id	sid	tid	token	lemma	pos
ejpam-3279	1	1	european	european	PROPN
ejpam-3279	1	2	journal	journal	PROPN
ejpam-3279	1	3	of	of	ADP
ejpam-3279	1	4	pure	pure	ADJ
ejpam-3279	1	5	and	and	CCONJ
ejpam-3279	1	6	applied	apply	VERB
ejpam-3279	1	7	mathematics	mathematic	NOUN
ejpam-3279	1	8	vol	vol	NOUN
ejpam-3279	1	9	.	.	PUNCT
ejpam-3279	2	1	11	11	NUM
ejpam-3279	2	2	,	,	PUNCT
ejpam-3279	2	3	no	no	INTJ
ejpam-3279	2	4	.	.	NOUN
ejpam-3279	2	5	3	3	NUM
ejpam-3279	2	6	,	,	PUNCT
ejpam-3279	2	7	2018	2018	NUM
ejpam-3279	2	8	,	,	PUNCT
ejpam-3279	2	9	823	823	NUM
ejpam-3279	2	10	-	-	SYM
ejpam-3279	2	11	833	833	NUM
ejpam-3279	2	12	issn	issn	PROPN
ejpam-3279	2	13	1307	1307	NUM
ejpam-3279	2	14	-	-	SYM
ejpam-3279	2	15	5543	5543	NUM
ejpam-3279	2	16	–	–	PUNCT
ejpam-3279	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3279	2	18	published	publish	VERB
ejpam-3279	2	19	by	by	ADP
ejpam-3279	2	20	new	new	PROPN
ejpam-3279	2	21	york	york	PROPN
ejpam-3279	2	22	business	business	PROPN
ejpam-3279	2	23	global	global	PROPN
ejpam-3279	2	24	some	some	DET
ejpam-3279	2	25	results	result	NOUN
ejpam-3279	2	26	on	on	ADP
ejpam-3279	2	27	projective	projective	ADJ
ejpam-3279	2	28	curvature	curvature	NOUN
ejpam-3279	2	29	tensor	tensor	NOUN
ejpam-3279	2	30	of	of	ADP
ejpam-3279	2	31	nearly	nearly	ADV
ejpam-3279	2	32	cosymplectic	cosymplectic	ADJ
ejpam-3279	2	33	manifold	manifold	ADJ
ejpam-3279	2	34	nawaf	nawaf	PROPN
ejpam-3279	2	35	jaber	jaber	PROPN
ejpam-3279	2	36	mohammed1	mohammed1	PROPN
ejpam-3279	2	37	,	,	PUNCT
ejpam-3279	2	38	habeeb	habeeb	PROPN
ejpam-3279	2	39	mtashar	mtashar	VERB
ejpam-3279	2	40	abood2,∗	abood2,∗	PROPN
ejpam-3279	2	41	1,2	1,2	NUM
ejpam-3279	2	42	department	department	NOUN
ejpam-3279	2	43	of	of	ADP
ejpam-3279	2	44	mathematics	mathematic	NOUN
ejpam-3279	2	45	,	,	PUNCT
ejpam-3279	2	46	faculty	faculty	NOUN
ejpam-3279	2	47	of	of	ADP
ejpam-3279	2	48	education	education	NOUN
ejpam-3279	2	49	for	for	ADP
ejpam-3279	2	50	pure	pure	ADJ
ejpam-3279	2	51	sciences	science	NOUN
ejpam-3279	2	52	,	,	PUNCT
ejpam-3279	2	53	university	university	NOUN
ejpam-3279	2	54	of	of	ADP
ejpam-3279	2	55	basra	basra	PROPN
ejpam-3279	2	56	,	,	PUNCT
ejpam-3279	2	57	basra	basra	PROPN
ejpam-3279	2	58	,	,	PUNCT
ejpam-3279	2	59	iraq	iraq	PROPN
ejpam-3279	2	60	abstract	abstract	NOUN
