam-3129	204	32	order	order	NOUN
ejpam-3129	204	33	k.	k.	PROPN
ejpam-3129	204	34	p.	p.	NOUN
ejpam-3129	204	35	bahmandoust	bahmandoust	PROPN
ejpam-3129	204	36	,	,	PUNCT
ejpam-3129	204	37	d.	d.	PROPN
ejpam-3129	204	38	latifi	latifi	PROPN
ejpam-3129	204	39	/	/	SYM
ejpam-3129	204	40	eur	eur	PROPN
ejpam-3129	204	41	.	.	PUNCT
ejpam-3129	205	1	j.	j.	PROPN
ejpam-3129	205	2	pure	pure	PROPN
ejpam-3129	205	3	appl	appl	PROPN
ejpam-3129	205	4	.	.	PROPN
ejpam-3129	205	5	math	math	PROPN
ejpam-3129	205	6	,	,	PUNCT
ejpam-3129	205	7	10	10	NUM
ejpam-3129	205	8	(	(	PUNCT
ejpam-3129	205	9	5	5	NUM
ejpam-3129	205	10	)	)	PUNCT
ejpam-3129	205	11	(	(	PUNCT
ejpam-3129	205	12	2017	2017	NUM
ejpam-3129	205	13	)	)	PUNCT
ejpam-3129	205	14	,	,	PUNCT
ejpam-3129	205	15	1099	1099	NUM
ejpam-3129	205	16	-	-	SYM
ejpam-3129	205	17	1111	1111	NUM
ejpam-3129	205	18	1107	1107	NUM
ejpam-3129	205	19	proof	proof	NOUN
ejpam-3129	205	20	:	:	PUNCT
ejpam-3129	205	21	let	let	VERB
ejpam-3129	205	22	t	t	NOUN
ejpam-3129	205	23	=	=	SYM
ejpam-3129	205	24	id−	id−	NUM
ejpam-3129	205	25	σ∗.	σ∗.	NOUN
ejpam-3129	205	26	we	we	PRON
ejpam-3129	205	27	have	have	VERB
ejpam-3129	205	28	to	to	PART
ejpam-3129	205	29	show	show	VERB
ejpam-3129	205	30	that	that	SCONJ
ejpam-3129	205	31	g0	g0	PROPN
ejpam-3129	205	32	t	t	PROPN
ejpam-3129	205	33	=	=	SYM
ejpam-3129	205	34	h.	h.	NOUN
ejpam-3129	205	35	clearly	clearly	ADV
ejpam-3129	205	36	h	h	PRON
ejpam-3129	206	1	=	=	PUNCT
ejpam-3129	206	2	kert	kert	PROPN
ejpam-3129	206	3	and	and	CCONJ
ejpam-3129	206	4	hence	hence	ADV
ejpam-3129	206	5	h	h	PROPN
ejpam-3129	206	6	⊂	⊂	PROPN
ejpam-3129	206	7	g0	g0	PROPN
ejpam-3129	206	8	t	t	PROPN
ejpam-3129	206	9	.	.	PUNCT
ejpam-3129	207	1	suppose	suppose	VERB
ejpam-3129	207	2	now	now	ADV
ejpam-3129	207	3	that	that	SCONJ
ejpam-3129	207	4	there	there	PRON
ejpam-3129	207	5	is	be	VERB
ejpam-3129	207	6	x	x	PROPN
ejpam-3129	207	7	∈	∈	PROPN
ejpam-3129	207	8	g0	g0	PROPN
ejpam-3129	207	9	t	t	PROPN
ejpam-3129	207	10	such	such	ADJ
ejpam-3129	207	11	that	that	PRON
ejpam-3129	207	12	x	x	PRON
ejpam-3129	207	13	is	be	AUX
ejpam-3129	207	14	not	not	PART
ejpam-3129	207	15	in	in	ADP
ejpam-3129	207	16	h.	h.	NOUN
ejpam-3129	207	17	without	without	ADP
ejpam-3129	207	18	loss	loss	NOUN
ejpam-3129	207	19	of	of	ADP
ejpam-3129	207	20	generality	generality	NOUN
ejpam-3129	207	21	we	we	PRON
ejpam-3129	207	22	assume	assume	VERB
ejpam-3129	207	23	that	that	SCONJ
ejpam-3129	207	24	tx	tx	VERB
ejpam-3129	207	25	6=	6=	ADP
ejpam-3129	207	26	0	0	NUM
ejpam-3129	207	27	,	,	PUNCT
ejpam-3129	207	28	t	t	PROPN
ejpam-3129	207	29	2x	2x	NUM
ejpam-3129	208	1	=	=	SYM
ejpam-3129	208	2	0	0	X
ejpam-3129	208	3	.	.	PUNCT
ejpam-3129	209	1	then	then	ADV
ejpam-3129	209	2	we	we	PRON
ejpam-3129	209	3	get	get	VERB
ejpam-3129	209	4	σ∗x	σ∗x	NOUN
ejpam-3129	209	5	=	=	SYM
ejpam-3129	209	6	tx	tx	PROPN
ejpam-3129	209	7	−	−	PROPN
ejpam-3129	209	8	σ2∗x	σ2∗x	PROPN
ejpam-3129	210	1	=	=	PUNCT
ejpam-3129	210	2	x	x	SYM
ejpam-3129	210	3	−	−	NOUN
ejpam-3129	210	4	σ∗(x	σ∗(x	NOUN
ejpam-3129	210	5	−	−	NOUN
ejpam-3129	210	6	σ∗x	σ∗x	NOUN
ejpam-3129	210	7	)	)	PUNCT
ejpam-3129	210	8	.	.	PUNCT
ejpam-3129	211	1	let	let	VERB
ejpam-3129	211	2	z	z	NOUN
ejpam-3129	211	3	=	=	SYM
ejpam-3129	212	1	σ∗(x	σ∗(x	PRON
ejpam-3129	212	2	−	−	NOUN
ejpam-3129	212	3	σ∗x	σ∗x	NOUN
ejpam-3129	212	4	)	)	PUNCT
ejpam-3129	212	5	=	=	SYM
ejpam-3129	212	6	tx	tx	PROPN
ejpam-3129	212	7	.	.	PUNCT
ejpam-3129	213	1	so	so	ADV
ejpam-3129	213	2	we	we	PRON
ejpam-3129	213	3	have	have	VERB
ejpam-3129	213	4	σ∗x	σ∗x	NOUN
ejpam-3129	213	5	=	=	SYM
ejpam-3129	213	6	x	x	SYM
ejpam-3129	213	7	−	−	PROPN
ejpam-3129	213	8	z	z	NOUN
ejpam-3129	213	9	and	and	CCONJ
ejpam-3129	213	10	σ∗z	σ∗z	PROPN
ejpam-3129	213	11	=	=	SYM
ejpam-3129	213	12	z.	z.	PROPN
ejpam-3129	213	13	hence	hence	ADV
ejpam-3129	213	14	by	by	ADP
ejpam-3129	213	15	the	the	DET
ejpam-3129	213	16	induction	induction	NOUN
ejpam-3129	213	17	we	we	PRON
ejpam-3129	213	18	get	get	VERB
ejpam-3129	213	19	σ2∗x	σ2∗x	PROPN
ejpam-3129	213	20	=	=	PUNCT
ejpam-3129	213	21	x	x	SYM
ejpam-3129	213	22	−	−	NOUN
ejpam-3129	213	23	2z	2z	ADJ
ejpam-3129	213	24	.	.	PUNCT
ejpam-3129	213	25	.	.	PUNCT
ejpam-3129	213	26	.	.	PUNCT
ejpam-3129	214	1	σk∗x	σk∗x	NOUN
ejpam-3129	214	2	=	=	PUNCT
ejpam-3129	215	1	x	x	PUNCT
ejpam-3129	215	2	−	−	PROPN
ejpam-3129	215	3	kz	kz	PROPN
ejpam-3129	215	4	now	now	ADV
ejpam-3129	215	5	since	since	SCONJ
ejpam-3129	215	6	σk∗x	σk∗x	NOUN
ejpam-3129	215	7	=	=	SYM
ejpam-3129	215	8	x	x	NOUN
ejpam-3129	215	9	,	,	PUNCT
ejpam-3129	215	10	we	we	PRON
ejpam-3129	215	11	get	get	VERB
ejpam-3129	215	12	z	z	NOUN
ejpam-3129	215	13	=	=	SYM
ejpam-3129	215	14	0	0	NUM
ejpam-3129	215	15	,	,	PUNCT
ejpam-3129	215	16	a	a	DET
ejpam-3129	215	17	contradiction	contradiction	NOUN
ejpam-3129	215	18	.	.	PUNCT
ejpam-3129	216	1	this	this	PRON
ejpam-3129	216	2	completes	complete	VERB
ejpam-3129	216	3	the	the	DET
ejpam-3129	216	4	proof	proof	NOUN
ejpam-3129	216	5	.	.	PUNCT
ejpam-3129	217	1	�	�	PROPN
ejpam-3129	217	2	theorem	theorem	VERB
ejpam-3129	217	3	5	5	NUM
ejpam-3129	217	4	.	.	PUNCT
ejpam-3129	218	1	let	let	AUX
ejpam-3129	218	2	(	(	PUNCT
ejpam-3129	218	3	g	g	NOUN
ejpam-3129	218	4	,	,	PUNCT
ejpam-3129	218	5	h	h	NOUN
ejpam-3129	218	6	,	,	PUNCT
ejpam-3129	218	7	σ	σ	PROPN
ejpam-3129	218	8	)	)	PUNCT
ejpam-3129	218	9	be	be	AUX
ejpam-3129	218	10	a	a	DET
ejpam-3129	218	11	regular	regular	ADJ
ejpam-3129	218	12	homogeneous	homogeneous	ADJ
ejpam-3129	218	13	s−manifold	s−manifold	NOUN
ejpam-3129	218	14	,	,	PUNCT
ejpam-3129	218	15	π	π	X
ejpam-3129	218	16	:	:	PUNCT
ejpam-3129	218	17	g	g	ADP
ejpam-3129	218	18	−→	−→	NOUN
ejpam-3129	218	19	g	g	PROPN
ejpam-3129	218	20	/	/	SYM
ejpam-3129	218	21	h	h	NOUN
ejpam-3129	218	22	the	the	DET
ejpam-3129	218	23	canonical	canonical	ADJ
ejpam-3129	218	24	projection	projection	NOUN
ejpam-3129	218	25	and	and	CCONJ
ejpam-3129	218	26	let	let	VERB
ejpam-3129	218	27	f	f	PRON
ejpam-3129	218	28	be	be	AUX
ejpam-3129	218	29	a	a	DET
ejpam-3129	218	30	g−invariant	g−invariant	NOUN
ejpam-3129	218	31	finsler	finsler	NOUN
ejpam-3129	218	32	metric	metric	ADJ
ejpam-3129	218	33	on	on	ADP
ejpam-3129	218	34	g	g	PROPN
ejpam-3129	218	35	/	/	SYM
ejpam-3129	218	36	h	h	NOUN
ejpam-3129	218	37	such	such	ADJ
ejpam-3129	218	38	that	that	SCONJ
ejpam-3129	218	39	the	the	DET
ejpam-3129	218	40	transformation	transformation	NOUN
ejpam-3129	218	41	s	s	VERB
ejpam-3129	218	42	of	of	ADP
ejpam-3129	218	43	g	g	NOUN
ejpam-3129	218	44	/	/	SYM
ejpam-3129	218	45	h	h	NOUN
ejpam-3129	218	46	determined	determine	VERB
ejpam-3129	218	47	by	by	ADP
ejpam-3129	218	48	σ	σ	NOUN
ejpam-3129	218	49	,	,	PUNCT
ejpam-3129	219	1	i.e.	i.e.	X
ejpam-3129	219	2	s	s	AUX
ejpam-3129	219	3	◦	◦	NOUN
ejpam-3129	219	4	π	π	NOUN
ejpam-3129	219	5	=	=	SYM
ejpam-3129	219	6	π	π	PROPN
ejpam-3129	219	7	◦	◦	NOUN
ejpam-3129	219	8	σ	σ	PROPN
ejpam-3129	219	9	is	be	AUX
ejpam-3129	219	10	metric	metric	ADJ
ejpam-3129	219	11	preserving	preserve	VERB
ejpam-3129	219	12	at	at	ADP
ejpam-3129	219	13	the	the	DET
ejpam-3129	219	14	origin	origin	NOUN
ejpam-3129	219	15	eh	eh	INTJ
ejpam-3129	219	16	of	of	ADP
ejpam-3129	219	17	g	g	PROPN
ejpam-3129	219	18	/	/	SYM
ejpam-3129	219	19	h.	h.	PROPN
ejpam-3129	219	20	then	then	ADV
ejpam-3129	219	21	g	g	PROPN
ejpam-3129	219	22	/	/	SYM
ejpam-3129	219	23	h	h	PROPN
ejpam-3129	219	24	is	be	AUX
ejpam-3129	219	25	a	a	DET
ejpam-3129	219	26	finslerian	finslerian	ADJ
ejpam-3129	219	27	s−manifold	s−manifold	NOUN
ejpam-3129	219	28	and	and	CCONJ
ejpam-3129	219	29	the	the	DET
ejpam-3129	219	30	symmetry	symmetry	NOUN
ejpam-3129	219	31	sx	sx	PROPN
ejpam-3129	219	32	is	be	AUX
ejpam-3129	219	33	given	give	VERB
ejpam-3129	219	34	by	by	ADP
ejpam-3129	219	35	sx	sx	PROPN
ejpam-3129	219	36	=	=	SYM
ejpam-3129	219	37	g	g	PROPN
ejpam-3129	219	38	◦	◦	NOUN
ejpam-3129	219	39	s	s	PART
ejpam-3129	219	40	◦	◦	NOUN
ejpam-3129	219	41	g−1	g−1	ADJ
ejpam-3129	219	42	g	g	NOUN
ejpam-3129	219	43	∈	∈	PROPN
ejpam-3129	219	44	g	g	PROPN
ejpam-3129	219	45	,	,	PUNCT
ejpam-3129	219	46	x	x	PUNCT
ejpam-3129	219	47	=	=	SYM
ejpam-3129	219	48	π(g	π(g	NOUN
ejpam-3129	219	49	)	)	PUNCT
ejpam-3129	219	50	proof	proof	NOUN
ejpam-3129	219	51	:	:	PUNCT
ejpam-3129	219	52	we	we	PRON
ejpam-3129	219	53	will	will	AUX
ejpam-3129	219	54	identify	identify	VERB
ejpam-3129	219	55	the	the	DET
ejpam-3129	219	56	elements	element	NOUN
ejpam-3129	219	57	of	of	ADP
ejpam-3129	219	58	g	g	NOUN
ejpam-3129	219	59	with	with	ADP
ejpam-3129	219	60	the	the	DET
ejpam-3129	219	61	corresponding	corresponding	ADJ
ejpam-3129	219	62	transformations	transformation	NOUN
ejpam-3129	219	63	of	of	ADP
ejpam-3129	219	64	m	m	NOUN
ejpam-3129	219	65	=	=	ADJ
ejpam-3129	219	66	g	g	PROPN
ejpam-3129	219	67	/	/	SYM
ejpam-3129	219	68	h.	h.	PROPN
ejpam-3129	219	69	choose	choose	VERB
ejpam-3129	219	70	g	g	PROPN
ejpam-3129	219	71	∈	∈	PROPN
ejpam-3129	219	72	g	g	PROPN
ejpam-3129	219	73	and	and	CCONJ
ejpam-3129	219	74	x	x	SYM
ejpam-3129	219	75	∈m	∈m	NOUN
ejpam-3129	219	76	then	then	ADV
ejpam-3129	219	77	x	x	ADP
ejpam-3129	219	78	=	=	SYM
ejpam-3129	219	79	π(g′	π(g′	PROPN
ejpam-3129	219	80	)	)	PUNCT
ejpam-3129	219	81	for	for	ADP
ejpam-3129	219	82	some	some	DET
ejpam-3129	219	83	g′	g′	NOUN
ejpam-3129	219	84	∈	∈	PROPN
ejpam-3129	219	85	g.	g.	NOUN
ejpam-3129	219	86	now	now	ADV
ejpam-3129	219	87	,	,	PUNCT
ejpam-3129	219	88	(	(	PUNCT
ejpam-3129	219	89	s	s	AUX
ejpam-3129	219	90	◦	◦	NOUN
ejpam-3129	219	91	g	g	NOUN
ejpam-3129	219	92	◦	◦	PROPN
ejpam-3129	219	93	s−1)(x	s−1)(x	PROPN
ejpam-3129	219	94	)	)	PUNCT
ejpam-3129	220	1	=	=	PRON
ejpam-3129	221	1	(	(	PUNCT
ejpam-3129	221	2	s	s	AUX
ejpam-3129	221	3	◦	◦	NOUN
ejpam-3129	221	4	g	g	NOUN
ejpam-3129	221	5	◦	◦	NOUN
ejpam-3129	221	6	s−1	s−1	ADJ
ejpam-3129	221	7	◦	◦	NOUN
ejpam-3129	221	8	π)(g′	π)(g′	NOUN
ejpam-3129	221	9	)	)	PUNCT
ejpam-3129	222	1	=	=	SYM
ejpam-3129	222	2	(	(	PUNCT
ejpam-3129	222	3	s	s	AUX
ejpam-3129	222	4	◦	◦	NOUN
ejpam-3129	222	5	g	g	ADP
ejpam-3129	222	6	◦	◦	NOUN
ejpam-3129	222	7	π)(σ−1(g′	π)(σ−1(g′	PROPN
ejpam-3129	222	8	)	)	PUNCT
ejpam-3129	222	9	)	)	PUNCT
ejpam-3129	223	1	=	=	PUNCT
ejpam-3129	223	2	(	(	PUNCT
ejpam-3129	223	3	s	s	AUX
ejpam-3129	223	4	◦	◦	NOUN
ejpam-3129	223	5	π)(gσ−1(g′	π)(gσ−1(g′	PROPN
ejpam-3129	223	6	)	)	PUNCT
ejpam-3129	223	7	)	)	PUNCT
ejpam-3129	224	1	=	=	PUNCT
ejpam-3129	224	2	(	(	PUNCT
ejpam-3129	224	3	π	π	PROPN
ejpam-3129	224	4	◦	◦	PROPN
ejpam-3129	224	5	σ)(gσ−1(g′	σ)(gσ−1(g′	PROPN
ejpam-3129	224	6	)	)	PUNCT
ejpam-3129	224	7	)	)	PUNCT
ejpam-3129	225	1	=	=	SYM
ejpam-3129	225	2	π(σ(g)g′	π(σ(g)g′	PROPN
ejpam-3129	225	3	)	)	PUNCT
ejpam-3129	225	4	=	=	PUNCT
ejpam-3129	226	1	σ(g)[π(g′	σ(g)[π(g′	NOUN
ejpam-3129	226	2	)	)	PUNCT
ejpam-3129	226	3	]	]	PUNCT
ejpam-3129	227	1	=	=	PUNCT
ejpam-3129	227	2	σ(g)(x	σ(g)(x	NUM
ejpam-3129	227	3	)	)	PUNCT
ejpam-3129	227	4	.	.	PUNCT
ejpam-3129	228	1	hence	hence	ADV
ejpam-3129	228	2	we	we	PRON
ejpam-3129	228	3	get	get	VERB
ejpam-3129	228	4	s	s	PRON
ejpam-3129	228	5	◦	◦	NOUN
ejpam-3129	228	6	g	g	NOUN
ejpam-3129	228	7	◦	◦	NOUN
ejpam-3129	228	8	s−1	s−1	PROPN
ejpam-3129	228	9	=	=	SYM
ejpam-3129	228	10	σ(g	σ(g	NOUN
ejpam-3129	228	11	)	)	PUNCT
ejpam-3129	228	12	g	g	NOUN
ejpam-3129	228	13	∈	∈	PROPN
ejpam-3129	228	14	g	g	PROPN
ejpam-3129	228	15	(	(	PUNCT
ejpam-3129	228	16	1	1	NUM
ejpam-3129	228	17	)	)	PUNCT
ejpam-3129	228	18	so	so	ADV
ejpam-3129	228	19	for	for	SCONJ
ejpam-3129	228	20	h	h	NOUN
ejpam-3129	228	21	∈	∈	PROPN
ejpam-3129	228	22	h	h	NOUN
ejpam-3129	229	1	we	we	PRON
ejpam-3129	229	2	obtain	obtain	VERB
ejpam-3129	229	3	s	s	PART
ejpam-3129	229	4	◦	◦	NOUN
ejpam-3129	229	5	h	h	NOUN
ejpam-3129	229	6	◦	◦	NOUN
ejpam-3129	229	7	s−1	s−1	ADJ
ejpam-3129	229	8	=	=	SYM
ejpam-3129	229	9	h	h	NOUN
ejpam-3129	229	10	and	and	CCONJ
ejpam-3129	229	11	hence	hence	ADV
ejpam-3129	229	12	h	h	NOUN
ejpam-3129	229	13	◦	◦	NOUN
ejpam-3129	229	14	s	s	PART
ejpam-3129	229	15	◦	◦	NOUN
ejpam-3129	229	16	h−1	h−1	PROPN
ejpam-3129	229	17	=	=	PUNCT
ejpam-3129	230	1	s.	s.	PROPN
ejpam-3129	230	2	consequently	consequently	ADV
ejpam-3129	230	3	the	the	DET
ejpam-3129	230	4	transformation	transformation	NOUN
ejpam-3129	230	5	g	g	ADP
ejpam-3129	230	6	◦	◦	NOUN
ejpam-3129	230	7	s	s	PART
ejpam-3129	230	8	◦	◦	NOUN
ejpam-3129	230	9	g−1	g−1	PROPN
ejpam-3129	230	10	always	always	ADV
ejpam-3129	230	11	depends	depend	VERB
ejpam-3129	230	12	only	only	ADV
ejpam-3129	230	13	on	on	ADP
ejpam-3129	230	14	π(g	π(g	PROPN
ejpam-3129	230	15	)	)	PUNCT
ejpam-3129	230	16	and	and	CCONJ
ejpam-3129	230	17	sπ(g	sπ(g	NUM
ejpam-3129	230	18	)	)	PUNCT
ejpam-3129	230	19	=	=	SYM
ejpam-3129	230	20	g	g	ADP
ejpam-3129	230	21	◦	◦	NOUN
ejpam-3129	230	22	s	s	PART
ejpam-3129	230	23	◦	◦	NOUN
ejpam-3129	230	24	g−1	g−1	ADJ
ejpam-3129	230	25	g	g	NOUN
ejpam-3129	230	26	∈	∈	PROPN
ejpam-3129	230	27	g	g	PROPN
ejpam-3129	230	28	defines	define	VERB
ejpam-3129	230	29	a	a	DET
ejpam-3129	230	30	family	family	NOUN
ejpam-3129	230	31	{	{	PUNCT
ejpam-3129	230	32	sx|x	sx|x	PROPN
ejpam-3129	230	33	∈	∈	PROPN
ejpam-3129	230	34	m	m	NOUN
ejpam-3129	230	35	}	}	PUNCT
ejpam-3129	230	36	of	of	ADP
ejpam-3129	230	37	diffeomorphisms	diffeomorphism	NOUN
ejpam-3129	230	38	of	of	ADP
ejpam-3129	230	39	m	m	PROPN
ejpam-3129	230	40	.	.	PUNCT
ejpam-3129	231	1	we	we	PRON
ejpam-3129	231	2	can	can	AUX
ejpam-3129	231	3	also	also	ADV
ejpam-3129	231	4	easily	easily	ADV
ejpam-3129	231	5	that	that	SCONJ
ejpam-3129	231	6	(	(	PUNCT
ejpam-3129	231	7	x	x	X
ejpam-3129	231	8	,	,	PUNCT
ejpam-3129	231	9	y	y	NOUN
ejpam-3129	231	10	)	)	PUNCT
ejpam-3129	231	11	−→	−→	NOUN
ejpam-3129	231	12	sx(y	sx(y	NOUN
ejpam-3129	231	13	)	)	PUNCT
ejpam-3129	231	14	is	be	AUX
ejpam-3129	231	15	differentiable	differentiable	ADJ
ejpam-3129	231	16	.	.	PUNCT
ejpam-3129	232	1	further	far	ADV
ejpam-3129	232	2	for	for	ADP
ejpam-3129	232	3	x	x	SYM
ejpam-3129	232	4	∈m	∈m	NOUN
ejpam-3129	232	5	,	,	PUNCT
ejpam-3129	232	6	x	x	SYM
ejpam-3129	232	7	=	=	SYM
ejpam-3129	232	8	π(g	π(g	PROPN
ejpam-3129	232	9	)	)	PUNCT
ejpam-3129	232	10	we	we	PRON
ejpam-3129	232	11	have	have	VERB
ejpam-3129	232	12	x	x	X
ejpam-3129	232	13	=	=	SYM
ejpam-3129	232	14	g(o	g(o	PROPN
ejpam-3129	232	15	)	)	PUNCT
ejpam-3129	232	16	and	and	CCONJ
ejpam-3129	232	17	hence	hence	ADV
ejpam-3129	232	18	sx(x	sx(x	ADV
ejpam-3129	232	19	)	)	PUNCT
ejpam-3129	233	1	=	=	SYM
ejpam-3129	233	2	(	(	PUNCT
ejpam-3129	233	3	g	g	PART
ejpam-3129	233	4	◦	◦	NOUN
ejpam-3129	233	5	s	s	PART
ejpam-3129	233	6	◦	◦	NOUN
ejpam-3129	233	7	g−1)(x	g−1)(x	NOUN
ejpam-3129	233	8	)	)	PUNCT
ejpam-3129	233	9	=	=	SYM
ejpam-3129	234	1	x	x	X
ejpam-3129	234	2	,	,	PUNCT
ejpam-3129	234	3	p.	p.	NOUN
ejpam-3129	234	4	bahmandoust	bahmandoust	NOUN
ejpam-3129	234	5	,	,	PUNCT
ejpam-3129	234	6	d.	d.	PROPN
ejpam-3129	234	7	latifi	latifi	PROPN
ejpam-3129	234	8	/	/	SYM
ejpam-3129	234	9	eur	eur	PROPN
ejpam-3129	234	10	.	.	PUNCT
ejpam-3129	235	1	j.	j.	PROPN
ejpam-3129	235	2	pure	pure	PROPN
ejpam-3129	235	3	appl	appl	PROPN
ejpam-3129	235	4	.	.	PROPN
ejpam-3129	235	5	math	math	PROPN
ejpam-3129	235	6	,	,	PUNCT
ejpam-3129	235	7	10	10	NUM
ejpam-3129	235	8	(	(	PUNCT
ejpam-3129	235	9	5	5	NUM
ejpam-3129	235	10	)	)	PUNCT
ejpam-3129	235	11	(	(	PUNCT
ejpam-3129	235	12	2017	2017	NUM
ejpam-3129	235	13	)	)	PUNCT
ejpam-3129	235	14	,	,	PUNCT
ejpam-3129	235	15	1099	1099	NUM
ejpam-3129	235	16	-	-	SYM
ejpam-3129	235	17	1111	1111	NUM
ejpam-3129	235	18	1108	1108	NUM
ejpam-3129	235	19	because	because	SCONJ
ejpam-3129	235	20	s(o	s(o	ADV
ejpam-3129	235	21	)	)	PUNCT
ejpam-3129	235	22	=	=	SYM
ejpam-3129	236	1	o.	o.	NOUN
ejpam-3129	236	2	now	now	ADV