ejpam-3279	2	61	.	.	PUNCT
ejpam-3279	3	1	in	in	ADP
ejpam-3279	3	2	the	the	DET
ejpam-3279	3	3	nearly	nearly	ADV
ejpam-3279	3	4	cosymplectic	cosymplectic	ADJ
ejpam-3279	3	5	manifold	manifold	ADJ
ejpam-3279	3	6	,	,	PUNCT
ejpam-3279	3	7	defined	define	VERB
ejpam-3279	3	8	a	a	DET
ejpam-3279	3	9	tensor	tensor	NOUN
ejpam-3279	3	10	of	of	ADP
ejpam-3279	3	11	type	type	NOUN
ejpam-3279	3	12	(	(	PUNCT
ejpam-3279	3	13	4,0	4,0	NUM
ejpam-3279	3	14	)	)	PUNCT
ejpam-3279	3	15	,	,	PUNCT
ejpam-3279	3	16	it	it	PRON
ejpam-3279	3	17	’s	’s	AUX
ejpam-3279	3	18	called	call	VERB
ejpam-3279	3	19	a	a	DET
ejpam-3279	3	20	projective	projective	ADJ
ejpam-3279	3	21	curvature	curvature	NOUN
ejpam-3279	3	22	tensor	tensor	NOUN
ejpam-3279	3	23	.	.	PUNCT
ejpam-3279	4	1	in	in	ADP
ejpam-3279	4	2	this	this	DET
ejpam-3279	4	3	article	article	NOUN
ejpam-3279	4	4	we	we	PRON
ejpam-3279	4	5	discuss	discuss	VERB
ejpam-3279	4	6	an	an	DET
ejpam-3279	4	7	interesting	interesting	ADJ
ejpam-3279	4	8	question	question	NOUN
ejpam-3279	4	9	;	;	PUNCT
ejpam-3279	4	10	what	what	PRON
ejpam-3279	4	11	the	the	DET
ejpam-3279	4	12	geometric	geometric	ADJ
ejpam-3279	4	13	meaning	meaning	NOUN
ejpam-3279	4	14	of	of	ADP
ejpam-3279	4	15	this	this	DET
ejpam-3279	4	16	tensor	tensor	NOUN
ejpam-3279	4	17	when	when	SCONJ
ejpam-3279	4	18	it	it	PRON
ejpam-3279	4	19	’s	’	VERB
ejpam-3279	4	20	act	act	VERB
ejpam-3279	4	21	on	on	ADP
ejpam-3279	4	22	nearly	nearly	ADV
ejpam-3279	4	23	cosymplectic	cosymplectic	ADJ
ejpam-3279	4	24	manifold	manifold	ADJ
ejpam-3279	4	25	?	?	PUNCT
ejpam-3279	5	1	the	the	DET
ejpam-3279	5	2	answer	answer	NOUN
ejpam-3279	5	3	of	of	ADP
ejpam-3279	5	4	this	this	DET
ejpam-3279	5	5	question	question	NOUN
ejpam-3279	5	6	leads	lead	VERB
ejpam-3279	5	7	to	to	PART
ejpam-3279	5	8	get	get	VERB
ejpam-3279	5	9	an	an	DET
ejpam-3279	5	10	application	application	NOUN
ejpam-3279	5	11	on	on	ADP
ejpam-3279	5	12	einstein	einstein	ADJ
ejpam-3279	5	13	space	space	NOUN
ejpam-3279	5	14	.	.	PUNCT
ejpam-3279	6	1	in	in	ADP
ejpam-3279	6	2	particular	particular	ADJ
ejpam-3279	6	3	,	,	PUNCT
ejpam-3279	6	4	the	the	DET
ejpam-3279	6	5	necessary	necessary	ADJ
ejpam-3279	6	6	and	and	CCONJ
ejpam-3279	6	7	sufficient	sufficient	ADJ
ejpam-3279	6	8	conditions	condition	NOUN
ejpam-3279	6	9	that	that	SCONJ