ejpam-3129	236	3	for	for	ADP
ejpam-3129	236	4	x	x	X
ejpam-3129	236	5	,	,	PUNCT
ejpam-3129	236	6	y	y	PROPN
ejpam-3129	236	7	∈m	∈m	NOUN
ejpam-3129	236	8	put	put	VERB
ejpam-3129	236	9	sx	sx	NOUN
ejpam-3129	236	10	=	=	SYM
ejpam-3129	236	11	g	g	PROPN
ejpam-3129	236	12	◦	◦	NOUN
ejpam-3129	236	13	s	s	PART
ejpam-3129	236	14	◦	◦	NOUN
ejpam-3129	236	15	g−1	g−1	PROPN
ejpam-3129	236	16	,	,	PUNCT
ejpam-3129	236	17	sy	sy	NOUN
ejpam-3129	236	18	=	=	PUNCT
ejpam-3129	236	19	g′	g′	NOUN
ejpam-3129	236	20	◦	◦	NOUN
ejpam-3129	236	21	s	s	PART
ejpam-3129	236	22	◦	◦	NOUN
ejpam-3129	236	23	(	(	PUNCT
ejpam-3129	236	24	g′)−1	g′)−1	NOUN
ejpam-3129	236	25	,	,	PUNCT
ejpam-3129	236	26	where	where	SCONJ
ejpam-3129	236	27	x	x	X
ejpam-3129	236	28	=	=	SYM
ejpam-3129	236	29	g(o	g(o	PROPN
ejpam-3129	236	30	)	)	PUNCT
ejpam-3129	236	31	and	and	CCONJ
ejpam-3129	236	32	y	y	PROPN
ejpam-3129	236	33	=	=	PUNCT
ejpam-3129	236	34	g′(o	g′(o	PROPN
ejpam-3129	236	35	)	)	PUNCT
ejpam-3129	236	36	.	.	PUNCT
ejpam-3129	237	1	then	then	ADV
ejpam-3129	237	2	(	(	PUNCT
ejpam-3129	237	3	g	g	PROPN
ejpam-3129	237	4	◦	◦	NOUN
ejpam-3129	237	5	s	s	PART
ejpam-3129	237	6	◦	◦	NOUN
ejpam-3129	237	7	g−1	g−1	VERB
ejpam-3129	237	8	◦	◦	NOUN
ejpam-3129	237	9	g′	g′	NOUN
ejpam-3129	237	10	◦	◦	NOUN
ejpam-3129	237	11	s−1)(o	s−1)(o	PROPN
ejpam-3129	237	12	)	)	PUNCT
ejpam-3129	237	13	=	=	SYM
ejpam-3129	237	14	sx(g′(o	sx(g′(o	PROPN
ejpam-3129	237	15	)	)	PUNCT
ejpam-3129	237	16	)	)	PUNCT
ejpam-3129	238	1	=	=	SYM
ejpam-3129	238	2	sx(y	sx(y	NOUN
ejpam-3129	238	3	)	)	PUNCT
ejpam-3129	238	4	,	,	PUNCT
ejpam-3129	238	5	on	on	ADP
ejpam-3129	238	6	the	the	DET
ejpam-3129	238	7	other	other	ADJ
ejpam-3129	238	8	hand	hand	NOUN
ejpam-3129	238	9	,	,	PUNCT
ejpam-3129	238	10	(	(	PUNCT
ejpam-3129	238	11	1	1	X
ejpam-3129	238	12	)	)	PUNCT
ejpam-3129	238	13	yields	yield	NOUN
ejpam-3129	238	14	g	g	ADP
ejpam-3129	238	15	◦	◦	NOUN
ejpam-3129	238	16	s	s	SYM
ejpam-3129	238	17	◦	◦	NOUN
ejpam-3129	238	18	g−1	g−1	ADJ
ejpam-3129	238	19	◦	◦	NOUN
ejpam-3129	238	20	g′	g′	NOUN
ejpam-3129	238	21	◦	◦	NOUN
ejpam-3129	238	22	s−1	s−1	PROPN
ejpam-3129	238	23	=	=	SYM
ejpam-3129	238	24	gσ(g−1g′	gσ(g−1g′	NUM
ejpam-3129	238	25	)	)	PUNCT
ejpam-3129	238	26	.	.	PUNCT
ejpam-3129	239	1	thus	thus	ADV
ejpam-3129	239	2	,	,	PUNCT
ejpam-3129	239	3	the	the	DET
ejpam-3129	239	4	map	map	NOUN
ejpam-3129	239	5	g	g	ADP
ejpam-3129	239	6	◦	◦	NOUN
ejpam-3129	239	7	s	s	SYM
ejpam-3129	239	8	◦	◦	NOUN
ejpam-3129	239	9	g−1	g−1	ADJ
ejpam-3129	239	10	◦	◦	NOUN
ejpam-3129	239	11	g′	g′	NOUN
ejpam-3129	239	12	◦	◦	NOUN
ejpam-3129	239	13	s−1	s−1	PROPN
ejpam-3129	239	14	coincides	coincide	VERB
ejpam-3129	239	15	with	with	ADP
ejpam-3129	239	16	the	the	DET
ejpam-3129	239	17	action	action	NOUN
ejpam-3129	239	18	of	of	ADP
ejpam-3129	239	19	an	an	DET
ejpam-3129	239	20	element	element	NOUN
ejpam-3129	239	21	g′′	g′′	PROPN
ejpam-3129	239	22	∈	∈	PROPN
ejpam-3129	239	23	g	g	PROPN
ejpam-3129	239	24	,	,	PUNCT
ejpam-3129	239	25	g′′(o	g′′(o	X
ejpam-3129	239	26	)	)	PUNCT
ejpam-3129	239	27	=	=	SYM
ejpam-3129	239	28	sx(y	sx(y	NOUN
ejpam-3129	239	29	)	)	PUNCT
ejpam-3129	239	30	.	.	PUNCT
ejpam-3129	240	1	now	now	ADV
ejpam-3129	240	2	sx	sx	VERB
ejpam-3129	240	3	◦	◦	NOUN
ejpam-3129	240	4	sy	sy	NOUN
ejpam-3129	240	5	=	=	SYM
ejpam-3129	240	6	g	g	PROPN
ejpam-3129	240	7	◦	◦	NOUN
ejpam-3129	240	8	s	s	PART
ejpam-3129	240	9	◦	◦	NOUN
ejpam-3129	240	10	g−1	g−1	VERB
ejpam-3129	240	11	◦	◦	NOUN
ejpam-3129	240	12	g′	g′	NOUN
ejpam-3129	240	13	◦	◦	NOUN
ejpam-3129	240	14	s	s	PART
ejpam-3129	240	15	◦	◦	NOUN
ejpam-3129	240	16	(	(	PUNCT
ejpam-3129	240	17	g′)−1	g′)−1	NOUN
ejpam-3129	240	18	=	=	SYM
ejpam-3129	240	19	g′′	g′′	PROPN
ejpam-3129	241	1	◦	◦	NOUN
ejpam-3129	241	2	s	s	PART
ejpam-3129	241	3	◦	◦	NOUN
ejpam-3129	241	4	(	(	PUNCT
ejpam-3129	241	5	g′′)−1	g′′)−1	VERB
ejpam-3129	241	6	◦	◦	NOUN
ejpam-3129	241	7	g	g	NOUN
ejpam-3129	241	8	◦	◦	NOUN
ejpam-3129	241	9	s	s	PART
ejpam-3129	241	10	◦	◦	NOUN
ejpam-3129	241	11	g−1	g−1	PROPN
ejpam-3129	241	12	=	=	SYM
ejpam-3129	241	13	ssx(y	ssx(y	PROPN
ejpam-3129	241	14	)	)	PUNCT
ejpam-3129	241	15	◦	◦	NOUN
ejpam-3129	241	16	sx	sx	PROPN
ejpam-3129	241	17	.	.	PUNCT
ejpam-3129	242	1	it	it	PRON
ejpam-3129	242	2	remains	remain	VERB
ejpam-3129	242	3	to	to	PART
ejpam-3129	242	4	prove	prove	VERB
ejpam-3129	242	5	that	that	SCONJ
ejpam-3129	242	6	sx∗	sx∗	PROPN
ejpam-3129	242	7	has	have	VERB
ejpam-3129	242	8	no	no	DET
ejpam-3129	242	9	fixed	fix	VERB
ejpam-3129	242	10	vector	vector	NOUN
ejpam-3129	242	11	except	except	SCONJ
ejpam-3129	242	12	the	the	DET
ejpam-3129	242	13	null	null	ADJ
ejpam-3129	242	14	vector	vector	NOUN
ejpam-3129	242	15	.	.	PUNCT
ejpam-3129	243	1	if	if	SCONJ
ejpam-3129	243	2	we	we	PRON
ejpam-3129	243	3	identify	identify	VERB
ejpam-3129	243	4	g	g	NOUN
ejpam-3129	243	5	with	with	ADP
ejpam-3129	243	6	teg	teg	PROPN
ejpam-3129	243	7	,	,	PUNCT
ejpam-3129	243	8	then	then	ADV
ejpam-3129	243	9	the	the	DET
ejpam-3129	243	10	projection	projection	NOUN
ejpam-3129	243	11	π∗e	π∗e	PUNCT
ejpam-3129	243	12	:	:	PUNCT
ejpam-3129	243	13	teg	teg	PROPN
ejpam-3129	243	14	−→	−→	PROPN
ejpam-3129	243	15	tom	tom	PROPN
ejpam-3129	243	16	induces	induce	VERB
ejpam-3129	243	17	an	an	DET
ejpam-3129	243	18	isomorphism	isomorphism	NOUN
ejpam-3129	243	19	of	of	ADP
ejpam-3129	243	20	g1	g1	PROPN
ejpam-3129	243	21	t	t	PROPN
ejpam-3129	243	22	onto	onto	ADP
ejpam-3129	243	23	tom	tom	PROPN
ejpam-3129	243	24	.	.	PUNCT
ejpam-3129	244	1	from	from	ADP
ejpam-3129	244	2	the	the	DET
ejpam-3129	244	3	relation	relation	NOUN
ejpam-3129	244	4	π∗	π∗	PROPN
ejpam-3129	244	5	◦	◦	NOUN
ejpam-3129	244	6	σ∗	σ∗	ADV
ejpam-3129	244	7	=	=	PRON
ejpam-3129	244	8	s∗	s∗	VERB
ejpam-3129	244	9	◦	◦	NOUN
ejpam-3129	244	10	π∗	π∗	NOUN
ejpam-3129	244	11	we	we	PRON
ejpam-3129	244	12	can	can	AUX
ejpam-3129	244	13	see	see	VERB
ejpam-3129	244	14	that	that	DET
ejpam-3129	244	15	π∗	π∗	PROPN
ejpam-3129	244	16	◦	◦	PROPN
ejpam-3129	244	17	t	t	NOUN
ejpam-3129	244	18	=	=	PUNCT
ejpam-3129	244	19	(	(	PUNCT
ejpam-3129	244	20	io−	io−	NOUN
ejpam-3129	244	21	s∗o	s∗o	NUM
ejpam-3129	244	22	)	)	PUNCT
ejpam-3129	244	23	◦	◦	NOUN
ejpam-3129	244	24	π∗.	π∗.	ADJ
ejpam-3129	244	25	because	because	SCONJ
ejpam-3129	244	26	t	t	PROPN
ejpam-3129	244	27	is	be	AUX
ejpam-3129	244	28	an	an	DET
ejpam-3129	244	29	automorphism	automorphism	NOUN
ejpam-3129	244	30	on	on	ADP
ejpam-3129	244	31	g1	g1	PROPN
ejpam-3129	244	32	t	t	PROPN
ejpam-3129	244	33	,	,	PUNCT
ejpam-3129	244	34	io	io	PROPN
ejpam-3129	244	35	−	−	PROPN
ejpam-3129	244	36	s∗o	s∗o	NUM
ejpam-3129	244	37	is	be	AUX
ejpam-3129	244	38	an	an	DET
ejpam-3129	244	39	automorphism	automorphism	NOUN
ejpam-3129	244	40	of	of	ADP
ejpam-3129	244	41	tom	tom	PROPN
ejpam-3129	244	42	.	.	PUNCT
ejpam-3129	245	1	from	from	ADP
ejpam-3129	245	2	sπ(g	sπ(g	NUM
ejpam-3129	245	3	)	)	PUNCT
ejpam-3129	245	4	=	=	SYM
ejpam-3129	245	5	g	g	ADP
ejpam-3129	245	6	◦	◦	NOUN
ejpam-3129	245	7	s	s	PART
ejpam-3129	245	8	◦	◦	NOUN
ejpam-3129	245	9	g−1	g−1	PROPN
ejpam-3129	245	10	,	,	PUNCT
ejpam-3129	245	11	g	g	PROPN
ejpam-3129	245	12	∈	∈	PROPN
ejpam-3129	245	13	g	g	PROPN
ejpam-3129	245	14	,	,	PUNCT
ejpam-3129	245	15	x	x	PUNCT
ejpam-3129	245	16	=	=	SYM
ejpam-3129	245	17	π(g	π(g	PROPN
ejpam-3129	245	18	)	)	PUNCT
ejpam-3129	245	19	,	,	PUNCT
ejpam-3129	245	20	we	we	PRON
ejpam-3129	245	21	obtain	obtain	VERB
ejpam-3129	245	22	easily	easily	ADV
ejpam-3129	245	23	that	that	SCONJ
ejpam-3129	245	24	ip−sp	ip−sp	PROPN
ejpam-3129	245	25	is	be	AUX
ejpam-3129	245	26	an	an	DET
ejpam-3129	245	27	automorphism	automorphism	NOUN
ejpam-3129	245	28	of	of	ADP
ejpam-3129	245	29	tpm	tpm	PROPN
ejpam-3129	245	30	for	for	ADP
ejpam-3129	245	31	each	each	DET
ejpam-3129	245	32	p	p	NOUN
ejpam-3129	245	33	∈m	∈m	NOUN
ejpam-3129	245	34	.	.	PUNCT
ejpam-3129	246	1	thus	thus	ADV
ejpam-3129	246	2	{	{	PUNCT
ejpam-3129	246	3	sx|x	sx|x	PROPN
ejpam-3129	246	4	∈m	∈m	PROPN
ejpam-3129	246	5	}	}	PUNCT
ejpam-3129	246	6	is	be	AUX
ejpam-3129	246	7	a	a	DET
ejpam-3129	246	8	regular	regular	ADJ
ejpam-3129	246	9	s−structure	s−structure	NOUN
ejpam-3129	246	10	on	on	ADP
ejpam-3129	246	11	(	(	PUNCT
ejpam-3129	246	12	m	m	PROPN
ejpam-3129	246	13	,	,	PUNCT
ejpam-3129	246	14	f	f	PROPN
ejpam-3129	246	15	)	)	PUNCT
ejpam-3129	246	16	.	.	PUNCT
ejpam-3129	247	1	�	�	PROPN
ejpam-3129	247	2	corollary	corollary	NOUN
ejpam-3129	247	3	1	1	NUM
ejpam-3129	247	4	.	.	PUNCT
ejpam-3129	248	1	let	let	AUX
ejpam-3129	248	2	(	(	PUNCT
ejpam-3129	248	3	g	g	NOUN
ejpam-3129	248	4	,	,	PUNCT
ejpam-3129	248	5	h	h	NOUN
ejpam-3129	248	6	,	,	PUNCT
ejpam-3129	248	7	σ	σ	PROPN
ejpam-3129	248	8	)	)	PUNCT
ejpam-3129	248	9	be	be	AUX
ejpam-3129	248	10	a	a	DET
ejpam-3129	248	11	regular	regular	ADJ
ejpam-3129	248	12	homogeneous	homogeneous	ADJ
ejpam-3129	248	13	s−manifold	s−manifold	NOUN
ejpam-3129	248	14	of	of	ADP
ejpam-3129	248	15	order	order	NOUN
ejpam-3129	249	1	k	k	NOUN
ejpam-3129	249	2	,	,	PUNCT
ejpam-3129	249	3	with	with	ADP
ejpam-3129	249	4	the	the	DET
ejpam-3129	249	5	g−invariant	g−invariant	PROPN
ejpam-3129	249	6	finsler	finsler	NOUN
ejpam-3129	249	7	metric	metric	ADJ
ejpam-3129	249	8	f	f	PROPN
ejpam-3129	249	9	on	on	ADP
ejpam-3129	249	10	g	g	PROPN
ejpam-3129	249	11	/	/	SYM
ejpam-3129	249	12	h	h	NOUN
ejpam-3129	249	13	such	such	ADJ
ejpam-3129	249	14	that	that	SCONJ
ejpam-3129	249	15	the	the	DET
ejpam-3129	249	16	transformation	transformation	NOUN
ejpam-3129	249	17	s	s	VERB
ejpam-3129	249	18	of	of	ADP
ejpam-3129	249	19	g	g	NOUN
ejpam-3129	249	20	/	/	SYM
ejpam-3129	249	21	h	h	NOUN
ejpam-3129	249	22	determined	determine	VERB
ejpam-3129	249	23	by	by	ADP
ejpam-3129	249	24	π	π	PROPN
ejpam-3129	249	25	◦	◦	PROPN
ejpam-3129	249	26	σ	σ	X
ejpam-3129	249	27	=	=	SYM
ejpam-3129	249	28	s	s	PART
ejpam-3129	249	29	◦	◦	NOUN
ejpam-3129	249	30	π	π	NOUN
ejpam-3129	249	31	is	be	AUX
ejpam-3129	249	32	metric	metric	ADJ
ejpam-3129	249	33	preserving	preserve	VERB
ejpam-3129	249	34	at	at	ADP
ejpam-3129	249	35	the	the	DET
ejpam-3129	249	36	origin	origin	NOUN
ejpam-3129	249	37	eh	eh	INTJ
ejpam-3129	249	38	of	of	ADP
ejpam-3129	249	39	g	g	PROPN
ejpam-3129	249	40	/	/	SYM
ejpam-3129	249	41	h.	h.	PROPN
ejpam-3129	249	42	then	then	ADV
ejpam-3129	249	43	g	g	PROPN
ejpam-3129	249	44	/	/	SYM
ejpam-3129	249	45	h	h	PROPN
ejpam-3129	249	46	is	be	AUX
ejpam-3129	249	47	a	a	DET
ejpam-3129	249	48	finsler	finsler	NOUN
ejpam-3129	249	49	s−manifold	s−manifold	NOUN
ejpam-3129	249	50	of	of	ADP
ejpam-3129	249	51	order	order	NOUN
ejpam-3129	249	52	k.	k.	PROPN
ejpam-3129	249	53	proof	proof	NOUN
ejpam-3129	249	54	:	:	PUNCT
ejpam-3129	249	55	it	it	PRON
ejpam-3129	249	56	is	be	AUX
ejpam-3129	249	57	a	a	DET
ejpam-3129	249	58	consequence	consequence	NOUN
ejpam-3129	249	59	of	of	ADP
ejpam-3129	249	60	theorem	theorem	ADJ
ejpam-3129	249	61	4	4	NUM
ejpam-3129	249	62	and	and	CCONJ
ejpam-3129	249	63	theorem	theorem	VERB
ejpam-3129	249	64	5	5	NUM
ejpam-3129	249	65	.	.	PUNCT
ejpam-3129	249	66	�	�	PROPN
ejpam-3129	249	67	theorem	theorem	VERB
ejpam-3129	249	68	6	6	NUM
ejpam-3129	249	69	.	.	PUNCT
ejpam-3129	250	1	let	let	VERB
ejpam-3129	250	2	(	(	PUNCT
ejpam-3129	250	3	m	m	PROPN
ejpam-3129	250	4	,	,	PUNCT
ejpam-3129	250	5	f	f	PROPN
ejpam-3129	250	6	)	)	PUNCT
ejpam-3129	250	7	be	be	AUX
ejpam-3129	250	8	a	a	DET
ejpam-3129	250	9	finsler	finsler	NOUN
ejpam-3129	250	10	s−manifold	s−manifold	NOUN
ejpam-3129	250	11	and	and	CCONJ
ejpam-3129	250	12	o	o	X
ejpam-3129	250	13	∈m	∈m	NOUN
ejpam-3129	250	14	a	a	DET
ejpam-3129	250	15	fixed	fix	VERB
ejpam-3129	250	16	point	point	NOUN
ejpam-3129	250	17	.	.	PUNCT
ejpam-3129	251	1	let	let	VERB
ejpam-3129	251	2	g	g	NOUN
ejpam-3129	251	3	be	be	AUX
ejpam-3129	251	4	the	the	DET
ejpam-3129	251	5	identity	identity	NOUN
ejpam-3129	251	6	component	component	NOUN
ejpam-3129	251	7	of	of	ADP
ejpam-3129	251	8	the	the	DET
ejpam-3129	251	9	symmetry	symmetry	NOUN
ejpam-3129	251	10	preserving	preserve	VERB
ejpam-3129	251	11	group	group	NOUN
ejpam-3129	251	12	aut({m	aut({m	PROPN
ejpam-3129	251	13	,	,	PUNCT
ejpam-3129	251	14	sx	sx	PROPN
ejpam-3129	251	15	}	}	PUNCT
ejpam-3129	251	16	)	)	PUNCT
ejpam-3129	251	17	and	and	CCONJ
ejpam-3129	251	18	go	go	VERB
ejpam-3129	251	19	the	the	DET
ejpam-3129	251	20	isotropy	isotropy	ADJ
ejpam-3129	251	21	subgroup	subgroup	NOUN
ejpam-3129	251	22	of	of	ADP
ejpam-3129	251	23	g	g	PROPN
ejpam-3129	251	24	at	at	ADP
ejpam-3129	251	25	o.	o.	NOUN
ejpam-3129	251	26	define	define	VERB
ejpam-3129	251	27	a	a	DET
ejpam-3129	251	28	map	map	NOUN
ejpam-3129	252	1	σ	σ	NOUN
ejpam-3129	252	2	:	:	PUNCT
ejpam-3129	252	3	g	g	PROPN
ejpam-3129	252	4	−→	−→	NOUN
ejpam-3129	252	5	aut(m	aut(m	PROPN
ejpam-3129	252	6	,	,	PUNCT
ejpam-3129	252	7	{	{	PUNCT
ejpam-3129	252	8	sx	sx	NOUN
ejpam-3129	252	9	}	}	PUNCT
ejpam-3129	252	10	)	)	PUNCT
ejpam-3129	252	11	by	by	ADP
ejpam-3129	252	12	the	the	DET
ejpam-3129	252	13	formula	formula	NOUN
ejpam-3129	252	14	σ(g	σ(g	NOUN
ejpam-3129	252	15	)	)	PUNCT
ejpam-3129	252	16	=	=	PUNCT
ejpam-3129	252	17	so	so	ADV
ejpam-3129	252	18	◦	◦	VERB
ejpam-3129	252	19	g	g	NOUN
ejpam-3129	252	20	◦	◦	NOUN
ejpam-3129	252	21	s−1o	s−1o	NOUN
ejpam-3129	252	22	g	g	PROPN
ejpam-3129	252	23	∈	∈	PROPN
ejpam-3129	252	24	g.	g.	NOUN
ejpam-3129	252	25	then	then	ADV
ejpam-3129	252	26	σ	σ	PROPN
ejpam-3129	252	27	is	be	AUX
ejpam-3129	252	28	an	an	DET
ejpam-3129	252	29	automorphism	automorphism	NOUN
ejpam-3129	252	30	of	of	ADP
ejpam-3129	252	31	g	g	NOUN
ejpam-3129	252	32	,	,	PUNCT
ejpam-3129	252	33	and	and	CCONJ
ejpam-3129	252	34	(	(	PUNCT
ejpam-3129	252	35	g	g	NOUN
ejpam-3129	252	36	,	,	PUNCT
ejpam-3129	252	37	go	go	VERB
ejpam-3129	252	38	,	,	PUNCT
ejpam-3129	252	39	σ	σ	X
ejpam-3129	252	40	)	)	PUNCT
ejpam-3129	252	41	is	be	AUX
ejpam-3129	252	42	a	a	DET
ejpam-3129	252	43	regular	regular	ADJ
ejpam-3129	252	44	homogeneous	homogeneous	ADJ
ejpam-3129	252	45	s−manifold	s−manifold	NOUN
ejpam-3129	252	46	.	.	PUNCT
ejpam-3129	253	1	the	the	DET
ejpam-3129	253	2	symmetries	symmetry	NOUN
ejpam-3129	253	3	sx	sx	PROPN
ejpam-3129	253	4	are	be	AUX
ejpam-3129	253	5	given	give	VERB
ejpam-3129	253	6	by	by	ADP
ejpam-3129	253	7	the	the	DET
ejpam-3129	253	8	formula	formula	NOUN
ejpam-3129	253	9	sπ(g	sπ(g	PUNCT
ejpam-3129	253	10	)	)	PUNCT
ejpam-3129	254	1	=	=	SYM
ejpam-3129	255	1	g	g	ADP
ejpam-3129	255	2	◦	◦	NOUN
ejpam-3129	255	3	so	so	ADV
ejpam-3129	255	4	◦	◦	NOUN
ejpam-3129	255	5	g−1	g−1	PROPN
ejpam-3129	255	6	,	,	PUNCT
ejpam-3129	255	7	x	x	PUNCT
ejpam-3129	255	8	=	=	SYM
ejpam-3129	255	9	π(g	π(g	PROPN
ejpam-3129	255	10	)	)	PUNCT
ejpam-3129	255	11	and	and	CCONJ
ejpam-3129	255	12	m	m	NOUN
ejpam-3129	255	13	'	'	PART
ejpam-3129	255	14	g	g	NOUN
ejpam-3129	255	15	/	/	SYM
ejpam-3129	255	16	go	go	VERB
ejpam-3129	255	17	.	.	PUNCT
ejpam-3129	256	1	proof	proof	NOUN
ejpam-3129	256	2	:	:	PUNCT
ejpam-3129	256	3	by	by	ADP
ejpam-3129	256	4	theorem	theorem	NOUN
ejpam-3129	256	5	3	3	NUM
ejpam-3129	256	6	aut(m	aut(m	PROPN
ejpam-3129	256	7	,	,	PUNCT
ejpam-3129	256	8	{	{	PUNCT
ejpam-3129	256	9	sx	sx	NOUN
ejpam-3129	256	10	}	}	PUNCT
ejpam-3129	256	11	)	)	PUNCT
ejpam-3129	256	12	is	be	AUX
ejpam-3129	256	13	transitive	transitive	ADJ
ejpam-3129	256	14	on	on	ADP
ejpam-3129	256	15	m	m	NOUN
ejpam-3129	256	16	and	and	CCONJ
ejpam-3129	256	17	m	m	VERB
ejpam-3129	256	18	is	be	AUX
ejpam-3129	256	19	connected	connect	VERB
ejpam-3129	256	20	.	.	PUNCT
ejpam-3129	257	1	so	so	ADV
ejpam-3129	257	2	g	g	PROPN
ejpam-3129	257	3	is	be	AUX
ejpam-3129	257	4	also	also	ADV
ejpam-3129	257	5	transitive	transitive	ADJ
ejpam-3129	257	6	on	on	ADP
ejpam-3129	257	7	m	m	PROPN