ejpam-3279	6	10	a	a	DET
ejpam-3279	6	11	projective	projective	ADJ
ejpam-3279	6	12	tensor	tensor	NOUN
ejpam-3279	6	13	is	be	AUX
ejpam-3279	6	14	vanishes	vanishe	NOUN
ejpam-3279	6	15	are	be	AUX
ejpam-3279	6	16	found	find	VERB
ejpam-3279	6	17	.	.	PUNCT
ejpam-3279	7	1	2010	2010	NUM
ejpam-3279	7	2	mathematics	mathematic	NOUN
ejpam-3279	7	3	subject	subject	NOUN
ejpam-3279	7	4	classifications	classification	NOUN
ejpam-3279	7	5	:	:	PUNCT
ejpam-3279	7	6	53c55	53c55	NUM
ejpam-3279	7	7	,	,	PUNCT
ejpam-3279	7	8	53b35	53b35	NUM
ejpam-3279	7	9	key	key	ADJ
ejpam-3279	7	10	words	word	NOUN
ejpam-3279	7	11	and	and	CCONJ
ejpam-3279	7	12	phrases	phrase	NOUN
ejpam-3279	7	13	:	:	PUNCT
ejpam-3279	7	14	projective	projective	ADJ
ejpam-3279	7	15	curvature	curvature	NOUN
ejpam-3279	7	16	tensor	tensor	NOUN
ejpam-3279	7	17	,	,	PUNCT
ejpam-3279	7	18	almost	almost	ADV
ejpam-3279	7	19	contact	contact	NOUN
ejpam-3279	7	20	manifold	manifold	ADJ
ejpam-3279	7	21	,	,	PUNCT
ejpam-3279	7	22	nearly	nearly	ADV
ejpam-3279	7	23	cosymplectic	cosymplectic	ADJ
ejpam-3279	7	24	manifold	manifold	ADJ
ejpam-3279	7	25	1	1	NUM
ejpam-3279	7	26	.	.	PUNCT
ejpam-3279	8	1	introduction	introduction	NOUN
ejpam-3279	8	2	almost	almost	ADV
ejpam-3279	8	3	contact	contact	NOUN
ejpam-3279	8	4	manifold	manifold	ADJ
ejpam-3279	8	5	contains	contain	VERB
ejpam-3279	8	6	many	many	ADJ
ejpam-3279	8	7	varieties	variety	NOUN
ejpam-3279	8	8	,	,	PUNCT
ejpam-3279	8	9	one	one	NUM
ejpam-3279	8	10	of	of	ADP
ejpam-3279	8	11	the	the	DET
ejpam-3279	8	12	most	most	ADV
ejpam-3279	8	13	important	important	ADJ
ejpam-3279	8	14	of	of	ADP
ejpam-3279	8	15	them	they	PRON
ejpam-3279	8	16	is	be	AUX
ejpam-3279	8	17	called	call	VERB
ejpam-3279	8	18	a	a	DET
ejpam-3279	8	19	nearly	nearly	ADV
ejpam-3279	8	20	cosymplectic	cosymplectic	ADJ
ejpam-3279	8	21	manifold	manifold	ADJ
ejpam-3279	8	22	(	(	PUNCT
ejpam-3279	8	23	nc	nc	NOUN
ejpam-3279	8	24	-	-	ADJ
ejpam-3279	8	25	manifold	manifold	ADJ
ejpam-3279	8	26	)	)	PUNCT
ejpam-3279	8	27	.	.	PUNCT
ejpam-3279	9	1	there	there	PRON
ejpam-3279	9	2	have	have	VERB
ejpam-3279	9	3	many	many	ADJ
ejpam-3279	9	4	studies	study	NOUN
ejpam-3279	9	5	about	about	ADP
ejpam-3279	9	6	this	this	DET
ejpam-3279	9	7	manifold	manifold	NOUN
ejpam-3279	9	8	.	.	PUNCT
ejpam-3279	10	1	in	in	ADP
ejpam-3279	10	2	1974	1974	NUM