ejpam-3129	257	8	.	.	PUNCT
ejpam-3129	258	1	obviously	obviously	ADV
ejpam-3129	258	2	,	,	PUNCT
ejpam-3129	258	3	the	the	DET
ejpam-3129	258	4	map	map	NOUN
ejpam-3129	258	5	σ	σ	NOUN
ejpam-3129	258	6	given	give	VERB
ejpam-3129	258	7	by	by	ADP
ejpam-3129	258	8	σ(g	σ(g	NOUN
ejpam-3129	258	9	)	)	PUNCT
ejpam-3129	258	10	=	=	PUNCT
ejpam-3129	258	11	so	so	ADV
ejpam-3129	258	12	◦	◦	VERB
ejpam-3129	258	13	g	g	NOUN
ejpam-3129	258	14	◦	◦	NOUN
ejpam-3129	258	15	s−1o	s−1o	NOUN
ejpam-3129	258	16	g	g	PROPN
ejpam-3129	258	17	∈	∈	PROPN
ejpam-3129	258	18	g	g	PROPN
ejpam-3129	258	19	references	reference	NOUN
ejpam-3129	258	20	1109	1109	NUM
ejpam-3129	258	21	is	be	AUX
ejpam-3129	258	22	an	an	DET
ejpam-3129	258	23	isomorphism	isomorphism	NOUN
ejpam-3129	258	24	and	and	CCONJ
ejpam-3129	258	25	σ(g	σ(g	NOUN
ejpam-3129	258	26	)	)	PUNCT
ejpam-3129	258	27	=	=	SYM
ejpam-3129	259	1	g.	g.	NOUN
ejpam-3129	259	2	let	let	VERB
ejpam-3129	259	3	go	go	VERB
ejpam-3129	259	4	be	be	AUX
ejpam-3129	259	5	the	the	DET
ejpam-3129	259	6	isotropy	isotropy	ADJ
ejpam-3129	259	7	group	group	NOUN
ejpam-3129	259	8	of	of	ADP
ejpam-3129	259	9	g	g	PROPN
ejpam-3129	259	10	at	at	ADP
ejpam-3129	259	11	o	o	PROPN
ejpam-3129	259	12	,	,	PUNCT
ejpam-3129	259	13	then	then	ADV
ejpam-3129	259	14	m	m	PROPN
ejpam-3129	259	15	'	'	PART
ejpam-3129	259	16	g	g	NOUN
ejpam-3129	259	17	/	/	SYM
ejpam-3129	259	18	go	go	VERB
ejpam-3129	259	19	.	.	PUNCT
ejpam-3129	260	1	let	let	VERB
ejpam-3129	260	2	π	π	NOUN
ejpam-3129	260	3	:	:	PUNCT
ejpam-3129	260	4	g	g	ADP
ejpam-3129	260	5	−→	−→	NOUN
ejpam-3129	260	6	g	g	PROPN
ejpam-3129	260	7	/	/	SYM
ejpam-3129	260	8	go	go	VERB
ejpam-3129	260	9	'	'	VERB
ejpam-3129	260	10	m	m	AUX
ejpam-3129	260	11	be	be	AUX
ejpam-3129	260	12	the	the	DET
ejpam-3129	260	13	canonical	canonical	ADJ
ejpam-3129	260	14	projection	projection	NOUN
ejpam-3129	260	15	.	.	PUNCT
ejpam-3129	261	1	then	then	ADV
ejpam-3129	261	2	for	for	ADP
ejpam-3129	261	3	any	any	DET
ejpam-3129	261	4	g	g	PROPN
ejpam-3129	261	5	∈	∈	PROPN
ejpam-3129	261	6	g	g	NOUN
ejpam-3129	261	7	we	we	PRON
ejpam-3129	261	8	have	have	VERB
ejpam-3129	261	9	(	(	PUNCT
ejpam-3129	261	10	π	π	X
ejpam-3129	261	11	◦	◦	NOUN
ejpam-3129	261	12	σ)(g	σ)(g	ADJ
ejpam-3129	261	13	)	)	PUNCT
ejpam-3129	261	14	=	=	SYM
ejpam-3129	261	15	σ(g)(o	σ(g)(o	NUM
ejpam-3129	261	16	)	)	PUNCT
ejpam-3129	261	17	=	=	SYM
ejpam-3129	262	1	(	(	PUNCT
ejpam-3129	262	2	so	so	ADV
ejpam-3129	262	3	◦	◦	VERB
ejpam-3129	262	4	g	g	NOUN
ejpam-3129	262	5	◦	◦	NOUN
ejpam-3129	262	6	s−1o	s−1o	NOUN
ejpam-3129	262	7	)	)	PUNCT
ejpam-3129	262	8	(	(	PUNCT
ejpam-3129	262	9	o	o	NOUN
ejpam-3129	262	10	)	)	PUNCT
ejpam-3129	262	11	=	=	SYM
ejpam-3129	262	12	so(g(o	so(g(o	NOUN
ejpam-3129	262	13	)	)	PUNCT
ejpam-3129	262	14	)	)	PUNCT
ejpam-3129	263	1	=	=	SYM
ejpam-3129	263	2	(	(	PUNCT
ejpam-3129	263	3	so	so	ADV
ejpam-3129	263	4	◦	◦	VERB
ejpam-3129	263	5	π)(g	π)(g	NOUN
ejpam-3129	263	6	)	)	PUNCT
ejpam-3129	263	7	.	.	PUNCT
ejpam-3129	264	1	hence	hence	ADV
ejpam-3129	264	2	on	on	ADP
ejpam-3129	264	3	g	g	PROPN
ejpam-3129	264	4	we	we	PRON
ejpam-3129	264	5	have	have	VERB
ejpam-3129	264	6	π	π	PROPN
ejpam-3129	264	7	◦	◦	NOUN
ejpam-3129	264	8	σ	σ	NOUN
ejpam-3129	264	9	=	=	PUNCT
ejpam-3129	264	10	so	so	SCONJ
ejpam-3129	264	11	◦	◦	NOUN
ejpam-3129	264	12	π	π	X
ejpam-3129	264	13	.	.	PUNCT
ejpam-3129	265	1	(	(	PUNCT
ejpam-3129	265	2	2	2	NUM
ejpam-3129	265	3	)	)	PUNCT
ejpam-3129	265	4	because	because	SCONJ
ejpam-3129	265	5	g	g	PROPN
ejpam-3129	265	6	∈	∈	PROPN
ejpam-3129	265	7	g	g	PROPN
ejpam-3129	265	8	is	be	AUX
ejpam-3129	265	9	a	a	DET
ejpam-3129	265	10	symmetry	symmetry	NOUN
ejpam-3129	265	11	preserving	preserve	VERB
ejpam-3129	265	12	diffeomorphism	diffeomorphism	NOUN
ejpam-3129	265	13	,	,	PUNCT
ejpam-3129	265	14	we	we	PRON
ejpam-3129	265	15	have	have	VERB
ejpam-3129	265	16	g	g	NOUN
ejpam-3129	265	17	◦	◦	NOUN
ejpam-3129	265	18	sx	sx	PROPN
ejpam-3129	265	19	=	=	PUNCT
ejpam-3129	265	20	sg(x	sg(x	X
ejpam-3129	265	21	)	)	PUNCT
ejpam-3129	265	22	◦	◦	NOUN
ejpam-3129	265	23	g.	g.	NOUN
ejpam-3129	265	24	in	in	ADP
ejpam-3129	265	25	particular	particular	ADJ
ejpam-3129	265	26	,	,	PUNCT
ejpam-3129	265	27	for	for	ADP
ejpam-3129	265	28	each	each	DET
ejpam-3129	265	29	h	h	NOUN
ejpam-3129	265	30	∈	∈	PROPN
ejpam-3129	265	31	g	g	NOUN
ejpam-3129	265	32	we	we	PRON
ejpam-3129	265	33	have	have	VERB
ejpam-3129	265	34	σ(h	σ(h	NUM
ejpam-3129	265	35	)	)	PUNCT
ejpam-3129	265	36	=	=	PUNCT
ejpam-3129	266	1	so	so	SCONJ
ejpam-3129	266	2	◦	◦	NOUN
ejpam-3129	266	3	h	h	NOUN
ejpam-3129	266	4	◦	◦	NOUN
ejpam-3129	266	5	s−1o	s−1o	NOUN
ejpam-3129	266	6	=	=	SYM
ejpam-3129	266	7	sh(o	sh(o	X
ejpam-3129	266	8	)	)	PUNCT
ejpam-3129	266	9	◦	◦	NOUN
ejpam-3129	266	10	h	h	NOUN
ejpam-3129	266	11	◦	◦	NOUN
ejpam-3129	266	12	s−1o	s−1o	NOUN
ejpam-3129	266	13	=	=	SYM
ejpam-3129	266	14	h	h	NOUN
ejpam-3129	266	15	,	,	PUNCT
ejpam-3129	266	16	so	so	ADV
ejpam-3129	266	17	go	go	VERB
ejpam-3129	266	18	⊂	⊂	PRON
ejpam-3129	266	19	gσ	gσ	AUX
ejpam-3129	266	20	.	.	PUNCT
ejpam-3129	267	1	let	let	VERB
ejpam-3129	267	2	g	g	NOUN
ejpam-3129	267	3	,	,	PUNCT
ejpam-3129	267	4	go	go	VERB
ejpam-3129	267	5	,	,	PUNCT
ejpam-3129	267	6	g	g	PROPN
ejpam-3129	267	7	σ	σ	PROPN
ejpam-3129	267	8	denote	denote	VERB
ejpam-3129	267	9	the	the	DET
ejpam-3129	267	10	lie	lie	NOUN
ejpam-3129	267	11	algebra	algebra	NOUN
ejpam-3129	267	12	of	of	ADP
ejpam-3129	267	13	g	g	NOUN
ejpam-3129	267	14	,	,	PUNCT
ejpam-3129	267	15	go	go	VERB
ejpam-3129	267	16	,	,	PUNCT
ejpam-3129	267	17	g	g	PROPN
ejpam-3129	267	18	σ	σ	PROPN
ejpam-3129	267	19	respectively	respectively	ADV
ejpam-3129	267	20	from	from	ADP
ejpam-3129	267	21	(	(	PUNCT
ejpam-3129	267	22	1	1	X
ejpam-3129	267	23	)	)	PUNCT
ejpam-3129	267	24	we	we	PRON
ejpam-3129	267	25	have	have	VERB
ejpam-3129	267	26	π∗	π∗	NOUN
ejpam-3129	267	27	◦	◦	NOUN
ejpam-3129	267	28	σ∗	σ∗	NOUN
ejpam-3129	267	29	=	=	SYM
ejpam-3129	267	30	so	so	SCONJ
ejpam-3129	267	31	◦	◦	VERB
ejpam-3129	267	32	π∗	π∗	NOUN
ejpam-3129	267	33	on	on	ADP
ejpam-3129	267	34	g	g	PROPN
ejpam-3129	267	35	=	=	PROPN
ejpam-3129	267	36	teg	teg	PROPN
ejpam-3129	267	37	.	.	PUNCT
ejpam-3129	268	1	let	let	VERB
ejpam-3129	268	2	t	t	NOUN
ejpam-3129	268	3	=	=	PUNCT
ejpam-3129	269	1	i	i	PRON
ejpam-3129	269	2	−	−	PROPN
ejpam-3129	269	3	σ∗	σ∗	NOUN
ejpam-3129	269	4	,	,	PUNCT
ejpam-3129	269	5	hence	hence	ADV
ejpam-3129	269	6	on	on	ADP
ejpam-3129	269	7	g	g	PROPN
ejpam-3129	269	8	we	we	PRON
ejpam-3129	269	9	have	have	VERB
ejpam-3129	269	10	π∗	π∗	NOUN
ejpam-3129	269	11	◦	◦	PROPN
ejpam-3129	269	12	t	t	PROPN
ejpam-3129	270	1	=	=	SYM
ejpam-3129	270	2	(	(	PUNCT
ejpam-3129	270	3	i	i	PRON
ejpam-3129	270	4	−	−	VERB
ejpam-3129	270	5	so	so	ADV
ejpam-3129	270	6	)	)	PUNCT
ejpam-3129	270	7	◦	◦	NOUN
ejpam-3129	270	8	π∗.	π∗.	NUM
ejpam-3129	270	9	(	(	PUNCT
ejpam-3129	270	10	3	3	X
ejpam-3129	270	11	)	)	PUNCT
ejpam-3129	270	12	consider	consider	VERB
ejpam-3129	270	13	the	the	DET
ejpam-3129	270	14	decomposition	decomposition	NOUN
ejpam-3129	270	15	g	g	PROPN
ejpam-3129	270	16	=	=	PROPN
ejpam-3129	270	17	g0	g0	PROPN
ejpam-3129	270	18	t	t	PROPN
ejpam-3129	270	19	+	+	CCONJ
ejpam-3129	270	20	g1	g1	PROPN
ejpam-3129	270	21	t	t	PROPN
ejpam-3129	270	22	.	.	PUNCT
ejpam-3129	271	1	clearly	clearly	ADV
ejpam-3129	271	2	go	go	VERB
ejpam-3129	271	3	⊆	⊆	NUM
ejpam-3129	271	4	gσ	gσ	NOUN
ejpam-3129	271	5	⊆	⊆	NUM
ejpam-3129	271	6	g0	g0	PROPN
ejpam-3129	271	7	t	t	PROPN
ejpam-3129	271	8	.	.	PUNCT
ejpam-3129	272	1	now	now	ADV
ejpam-3129	272	2	we	we	PRON
ejpam-3129	272	3	show	show	VERB
ejpam-3129	272	4	that	that	PRON
ejpam-3129	272	5	go	go	VERB
ejpam-3129	272	6	=	=	NOUN
ejpam-3129	272	7	gσ	gσ	NOUN
ejpam-3129	272	8	=	=	PUNCT
ejpam-3129	272	9	g0	g0	PROPN
ejpam-3129	272	10	t	t	PROPN