ejpam-3279	10	3	,	,	PUNCT
ejpam-3279	10	4	blair	blair	PROPN
ejpam-3279	10	5	and	and	CCONJ
ejpam-3279	10	6	showers	shower	NOUN
ejpam-3279	10	7	[	[	X
ejpam-3279	10	8	4	4	X
ejpam-3279	10	9	]	]	PUNCT
ejpam-3279	10	10	have	have	AUX
ejpam-3279	10	11	got	get	VERB
ejpam-3279	10	12	some	some	PRON
ejpam-3279	10	13	of	of	ADP
ejpam-3279	10	14	the	the	DET
ejpam-3279	10	15	characteristics	characteristic	NOUN
ejpam-3279	10	16	of	of	ADP
ejpam-3279	10	17	nc	nc	PROPN
ejpam-3279	10	18	-	-	ADJ
ejpam-3279	10	19	manifold	manifold	NOUN
ejpam-3279	10	20	.	.	PUNCT
ejpam-3279	11	1	later	later	ADV
ejpam-3279	11	2	,	,	PUNCT
ejpam-3279	11	3	appeared	appear	VERB
ejpam-3279	11	4	many	many	ADJ
ejpam-3279	11	5	studies	study	NOUN
ejpam-3279	11	6	on	on	ADP
ejpam-3279	11	7	nc	nc	PROPN
ejpam-3279	11	8	-manifold	-manifold	PROPN
ejpam-3279	11	9	,	,	PUNCT
ejpam-3279	11	10	for	for	ADP
ejpam-3279	11	11	more	more	ADJ
ejpam-3279	11	12	details	detail	NOUN
ejpam-3279	11	13	we	we	PRON
ejpam-3279	11	14	refer	refer	VERB
ejpam-3279	11	15	to	to	ADP
ejpam-3279	11	16	[	[	X
ejpam-3279	11	17	2	2	NUM
ejpam-3279	11	18	]	]	PUNCT
ejpam-3279	11	19	,	,	PUNCT
ejpam-3279	11	20	[	[	X
ejpam-3279	11	21	7	7	X
ejpam-3279	11	22	]	]	PUNCT
ejpam-3279	11	23	and	and	CCONJ
ejpam-3279	11	24	[	[	X
ejpam-3279	11	25	8	8	NUM
ejpam-3279	11	26	]	]	PUNCT
ejpam-3279	11	27	.	.	PUNCT
ejpam-3279	12	1	in	in	ADP
ejpam-3279	12	2	2011	2011	NUM
ejpam-3279	12	3	,	,	PUNCT
ejpam-3279	12	4	kirichenko	kirichenko	PROPN
ejpam-3279	12	5	and	and	CCONJ
ejpam-3279	12	6	kusova	kusova	PROPN
ejpam-3279	12	7	[	[	X
ejpam-3279	12	8	14	14	NUM
ejpam-3279	12	9	]	]	PUNCT
ejpam-3279	12	10	studied	study	VERB
ejpam-3279	12	11	nc	nc	PROPN
ejpam-3279	12	12	-	-	ADJ
ejpam-3279	12	13	manifold	manifold	ADJ
ejpam-3279	12	14	in	in	ADP
ejpam-3279	12	15	gadjoined	gadjoined	ADJ
ejpam-3279	12	16	structure	structure	NOUN
ejpam-3279	12	17	space	space	NOUN
ejpam-3279	12	18	.	.	PUNCT
ejpam-3279	13	1	this	this	DET
ejpam-3279	13	2	method	method	NOUN
ejpam-3279	13	3	allowed	allow	VERB
ejpam-3279	13	4	the	the	DET
ejpam-3279	13	5	researchers	researcher	NOUN
ejpam-3279	13	6	to	to	PART
ejpam-3279	13	7	study	study	VERB
ejpam-3279	13	8	different	different	ADJ
ejpam-3279	13	9	geometric	geometric	ADJ
ejpam-3279	13	10	properties	property	NOUN
ejpam-3279	13	11	.	.	PUNCT
ejpam-3279	14	1	apart	apart	ADV
ejpam-3279	14	2	from	from	ADP
ejpam-3279	14	3	conformal	conformal	ADJ
ejpam-3279	14	4	curvature	curvature	NOUN
ejpam-3279	14	5	tensor	tensor	NOUN
ejpam-3279	14	6	,	,	PUNCT
ejpam-3279	14	7	the	the	DET
ejpam-3279	14	8	projective	projective	ADJ
ejpam-3279	14	9	curvature	curvature	NOUN
ejpam-3279	14	10	tensor	tensor	NOUN
ejpam-3279	14	11	is	be	AUX
ejpam-3279	14	12	another	another	DET
ejpam-3279	14	13	important	important	ADJ
ejpam-3279	14	14	tensor	tensor	NOUN
ejpam-3279	14	15	from	from	ADP
ejpam-3279	14	16	the	the	DET
ejpam-3279	14	17	differential	differential	ADJ
ejpam-3279	14	18	geometric	geometric	ADJ
ejpam-3279	14	19	point	point	NOUN
ejpam-3279	14	20	of	of	ADP
ejpam-3279	14	21	view	view	NOUN
ejpam-3279	14	22	.	.	PUNCT
ejpam-3279	15	1	in	in	ADP
ejpam-3279	15	2	1953	1953	NUM
ejpam-3279	15	3	,	,	PUNCT
ejpam-3279	15	4	yano	yano	PROPN
ejpam-3279	15	5	and	and	CCONJ
ejpam-3279	15	6	bochner	bochner	NOUN
ejpam-3279	15	7	[	[	X
ejpam-3279	15	8	19	19	NUM
ejpam-3279	15	9	]	]	PUNCT
ejpam-3279	15	10	,	,	PUNCT
ejpam-3279	15	11	proved	prove	VERB
ejpam-3279	15	12	that	that	SCONJ
ejpam-3279	15	13	a	a	DET
ejpam-3279	15	14	manifold	manifold	NOUN
ejpam-3279	15	15	is	be	AUX
ejpam-3279	15	16	projectively	projectively	ADV
ejpam-3279	15	17	flat	flat	ADJ
ejpam-3279	15	18	if	if	SCONJ
ejpam-3279	15	19	and	and	CCONJ
ejpam-3279	15	20	only	only	ADV
ejpam-3279	15	21	if	if	SCONJ
ejpam-3279	15	22	,	,	PUNCT
ejpam-3279	15	23	it	it	PRON
ejpam-3279	15	24	is	be	AUX
ejpam-3279	15	25	of	of	ADP
ejpam-3279	15	26	constant	constant	ADJ
ejpam-3279	15	27	curvature	curvature	NOUN
ejpam-3279	15	28	.	.	PUNCT
ejpam-3279	16	1	thus	thus	ADV
ejpam-3279	16	2	the	the	DET
ejpam-3279	16	3	projective	projective	ADJ
ejpam-3279	16	4	tensor	tensor	NOUN
ejpam-3279	16	5	measures	measure	NOUN
ejpam-3279	16	6	a	a	DET
ejpam-3279	16	7	riemannian	riemannian	ADJ
ejpam-3279	16	8	manifold	manifold	NOUN
ejpam-3279	16	9	to	to	PART
ejpam-3279	16	10	be	be	AUX
ejpam-3279	16	11	of	of	ADP
ejpam-3279	16	12	constant	constant	ADJ
ejpam-3279	16	13	curvature	curvature	NOUN
ejpam-3279	16	14	.	.	PUNCT
ejpam-3279	17	1	in	in	ADP
ejpam-3279	17	2	2009	2009	NUM
ejpam-3279	17	3	,	,	PUNCT
ejpam-3279	17	4	abood	abood	NOUN
ejpam-3279	17	5	and	and	CCONJ