ejpam-3129	272	11	.	.	PUNCT
ejpam-3129	273	1	suppose	suppose	VERB
ejpam-3129	273	2	that	that	SCONJ
ejpam-3129	273	3	there	there	PRON
ejpam-3129	273	4	is	be	VERB
ejpam-3129	273	5	a	a	DET
ejpam-3129	273	6	vector	vector	NOUN
ejpam-3129	273	7	x	x	SYM
ejpam-3129	273	8	∈	∈	PROPN
ejpam-3129	273	9	g0	g0	PROPN
ejpam-3129	273	10	t	t	PROPN
ejpam-3129	273	11	−	−	PROPN
ejpam-3129	273	12	go	go	VERB
ejpam-3129	273	13	.	.	PUNCT
ejpam-3129	274	1	then	then	ADV
ejpam-3129	274	2	x	x	PUNCT
ejpam-3129	274	3	′	′	NOUN
ejpam-3129	274	4	=	=	SYM
ejpam-3129	274	5	π∗(x	π∗(x	NOUN
ejpam-3129	274	6	)	)	PUNCT
ejpam-3129	274	7	is	be	AUX
ejpam-3129	274	8	a	a	DET
ejpam-3129	274	9	non	non	ADJ
ejpam-3129	274	10	-	-	ADJ
ejpam-3129	274	11	zero	zero	NUM
ejpam-3129	274	12	vector	vector	NOUN
ejpam-3129	274	13	of	of	ADP
ejpam-3129	274	14	to(m	to(m	NOUN
ejpam-3129	274	15	)	)	PUNCT
ejpam-3129	274	16	.	.	PUNCT
ejpam-3129	275	1	on	on	ADP
ejpam-3129	275	2	the	the	DET
ejpam-3129	275	3	other	other	ADJ
ejpam-3129	275	4	hand	hand	NOUN
ejpam-3129	275	5	,	,	PUNCT
ejpam-3129	275	6	t	t	PROPN
ejpam-3129	275	7	i(x	i(x	PROPN
ejpam-3129	275	8	)	)	PUNCT
ejpam-3129	276	1	=	=	SYM
ejpam-3129	276	2	0	0	NUM
ejpam-3129	277	1	for	for	ADP
ejpam-3129	277	2	some	some	DET
ejpam-3129	277	3	i	i	PROPN
ejpam-3129	277	4	,	,	PUNCT
ejpam-3129	277	5	and	and	CCONJ
ejpam-3129	277	6	from	from	ADP
ejpam-3129	277	7	(	(	PUNCT
ejpam-3129	277	8	2	2	X
ejpam-3129	277	9	)	)	PUNCT
ejpam-3129	277	10	we	we	PRON
ejpam-3129	277	11	obtain	obtain	VERB
ejpam-3129	277	12	(	(	PUNCT
ejpam-3129	277	13	i	i	PRON
ejpam-3129	277	14	−	−	VERB
ejpam-3129	277	15	so)ix	so)ix	PUNCT
ejpam-3129	278	1	′	′	NUM
ejpam-3129	278	2	=	=	NOUN
ejpam-3129	278	3	0	0	NUM
ejpam-3129	279	1	for	for	ADP
ejpam-3129	279	2	some	some	DET
ejpam-3129	279	3	i.	i.	NOUN
ejpam-3129	279	4	because	because	SCONJ
ejpam-3129	279	5	(	(	PUNCT
ejpam-3129	279	6	i	i	PRON
ejpam-3129	279	7	−	−	PROPN
ejpam-3129	279	8	s0	s0	PROPN
ejpam-3129	279	9	)	)	PUNCT
ejpam-3129	279	10	is	be	AUX
ejpam-3129	279	11	invertible	invertible	ADJ
ejpam-3129	279	12	,	,	PUNCT
ejpam-3129	279	13	we	we	PRON
ejpam-3129	279	14	get	get	VERB
ejpam-3129	279	15	x	x	X
ejpam-3129	279	16	′	′	NUM
ejpam-3129	279	17	=	=	SYM
ejpam-3129	279	18	0	0	NUM
ejpam-3129	279	19	,	,	PUNCT
ejpam-3129	279	20	a	a	DET
ejpam-3129	279	21	contradiction	contradiction	NOUN
ejpam-3129	279	22	.	.	PUNCT
ejpam-3129	280	1	hence	hence	ADV
ejpam-3129	280	2	go	go	VERB
ejpam-3129	280	3	=	=	SYM
ejpam-3129	280	4	gσ	gσ	NOUN
ejpam-3129	280	5	=	=	PUNCT
ejpam-3129	280	6	g0	g0	PROPN
ejpam-3129	280	7	t	t	PROPN
ejpam-3129	280	8	.	.	PUNCT
ejpam-3129	281	1	consequently	consequently	ADV
ejpam-3129	281	2	(	(	PUNCT
ejpam-3129	281	3	g	g	NOUN
ejpam-3129	281	4	,	,	PUNCT
ejpam-3129	281	5	go	go	VERB
ejpam-3129	281	6	,	,	PUNCT
ejpam-3129	281	7	σ	σ	X
ejpam-3129	281	8	)	)	PUNCT
ejpam-3129	281	9	is	be	AUX
ejpam-3129	281	10	a	a	DET
ejpam-3129	281	11	regular	regular	ADJ
ejpam-3129	281	12	homogeneous	homogeneous	ADJ
ejpam-3129	281	13	s−manifold	s−manifold	NOUN
ejpam-3129	281	14	.	.	PUNCT
ejpam-3129	282	1	because	because	SCONJ
ejpam-3129	282	2	g	g	PROPN
ejpam-3129	282	3	∈	∈	PROPN
ejpam-3129	282	4	g	g	PROPN
ejpam-3129	282	5	is	be	AUX
ejpam-3129	282	6	a	a	DET
ejpam-3129	282	7	symmetry	symmetry	NOUN
ejpam-3129	282	8	preserving	preserve	VERB
ejpam-3129	282	9	diffeomorphism	diffeomorphism	NOUN
ejpam-3129	282	10	we	we	PRON
ejpam-3129	282	11	get	get	VERB
ejpam-3129	282	12	sπ(g	sπ(g	PUNCT
ejpam-3129	282	13	)	)	PUNCT
ejpam-3129	282	14	=	=	PUNCT
ejpam-3129	282	15	sg(o	sg(o	X
ejpam-3129	282	16	)	)	PUNCT
ejpam-3129	282	17	=	=	SYM
ejpam-3129	283	1	g	g	PROPN
ejpam-3129	283	2	◦	◦	NOUN
ejpam-3129	283	3	so	so	ADV
ejpam-3129	283	4	◦	◦	VERB
ejpam-3129	283	5	g−1	g−1	PROPN
ejpam-3129	283	6	�	�	PROPN
ejpam-3129	283	7	references	reference	NOUN
ejpam-3129	283	8	[	[	X
ejpam-3129	283	9	1	1	NUM
ejpam-3129	283	10	]	]	PUNCT
ejpam-3129	283	11	d.	d.	PROPN
ejpam-3129	283	12	bao	bao	PROPN
ejpam-3129	283	13	,	,	PUNCT
ejpam-3129	283	14	s.	s.	PROPN
ejpam-3129	283	15	s.	s.	PROPN
ejpam-3129	283	16	chern	chern	PROPN
ejpam-3129	283	17	and	and	CCONJ
ejpam-3129	283	18	shen	shen	PROPN
ejpam-3129	283	19	,	,	PUNCT
ejpam-3129	283	20	an	an	DET
ejpam-3129	283	21	introduction	introduction	NOUN
ejpam-3129	283	22	to	to	ADP
ejpam-3129	283	23	riemann	riemann	PROPN
ejpam-3129	283	24	-	-	PUNCT
ejpam-3129	283	25	finsler	finsler	NOUN
ejpam-3129	283	26	geometry	geometry	NOUN
ejpam-3129	283	27	,	,	PUNCT
ejpam-3129	283	28	springer	springer	NOUN
ejpam-3129	283	29	-	-	PUNCT
ejpam-3129	283	30	verlag	verlag	PROPN
ejpam-3129	283	31	,	,	PUNCT
ejpam-3129	283	32	new	new	ADJ
ejpam-3129	283	33	-	-	PUNCT
ejpam-3129	283	34	york	york	NOUN
ejpam-3129	283	35	.	.	PUNCT
ejpam-3129	283	36	2000	2000	NUM
ejpam-3129	283	37	.	.	PUNCT
ejpam-3129	284	1	[	[	X
ejpam-3129	284	2	2	2	X
ejpam-3129	284	3	]	]	PUNCT
ejpam-3129	284	4	s.	s.	PROPN
ejpam-3129	284	5	deng	deng	PROPN
ejpam-3129	284	6	and	and	CCONJ
ejpam-3129	284	7	z.	z.	PROPN
ejpam-3129	284	8	hou	hou	PROPN
ejpam-3129	284	9	,	,	PUNCT
ejpam-3129	284	10	the	the	DET
ejpam-3129	284	11	group	group	NOUN
ejpam-3129	284	12	of	of	ADP
ejpam-3129	284	13	isometries	isometry	NOUN
ejpam-3129	284	14	of	of	ADP
ejpam-3129	284	15	a	a	DET
ejpam-3129	284	16	finsler	finsler	NOUN
ejpam-3129	284	17	space	space	NOUN
ejpam-3129	284	18	,	,	PUNCT
ejpam-3129	284	19	pacific	pacific	PROPN
ejpam-3129	284	20	.	.	PUNCT
ejpam-3129	285	1	j.	j.	PROPN
ejpam-3129	285	2	math	math	PROPN
ejpam-3129	285	3	.	.	PUNCT
ejpam-3129	286	1	207(1	207(1	NUM
ejpam-3129	286	2	)	)	PUNCT
ejpam-3129	286	3	(	(	PUNCT
ejpam-3129	286	4	2002	2002	NUM
ejpam-3129	286	5	)	)	PUNCT
ejpam-3129	286	6	149	149	NUM
ejpam-3129	286	7	-	-	SYM
ejpam-3129	286	8	155	155	NUM
ejpam-3129	286	9	.	.	PUNCT
ejpam-3129	287	1	references	reference	NOUN
ejpam-3129	287	2	1110	1110	NUM
ejpam-3129	287	3	[	[	X
ejpam-3129	287	4	3	3	NUM
ejpam-3129	287	5	]	]	PUNCT
ejpam-3129	287	6	s.	s.	PROPN
ejpam-3129	287	7	deng	deng	PROPN
ejpam-3129	287	8	,	,	PUNCT
ejpam-3129	287	9	z.	z.	PROPN
ejpam-3129	287	10	hou	hou	PROPN
ejpam-3129	287	11	,	,	PUNCT
ejpam-3129	287	12	invariant	invariant	ADJ
ejpam-3129	287	13	randers	rander	NOUN
ejpam-3129	287	14	metrics	metric	NOUN
ejpam-3129	287	15	on	on	ADP
ejpam-3129	287	16	homogeneous	homogeneous	ADJ
ejpam-3129	287	17	riemannian	riemannian	ADJ
ejpam-3129	287	18	manifolds	manifold	NOUN
ejpam-3129	287	19	,	,	PUNCT
ejpam-3129	287	20	j.	j.	PROPN
ejpam-3129	287	21	phys	phys	PROPN
ejpam-3129	287	22	.	.	PUNCT
ejpam-3129	288	1	a	a	DET
ejpam-3129	288	2	:	:	PUNCT
ejpam-3129	288	3	math	math	NOUN
ejpam-3129	288	4	.	.	PUNCT
ejpam-3129	289	1	gen	gen	PROPN
ejpam-3129	289	2	.	.	PROPN
ejpam-3129	289	3	37	37	NUM
ejpam-3129	289	4	(	(	PUNCT
ejpam-3129	289	5	2004	2004	NUM
ejpam-3129	289	6	)	)	PUNCT
ejpam-3129	289	7	4353	4353	NUM
ejpam-3129	289	8	-	-	SYM
ejpam-3129	289	9	4360	4360	NUM
ejpam-3129	289	10	.	.	PUNCT
ejpam-3129	290	1	corrigendum	corrigendum	PROPN
ejpam-3129	290	2	,	,	PUNCT
ejpam-3129	290	3	j.	j.	PROPN
ejpam-3129	290	4	phy	phy	PROPN
ejpam-3129	290	5	.	.	PUNCT
ejpam-3129	291	1	a	a	DET
ejpam-3129	291	2	:	:	PUNCT
ejpam-3129	291	3	math	math	NOUN
ejpam-3129	291	4	.	.	PUNCT
ejpam-3129	292	1	gen	gen	PROPN
ejpam-3129	292	2	.	.	PROPN
ejpam-3129	292	3	39	39	NUM
ejpam-3129	292	4	(	(	PUNCT
ejpam-3129	292	5	2006	2006	NUM
ejpam-3129	292	6	)	)	PUNCT
ejpam-3129	292	7	5249	5249	NUM
ejpam-3129	292	8	-	-	SYM
ejpam-3129	292	9	5250	5250	NUM
ejpam-3129	292	10	.	.	PUNCT
ejpam-3129	293	1	[	[	X
ejpam-3129	293	2	4	4	X
ejpam-3129	293	3	]	]	PUNCT
ejpam-3129	293	4	s.	s.	PROPN
ejpam-3129	293	5	deng	deng	PROPN
ejpam-3129	293	6	,	,	PUNCT
ejpam-3129	293	7	z.	z.	PROPN
ejpam-3129	293	8	hou	hou	PROPN
ejpam-3129	293	9	,	,	PUNCT
ejpam-3129	293	10	invariant	invariant	ADJ
ejpam-3129	293	11	finsler	finsler	NOUN
ejpam-3129	293	12	metrics	metric	NOUN
ejpam-3129	293	13	on	on	ADP
ejpam-3129	293	14	homogeneous	homogeneous	ADJ
ejpam-3129	293	15	manifolds	manifold	NOUN
ejpam-3129	293	16	,	,	PUNCT
ejpam-3129	293	17	j.	j.	PROPN
ejpam-3129	293	18	phy	phy	PROPN
ejpam-3129	293	19	.	.	PUNCT
ejpam-3129	294	1	a	a	DET
ejpam-3129	294	2	:	:	PUNCT
ejpam-3129	294	3	math	math	NOUN
ejpam-3129	294	4	.	.	PUNCT
ejpam-3129	295	1	gen	gen	PROPN
ejpam-3129	295	2	.	.	PROPN
ejpam-3129	295	3	37	37	NUM
ejpam-3129	295	4	(	(	PUNCT
ejpam-3129	295	5	2004	2004	NUM
ejpam-3129	295	6	)	)	PUNCT
ejpam-3129	295	7	8245	8245	NUM
ejpam-3129	295	8	-	-	SYM
ejpam-3129	295	9	8253	8253	NUM
ejpam-3129	295	10	.	.	PUNCT
ejpam-3129	296	1	[	[	X
ejpam-3129	296	2	5	5	X
ejpam-3129	296	3	]	]	PUNCT
ejpam-3129	296	4	s.	s.	PROPN
ejpam-3129	296	5	deng	deng	PROPN
ejpam-3129	296	6	,	,	PUNCT
ejpam-3129	296	7	homogeneous	homogeneous	ADJ
ejpam-3129	296	8	finsler	finsler	NOUN
ejpam-3129	296	9	spaces	space	NOUN
ejpam-3129	296	10	,	,	PUNCT
ejpam-3129	296	11	springer	springer	NOUN
ejpam-3129	296	12	,	,	PUNCT
ejpam-3129	296	13	new	new	ADJ
ejpam-3129	296	14	-	-	PUNCT
ejpam-3129	296	15	york	york	NOUN
ejpam-3129	296	16	,	,	PUNCT
ejpam-3129	296	17	2012	2012	NUM
ejpam-3129	296	18	.	.	PUNCT
ejpam-3129	297	1	[	[	X
ejpam-3129	297	2	6	6	NUM
ejpam-3129	297	3	]	]	PUNCT
ejpam-3129	297	4	s.	s.	PROPN
ejpam-3129	297	5	deng	deng	PROPN
ejpam-3129	297	6	and	and	CCONJ
ejpam-3129	297	7	z.	z.	PROPN
ejpam-3129	297	8	hou	hou	PROPN
ejpam-3129	297	9	,	,	PUNCT
ejpam-3129	297	10	on	on	ADP
ejpam-3129	297	11	symmetric	symmetric	ADJ
ejpam-3129	297	12	finsler	finsler	NOUN
ejpam-3129	297	13	spaces	space	NOUN
ejpam-3129	297	14	.	.	PUNCT
ejpam-3129	298	1	israel	israel	PROPN
ejpam-3129	298	2	j.	j.	PROPN
ejpam-3129	298	3	math	math	PROPN
ejpam-3129	298	4	.	.	PUNCT
ejpam-3129	299	1	162	162	NUM
ejpam-3129	299	2	(	(	PUNCT
ejpam-3129	299	3	2007	2007	NUM
ejpam-3129	299	4	)	)	PUNCT
ejpam-3129	299	5	197	197	NUM
ejpam-3129	299	6	-	-	SYM
ejpam-3129	299	7	219	219	NUM
ejpam-3129	299	8	.	.	PUNCT
ejpam-3129	300	1	[	[	X
ejpam-3129	300	2	7	7	X
ejpam-3129	300	3	]	]	X
ejpam-3129	300	4	p.	p.	NOUN
ejpam-3129	300	5	habibi	habibi	PROPN
ejpam-3129	300	6	,	,	PUNCT
ejpam-3129	300	7	a.	a.	PROPN
ejpam-3129	300	8	razavi	razavi	PROPN
ejpam-3129	300	9	,	,	PUNCT
ejpam-3129	300	10	on	on	ADP
ejpam-3129	300	11	generalized	generalized	ADJ
ejpam-3129	300	12	symmetric	symmetric	ADJ
ejpam-3129	300	13	finsler	finsler	NOUN
ejpam-3129	300	14	spaces	space	NOUN
ejpam-3129	300	15	,	,	PUNCT
ejpam-3129	300	16	geom	geom	NOUN
ejpam-3129	300	17	.	.	PUNCT
ejpam-3129	300	18	dedicata,149	dedicata,149	PROPN
ejpam-3129	300	19	(	(	PUNCT
ejpam-3129	300	20	2010	2010	NUM
ejpam-3129	300	21	)	)	PUNCT
ejpam-3129	300	22	121	121	NUM
ejpam-3129	300	23	-	-	SYM
ejpam-3129	300	24	127	127	NUM
ejpam-3129	300	25	[	[	X
ejpam-3129	300	26	8	8	NUM
ejpam-3129	300	27	]	]	PUNCT
ejpam-3129	300	28	s.	s.	PROPN
ejpam-3129	300	29	helgason	helgason	PROPN
ejpam-3129	300	30	,	,	PUNCT
ejpam-3129	300	31	differential	differential	ADJ
ejpam-3129	300	32	geometry	geometry	NOUN
ejpam-3129	300	33	,	,	PUNCT
ejpam-3129	300	34	lie	lie	NOUN
ejpam-3129	300	35	groups	group	NOUN
ejpam-3129	300	36	and	and	CCONJ
ejpam-3129	300	37	symmetric	symmetric	ADJ
ejpam-3129	300	38	space	space	NOUN
ejpam-3129	300	39	,	,	PUNCT
ejpam-3129	300	40	academic	academic	ADJ
ejpam-3129	300	41	press	press	NOUN
ejpam-3129	300	42	,	,	PUNCT
ejpam-3129	300	43	new	new	PROPN
ejpam-3129	300	44	york	york	PROPN
ejpam-3129	300	45	1978	1978	NUM
ejpam-3129	300	46	.	.	PUNCT
ejpam-3129	301	1	[	[	X
ejpam-3129	301	2	9	9	NUM
ejpam-3129	301	3	]	]	PUNCT
ejpam-3129	301	4	c.	c.	PROPN
ejpam-3129	301	5	w.	w.	PROPN
ejpam-3129	301	6	kim	kim	PROPN
ejpam-3129	301	7	,	,	PUNCT
ejpam-3129	301	8	locally	locally	ADV
ejpam-3129	301	9	symmetric	symmetric	ADJ
ejpam-3129	301	10	positively	positively	ADV
ejpam-3129	301	11	curved	curve	VERB
ejpam-3129	301	12	finsler	finsler	NOUN
ejpam-3129	301	13	spaces	space	NOUN
ejpam-3129	301	14	,	,	PUNCT
ejpam-3129	301	15	arch	arch	NOUN
ejpam-3129	301	16	.	.	PUNCT
ejpam-3129	302	1	math	math	NOUN
ejpam-3129	302	2	.	.	PUNCT
ejpam-3129	303	1	88	88	NUM
ejpam-3129	303	2	(	(	PUNCT
ejpam-3129	303	3	2007	2007	NUM
ejpam-3129	303	4	)	)	PUNCT
ejpam-3129	303	5	376	376	NUM
ejpam-3129	303	6	-	-	SYM
ejpam-3129	303	7	384	384	NUM
ejpam-3129	303	8	.	.	PUNCT
ejpam-3129	304	1	[	[	X
ejpam-3129	304	2	10	10	NUM
ejpam-3129	304	3	]	]	PUNCT
ejpam-3129	304	4	s.	s.	PROPN
ejpam-3129	304	5	kobayashi	kobayashi	PROPN
ejpam-3129	304	6	,	,	PUNCT
ejpam-3129	304	7	k.	k.	PROPN
ejpam-3129	304	8	nomizu	nomizu	PROPN
ejpam-3129	304	9	,	,	PUNCT
ejpam-3129	304	10	foundation	foundation	NOUN
ejpam-3129	304	11	of	of	ADP
ejpam-3129	304	12	differential	differential	PROPN
ejpam-3129	304	13	geometry	geometry	PROPN
ejpam-3129	304	14	i.	i.	PROPN
ejpam-3129	304	15	ii	ii	PROPN
ejpam-3129	304	16	.	.	PROPN
ejpam-3129	304	17	,	,	PUNCT
ejpam-3129	304	18	john	john	PROPN
ejpam-3129	304	19	wily	wily	PROPN
ejpam-3129	304	20	and	and	CCONJ
ejpam-3129	304	21	sons	son	NOUN
ejpam-3129	304	22	(	(	PUNCT
ejpam-3129	304	23	1963)(1969	1963)(1969	NUM
ejpam-3129	304	24	)	)	PUNCT
ejpam-3129	304	25	.	.	PUNCT
ejpam-3129	305	1	[	[	X
ejpam-3129	305	2	11	11	NUM
ejpam-3129	305	3	]	]	X
ejpam-3129	305	4	o.	o.	PROPN
ejpam-3129	305	5	kowalski	kowalski	PROPN
ejpam-3129	305	6	,	,	PUNCT
ejpam-3129	305	7	generalized	generalize	VERB
ejpam-3129	305	8	symmetric	symmetric	ADJ
ejpam-3129	305	9	spaces	space	NOUN
ejpam-3129	305	10	,	,	PUNCT
ejpam-3129	305	11	lecture	lecture	NOUN
ejpam-3129	305	12	notes	note	NOUN
ejpam-3129	305	13	in	in	ADP
ejpam-3129	305	14	mathematics	mathematic	NOUN
ejpam-3129	305	15	.	.	PUNCT
ejpam-3129	306	1	springer	springer	PROPN
ejpam-3129	306	2	verlag	verlag	PROPN
ejpam-3129	306	3	1980	1980	NUM
ejpam-3129	306	4	.	.	PUNCT
ejpam-3129	307	1	[	[	X
ejpam-3129	307	2	12	12	NUM
ejpam-3129	307	3	]	]	X
ejpam-3129	307	4	d.	d.	PROPN
ejpam-3129	307	5	latifi	latifi	PROPN
ejpam-3129	307	6	and	and	CCONJ
ejpam-3129	307	7	a.	a.	NOUN
ejpam-3129	307	8	razavi	razavi	PROPN
ejpam-3129	307	9	,	,	PUNCT
ejpam-3129	307	10	on	on	ADP
ejpam-3129	307	11	homogeneous	homogeneous	ADJ
ejpam-3129	307	12	finsler	finsler	NOUN
ejpam-3129	307	13	spaces	space	NOUN
ejpam-3129	307	14	,	,	PUNCT
ejpam-3129	307	15	rep	rep	PROPN
ejpam-3129	307	16	.	.	PROPN
ejpam-3129	307	17	math	math	NOUN
ejpam-3129	307	18	.	.	PUNCT
ejpam-3129	308	1	phys	phy	NOUN
ejpam-3129	308	2	,	,	PUNCT
ejpam-3129	308	3	57	57	NUM
ejpam-3129	308	4	(	(	PUNCT
ejpam-3129	308	5	2006	2006	NUM
ejpam-3129	308	6	)	)	PUNCT
ejpam-3129	308	7	357	357	NUM
ejpam-3129	308	8	-	-	SYM
ejpam-3129	308	9	366	366	NUM
ejpam-3129	308	10	.	.	PUNCT
ejpam-3129	309	1	erratum	erratum	PROPN
ejpam-3129	309	2	:	:	PUNCT
ejpam-3129	309	3	rep	rep	PROPN
ejpam-3129	309	4	.	.	PROPN
ejpam-3129	309	5	math	math	NOUN
ejpam-3129	309	6	.	.	PUNCT
ejpam-3129	310	1	phys	phy	NOUN
ejpam-3129	310	2	.	.	PUNCT
ejpam-3129	311	1	60(2007	60(2007	NUM
ejpam-3129	311	2	)	)	PUNCT
ejpam-3129	311	3	347	347	NUM
ejpam-3129	311	4	.	.	PUNCT
ejpam-3129	312	1	[	[	X
ejpam-3129	312	2	13	13	NUM
ejpam-3129	312	3	]	]	X
ejpam-3129	312	4	d.	d.	PROPN
ejpam-3129	312	5	latifi	latifi	PROPN
ejpam-3129	312	6	,	,	PUNCT
ejpam-3129	312	7	homogeneous	homogeneous	ADJ
ejpam-3129	312	8	geodesics	geodesic	NOUN
ejpam-3129	312	9	in	in	ADP
ejpam-3129	312	10	homogeneous	homogeneous	ADJ
ejpam-3129	312	11	finsler	finsler	NOUN
ejpam-3129	312	12	spaces	space	NOUN
ejpam-3129	312	13	,	,	PUNCT
ejpam-3129	312	14	j.	j.	PROPN
ejpam-3129	312	15	geom	geom	PROPN
ejpam-3129	312	16	.	.	PUNCT
ejpam-3129	313	1	phys	phy	NOUN
ejpam-3129	313	2	.	.	PUNCT
ejpam-3129	314	1	57	57	NUM
ejpam-3129	314	2	(	(	PUNCT