ejpam-3279	17	6	mohammed	mohammed	PROPN
ejpam-3279	18	1	[	[	X
ejpam-3279	18	2	1	1	NUM
ejpam-3279	18	3	]	]	PUNCT
ejpam-3279	18	4	,	,	PUNCT
ejpam-3279	18	5	studied	study	VERB
ejpam-3279	18	6	the	the	DET
ejpam-3279	18	7	projective	projective	ADJ
ejpam-3279	18	8	tensor	tensor	NOUN
ejpam-3279	18	9	on	on	ADP
ejpam-3279	18	10	almost	almost	ADV
ejpam-3279	18	11	hermitian	hermitian	ADJ
ejpam-3279	18	12	manifold	manifold	NOUN
ejpam-3279	18	13	and	and	CCONJ
ejpam-3279	18	14	they	they	PRON
ejpam-3279	18	15	are	be	AUX
ejpam-3279	18	16	found	find	VERB
ejpam-3279	18	17	some	some	DET
ejpam-3279	18	18	properties	property	NOUN
ejpam-3279	18	19	of	of	ADP
ejpam-3279	18	20	this	this	DET
ejpam-3279	18	21	tensor	tensor	NOUN
ejpam-3279	18	22	.	.	PUNCT
ejpam-3279	19	1	in	in	ADP
ejpam-3279	19	2	2010	2010	NUM
ejpam-3279	19	3	,	,	PUNCT
ejpam-3279	19	4	ghosh	ghosh	PROPN
ejpam-3279	19	5	[	[	X
ejpam-3279	19	6	9	9	NUM
ejpam-3279	19	7	]	]	PUNCT
ejpam-3279	19	8	found	find	VERB
ejpam-3279	19	9	some	some	DET
ejpam-3279	19	10	properties	property	NOUN
ejpam-3279	19	11	of	of	ADP
ejpam-3279	19	12	the	the	DET
ejpam-3279	19	13	projective	projective	ADJ
ejpam-3279	19	14	curvature	curvature	NOUN
ejpam-3279	19	15	tensor	tensor	NOUN
ejpam-3279	19	16	on	on	ADP
ejpam-3279	19	17	(	(	PUNCT
ejpam-3279	19	18	k	k	X
ejpam-3279	19	19	,	,	PUNCT
ejpam-3279	19	20	µ)-contact	µ)-contact	NOUN
ejpam-3279	19	21	manifolds	manifold	NOUN
ejpam-3279	19	22	.	.	PUNCT
ejpam-3279	20	1	in	in	ADP
ejpam-3279	20	2	2012	2012	NUM
ejpam-3279	20	3	,	,	PUNCT
ejpam-3279	20	4	de	de	X
ejpam-3279	20	5	and	and	CCONJ
ejpam-3279	20	6	de	de	ADP
ejpam-3279	20	7	a.	a.	NOUN
ejpam-3279	20	8	[	[	X
ejpam-3279	20	9	6	6	NUM
ejpam-3279	20	10	]	]	PUNCT
ejpam-3279	20	11	studied	study	VERB
ejpam-3279	20	12	the	the	DET
ejpam-3279	20	13	projective	projective	ADJ
ejpam-3279	20	14	curvature	curvature	NOUN
ejpam-3279	20	15	tensor	tensor	NOUN
ejpam-3279	20	16	on	on	ADP
ejpam-3279	20	17	k	k	PROPN
ejpam-3279	20	18	contact	contact	NOUN
ejpam-3279	20	19	manifolds	manifold	NOUN
ejpam-3279	20	20	.	.	PUNCT
ejpam-3279	21	1	∗corresponding	∗corresponde	VERB
ejpam-3279	21	2	author	author	NOUN
ejpam-3279	21	3	.	.	PUNCT
ejpam-3279	22	1	doi	doi	NOUN
ejpam-3279	22	2	:	:	PUNCT
ejpam-3279	22	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3279	https://doi.org/10.29020/nybg.ejpam.v11i3.3279	NOUN