ejpam-3129	314	3	2007	2007	NUM
ejpam-3129	314	4	)	)	PUNCT
ejpam-3129	314	5	1421	1421	NUM
ejpam-3129	314	6	-	-	SYM
ejpam-3129	314	7	1433	1433	NUM
ejpam-3129	314	8	.	.	PUNCT
ejpam-3129	315	1	[	[	X
ejpam-3129	315	2	14	14	NUM
ejpam-3129	315	3	]	]	X
ejpam-3129	315	4	d.	d.	PROPN
ejpam-3129	315	5	latifi	latifi	PROPN
ejpam-3129	315	6	,	,	PUNCT
ejpam-3129	315	7	naturally	naturally	ADV
ejpam-3129	315	8	reductive	reductive	ADJ
ejpam-3129	315	9	homogeneous	homogeneous	ADJ
ejpam-3129	315	10	randers	rander	NOUN
ejpam-3129	315	11	spaces	space	NOUN
ejpam-3129	315	12	,	,	PUNCT
ejpam-3129	315	13	j.	j.	PROPN
ejpam-3129	315	14	geom	geom	PROPN
ejpam-3129	315	15	.	.	PUNCT
ejpam-3129	316	1	phys	phy	NOUN
ejpam-3129	316	2	.	.	PUNCT
ejpam-3129	317	1	60	60	NUM
ejpam-3129	317	2	(	(	PUNCT
ejpam-3129	317	3	2010	2010	NUM
ejpam-3129	317	4	)	)	PUNCT
ejpam-3129	317	5	1968	1968	NUM
ejpam-3129	317	6	-	-	SYM
ejpam-3129	317	7	1973	1973	NUM
ejpam-3129	317	8	.	.	PUNCT
ejpam-3129	318	1	[	[	X
ejpam-3129	318	2	15	15	NUM
ejpam-3129	318	3	]	]	X
ejpam-3129	318	4	d.	d.	PROPN
ejpam-3129	318	5	latifi	latifi	PROPN
ejpam-3129	318	6	and	and	CCONJ
ejpam-3129	318	7	m.	m.	NOUN
ejpam-3129	318	8	toomanian	toomanian	NOUN
ejpam-3129	318	9	,	,	PUNCT
ejpam-3129	318	10	on	on	ADP
ejpam-3129	318	11	finsler	finsler	NOUN
ejpam-3129	318	12	σ−spaces	σ−space	NOUN
ejpam-3129	318	13	,	,	PUNCT
ejpam-3129	318	14	j.	j.	PROPN
ejpam-3129	318	15	contemp	contemp	PROPN
ejpam-3129	318	16	.	.	PUNCT
ejpam-3129	319	1	math	math	NOUN
ejpam-3129	319	2	.	.	PUNCT
ejpam-3129	320	1	anal	anal	ADJ
ejpam-3129	320	2	.	.	PUNCT
ejpam-3129	321	1	50	50	NUM
ejpam-3129	321	2	(	(	PUNCT
ejpam-3129	321	3	2015	2015	NUM
ejpam-3129	321	4	)	)	PUNCT
ejpam-3129	321	5	107	107	NUM
ejpam-3129	321	6	-	-	SYM
ejpam-3129	321	7	115	115	NUM
ejpam-3129	321	8	.	.	PUNCT
ejpam-3129	322	1	[	[	X
ejpam-3129	322	2	16	16	NUM
ejpam-3129	322	3	]	]	X
ejpam-3129	322	4	d.	d.	PROPN
ejpam-3129	322	5	latifi	latifi	PROPN
ejpam-3129	322	6	,	,	PUNCT
ejpam-3129	322	7	berwald	berwald	NOUN
ejpam-3129	322	8	manifolds	manifold	NOUN
ejpam-3129	322	9	with	with	ADP
ejpam-3129	322	10	parallel	parallel	ADJ
ejpam-3129	322	11	s−structures	s−structure	NOUN
ejpam-3129	322	12	,	,	PUNCT
ejpam-3129	322	13	acta	acta	PROPN
ejpam-3129	322	14	universitatis	universitatis	PROPN
ejpam-3129	322	15	apulensis	apulensis	NOUN
ejpam-3129	322	16	,	,	PUNCT
ejpam-3129	322	17	36	36	NUM
ejpam-3129	322	18	(	(	PUNCT
ejpam-3129	322	19	2013	2013	NUM
ejpam-3129	322	20	)	)	PUNCT
ejpam-3129	322	21	79	79	NUM
ejpam-3129	322	22	-	-	SYM
ejpam-3129	322	23	86	86	NUM
ejpam-3129	322	24	.	.	PUNCT
ejpam-3129	323	1	[	[	X
ejpam-3129	323	2	17	17	NUM
ejpam-3129	323	3	]	]	X
ejpam-3129	323	4	d.	d.	PROPN
ejpam-3129	323	5	latifi	latifi	PROPN
ejpam-3129	323	6	and	and	CCONJ
ejpam-3129	323	7	a.	a.	PROPN
ejpam-3129	323	8	razavi	razavi	PROPN
ejpam-3129	323	9	,	,	PUNCT
ejpam-3129	323	10	bi	bi	ADJ
ejpam-3129	323	11	-	-	ADJ
ejpam-3129	323	12	invariant	invariant	ADJ
ejpam-3129	323	13	finsler	finsler	NOUN
ejpam-3129	323	14	metrics	metric	NOUN
ejpam-3129	323	15	on	on	ADP
ejpam-3129	323	16	lie	lie	NOUN
ejpam-3129	323	17	groups	group	NOUN
ejpam-3129	323	18	,	,	PUNCT
ejpam-3129	323	19	australian	australian	ADJ
ejpam-3129	323	20	journal	journal	NOUN
ejpam-3129	323	21	of	of	ADP
ejpam-3129	323	22	basic	basic	ADJ
ejpam-3129	323	23	and	and	CCONJ
ejpam-3129	323	24	applied	applied	ADJ
ejpam-3129	323	25	sciences	science	NOUN
ejpam-3129	323	26	,	,	PUNCT
ejpam-3129	323	27	5	5	NUM
ejpam-3129	323	28	(	(	PUNCT
ejpam-3129	323	29	12	12	NUM
ejpam-3129	323	30	)	)	PUNCT
ejpam-3129	323	31	(	(	PUNCT
ejpam-3129	323	32	2011	2011	NUM
ejpam-3129	323	33	)	)	PUNCT
ejpam-3129	323	34	507	507	NUM
ejpam-3129	323	35	-	-	SYM
ejpam-3129	323	36	511	511	NUM
ejpam-3129	323	37	.	.	PUNCT
ejpam-3129	324	1	[	[	X
ejpam-3129	324	2	18	18	NUM
ejpam-3129	324	3	]	]	PUNCT
ejpam-3129	324	4	a.	a.	NOUN
ejpam-3129	324	5	j.	j.	PROPN
ejpam-3129	324	6	ledger	ledger	PROPN
ejpam-3129	324	7	,	,	PUNCT
ejpam-3129	324	8	m.	m.	NOUN
ejpam-3129	324	9	obata	obata	NOUN
ejpam-3129	324	10	,	,	PUNCT
ejpam-3129	324	11	affine	affine	NOUN
ejpam-3129	324	12	and	and	CCONJ
ejpam-3129	324	13	riemannian	riemannian	ADJ
ejpam-3129	324	14	s	s	NOUN
ejpam-3129	324	15	-	-	PUNCT
ejpam-3129	324	16	manifolds	manifold	NOUN
ejpam-3129	324	17	,	,	PUNCT
ejpam-3129	324	18	j.	j.	PROPN
ejpam-3129	324	19	differential	differential	PROPN
ejpam-3129	324	20	geometry	geometry	PROPN
ejpam-3129	324	21	2(1968	2(1968	NUM
ejpam-3129	324	22	)	)	PUNCT
ejpam-3129	324	23	451	451	NUM
ejpam-3129	324	24	-	-	SYM
ejpam-3129	324	25	459	459	NUM
ejpam-3129	324	26	.	.	PUNCT
ejpam-3129	325	1	[	[	X
ejpam-3129	325	2	19	19	NUM
ejpam-3129	325	3	]	]	PUNCT
ejpam-3129	325	4	a.	a.	NOUN
ejpam-3129	325	5	j.	j.	PROPN
ejpam-3129	325	6	ledger	ledger	PROPN
ejpam-3129	325	7	,	,	PUNCT
ejpam-3129	325	8	espaces	espaces	PROPN
ejpam-3129	325	9	de	de	PROPN
ejpam-3129	325	10	riemann	riemann	PROPN
ejpam-3129	325	11	symetriques	symetriques	PROPN
ejpam-3129	325	12	generalises	generalise	VERB
ejpam-3129	325	13	,	,	PUNCT
ejpam-3129	325	14	c.	c.	PROPN
ejpam-3129	325	15	r.	r.	PROPN
ejpam-3129	325	16	acad	acad	PROPN
ejpam-3129	325	17	.	.	PUNCT
ejpam-3129	326	1	sc	sc	PROPN
ejpam-3129	326	2	.	.	PROPN
ejpam-3129	326	3	paris	paris	PROPN
ejpam-3129	326	4	,	,	PUNCT
ejpam-3129	326	5	264(1967	264(1967	NUM
ejpam-3129	326	6	)	)	PUNCT
ejpam-3129	326	7	947	947	NUM
ejpam-3129	326	8	-	-	SYM
ejpam-3129	326	9	948	948	NUM
ejpam-3129	326	10	.	.	PUNCT
ejpam-3129	326	11	references	reference	NOUN
ejpam-3129	326	12	1111	1111	NUM
ejpam-3129	327	1	[	[	X
ejpam-3129	327	2	20	20	NUM
ejpam-3129	327	3	]	]	X
ejpam-3129	327	4	o.	o.	NOUN
ejpam-3129	327	5	loos	loo	NOUN
ejpam-3129	327	6	,	,	PUNCT
ejpam-3129	327	7	symmetric	symmetric	ADJ
ejpam-3129	327	8	spaces	space	NOUN
ejpam-3129	327	9	i	i	PRON
ejpam-3129	327	10	,	,	PUNCT
ejpam-3129	327	11	general	general	ADJ
ejpam-3129	327	12	theory	theory	NOUN
ejpam-3129	327	13	,	,	PUNCT
ejpam-3129	327	14	benjamin	benjamin	PROPN
ejpam-3129	327	15	,	,	PUNCT
ejpam-3129	327	16	new	new	PROPN
ejpam-3129	327	17	york	york	PROPN
ejpam-3129	327	18	1969	1969	NUM
ejpam-3129	327	19	.	.	PUNCT
ejpam-3129	328	1	[	[	X
ejpam-3129	328	2	21	21	NUM
ejpam-3129	328	3	]	]	PUNCT
ejpam-3129	328	4	a.	a.	NOUN
ejpam-3129	328	5	j.	j.	PROPN
ejpam-3129	328	6	ledger	ledger	PROPN
ejpam-3129	328	7	,	,	PUNCT
ejpam-3129	328	8	a.	a.	PROPN
ejpam-3129	328	9	r.	r.	PROPN
ejpam-3129	328	10	razavi	razavi	PROPN
ejpam-3129	328	11	,	,	PUNCT
ejpam-3129	328	12	reduced	reduce	VERB
ejpam-3129	328	13	σ−spaces	σ−space	NOUN
ejpam-3129	328	14	,	,	PUNCT
ejpam-3129	328	15	illinois	illinois	PROPN
ejpam-3129	328	16	j.	j.	PROPN
ejpam-3129	328	17	math	math	PROPN
ejpam-3129	328	18	.	.	PUNCT
ejpam-3129	329	1	26	26	NUM
ejpam-3129	329	2	(	(	PUNCT
ejpam-3129	329	3	1982	1982	NUM
ejpam-3129	329	4	)	)	PUNCT
ejpam-3129	329	5	272	272	NUM
ejpam-3129	329	6	-	-	SYM
ejpam-3129	329	7	292	292	NUM
ejpam-3129	329	8	.	.	PUNCT
ejpam-3129	330	1	[	[	X
ejpam-3129	330	2	22	22	NUM
ejpam-3129	330	3	]	]	PUNCT
ejpam-3129	330	4	z.	z.	PROPN
ejpam-3129	330	5	i.	i.	PROPN
ejpam-3129	330	6	szabó	szabó	PROPN
ejpam-3129	330	7	,	,	PUNCT
ejpam-3129	330	8	generalized	generalized	ADJ
ejpam-3129	330	9	spaces	space	NOUN
ejpam-3129	330	10	with	with	ADP
ejpam-3129	330	11	many	many	ADJ
ejpam-3129	330	12	isometries	isometry	NOUN
ejpam-3129	330	13	,	,	PUNCT
ejpam-3129	330	14	geom	geom	PROPN
ejpam-3129	330	15	.	.	PUNCT
ejpam-3129	330	16	dedicata	dedicata	PROPN
ejpam-3129	330	17	,	,	PUNCT
ejpam-3129	330	18	11	11	NUM
ejpam-3129	330	19	(	(	PUNCT
ejpam-3129	330	20	1981	1981	NUM
ejpam-3129	330	21	)	)	PUNCT
ejpam-3129	330	22	369	369	NUM
ejpam-3129	330	23	-	-	SYM
ejpam-3129	330	24	383	383	NUM
ejpam-3129	330	25	.	.	PUNCT