ejpam-3279	22	4	email	email	NOUN
ejpam-3279	22	5	addresses	address	NOUN
ejpam-3279	22	6	:	:	PUNCT
ejpam-3279	22	7	nawafjaber80@yahoo.com	nawafjaber80@yahoo.com	X
ejpam-3279	22	8	(	(	PUNCT
ejpam-3279	22	9	n.	n.	PROPN
ejpam-3279	22	10	j.	j.	PROPN
ejpam-3279	22	11	mohammed	mohammed	PROPN
ejpam-3279	22	12	)	)	PUNCT
ejpam-3279	22	13	,	,	PUNCT
ejpam-3279	22	14	iraqsafwan2006@gmail.com	iraqsafwan2006@gmail.com	X
ejpam-3279	23	1	(	(	PUNCT
ejpam-3279	23	2	h.	h.	PROPN
ejpam-3279	23	3	m.	m.	PROPN
ejpam-3279	23	4	abood	abood	PROPN
ejpam-3279	23	5	)	)	PUNCT
ejpam-3279	23	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3279	24	1	823	823	NUM
ejpam-3279	24	2	c	c	X
ejpam-3279	24	3	©	©	PROPN
ejpam-3279	24	4	2018	2018	NUM
ejpam-3279	24	5	ejpam	ejpam	VERB
ejpam-3279	24	6	all	all	DET
ejpam-3279	24	7	rights	right	NOUN
ejpam-3279	24	8	reserved	reserve	VERB
ejpam-3279	24	9	.	.	PUNCT
ejpam-3279	25	1	n.	n.	PROPN
ejpam-3279	25	2	j.	j.	PROPN
ejpam-3279	25	3	mohammed	mohammed	PROPN
ejpam-3279	25	4	,	,	PUNCT
ejpam-3279	25	5	h.	h.	PROPN
ejpam-3279	25	6	m.	m.	PROPN
ejpam-3279	25	7	abood	abood	PROPN
ejpam-3279	25	8	/	/	SYM
ejpam-3279	25	9	eur	eur	PROPN
ejpam-3279	25	10	.	.	PUNCT
ejpam-3279	26	1	j.	j.	PROPN
ejpam-3279	26	2	pure	pure	PROPN
ejpam-3279	26	3	appl	appl	PROPN
ejpam-3279	26	4	.	.	PROPN
ejpam-3279	26	5	math	math	PROPN
ejpam-3279	26	6	,	,	PUNCT
ejpam-3279	26	7	11	11	NUM
ejpam-3279	26	8	(	(	PUNCT
ejpam-3279	26	9	3	3	NUM
ejpam-3279	26	10	)	)	PUNCT
ejpam-3279	26	11	(	(	PUNCT
ejpam-3279	26	12	2018	2018	NUM
ejpam-3279	26	13	)	)	PUNCT
ejpam-3279	26	14	,	,	PUNCT
ejpam-3279	26	15	823	823	NUM
ejpam-3279	26	16	-	-	SYM
ejpam-3279	26	17	833	833	NUM
ejpam-3279	26	18	824	824	NUM
ejpam-3279	26	19	2	2	NUM
ejpam-3279	26	20	.	.	PUNCT
ejpam-3279	26	21	preliminaries	preliminary	NOUN
ejpam-3279	26	22	this	this	DET
ejpam-3279	26	23	section	section	NOUN
ejpam-3279	26	24	shows	show	VERB
ejpam-3279	26	25	a	a	DET
ejpam-3279	26	26	simple	simple	ADJ
ejpam-3279	26	27	overview	overview	NOUN
ejpam-3279	26	28	of	of	ADP
ejpam-3279	26	29	the	the	DET
ejpam-3279	26	30	basic	basic	ADJ
ejpam-3279	26	31	concepts	concept	NOUN
ejpam-3279	26	32	that	that	PRON
ejpam-3279	26	33	pertain	pertain	VERB
ejpam-3279	26	34	to	to	ADP
ejpam-3279	26	35	the	the	DET
ejpam-3279	26	36	subject	subject	NOUN
ejpam-3279	26	37	of	of	ADP
ejpam-3279	26	38	our	our	PRON
ejpam-3279	26	39	study	study	NOUN
ejpam-3279	26	40	.	.	PUNCT
ejpam-3279	27	1	definition	definition	NOUN
ejpam-3279	27	2	2.1	2.1	NUM
ejpam-3279	27	3	.	.	PUNCT
ejpam-3279	28	1	[	[	X
ejpam-3279	28	2	3	3	X
ejpam-3279	28	3	]	]	PUNCT
ejpam-3279	28	4	suppose	suppose	VERB
ejpam-3279	28	5	that	that	SCONJ
ejpam-3279	28	6	m	m	PROPN
ejpam-3279	28	7	is	be	AUX
ejpam-3279	28	8	2n	2n	NUM
ejpam-3279	28	9	+	+	CCONJ
ejpam-3279	28	10	1	1	NUM
ejpam-3279	28	11	-	-	PUNCT
ejpam-3279	28	12	dimensional	dimensional	ADJ
ejpam-3279	28	13	smooth	smooth	ADJ
ejpam-3279	28	14	manifold	manifold	NOUN
ejpam-3279	28	15	.	.	PUNCT
ejpam-3279	29	1	the	the	DET
ejpam-3279	29	2	set	set	NOUN
ejpam-3279	29	3	of	of	ADP
ejpam-3279	29	4	smooth	smooth	ADJ
ejpam-3279	29	5	manifold	manifold	ADJ
ejpam-3279	29	6	and	and	CCONJ
ejpam-3279	29	7	tensors	tensor	NOUN
ejpam-3279	29	8	(	(	PUNCT
ejpam-3279	29	9	m	m	PROPN
ejpam-3279	29	10	,	,	PUNCT
ejpam-3279	29	11	η	η	PROPN
ejpam-3279	29	12	,	,	PUNCT
ejpam-3279	29	13	ξ	ξ	PROPN
ejpam-3279	29	14	,	,	PUNCT
ejpam-3279	29	15	φ	φ	NOUN
ejpam-3279	29	16	,	,	PUNCT
ejpam-3279	29	17	g	g	NOUN
ejpam-3279	29	18	)	)	PUNCT
ejpam-3279	29	19	is	be	AUX
ejpam-3279	29	20	called	call	VERB
ejpam-3279	29	21	an	an	DET
ejpam-3279	29	22	almost	almost	ADV
ejpam-3279	29	23	contact	contact	NOUN
ejpam-3279	29	24	metric	metric	ADJ
ejpam-3279	29	25	manifold	manifold	ADJ
ejpam-3279	29	26	(	(	PUNCT
ejpam-3279	29	27	ac	ac	ADJ
ejpam-3279	29	28	-	-	ADJ
ejpam-3279	29	29	manifold	manifold	ADJ
ejpam-3279	29	30	)	)	PUNCT
ejpam-3279	29	31	if	if	SCONJ
ejpam-3279	29	32	such	such	ADJ
ejpam-3279	29	33	that	that	PRON
ejpam-3279	29	34	:	:	PUNCT
ejpam-3279	29	35	η(ξ	η(ξ	ADJ
ejpam-3279	29	36	)	)	PUNCT
ejpam-3279	29	37	=	=	SYM
ejpam-3279	29	38	1	1	NUM
ejpam-3279	29	39	,	,	PUNCT
ejpam-3279	29	40	φ(ξ	φ(ξ	NOUN
ejpam-3279	29	41	)	)	PUNCT
ejpam-3279	29	42	=	=	SYM
ejpam-3279	29	43	0	0	NUM
ejpam-3279	29	44	,	,	PUNCT
ejpam-3279	29	45	η	η	PROPN
ejpam-3279	29	46	◦	◦	NOUN
ejpam-3279	29	47	φ	φ	NUM
ejpam-3279	29	48	=	=	SYM
ejpam-3279	29	49	0	0	PROPN
ejpam-3279	29	50	and	and	CCONJ
ejpam-3279	29	51	φ2	φ2	PROPN
ejpam-3279	29	52	=	=	SYM
ejpam-3279	29	53	−id	−id	PROPN
ejpam-3279	29	54	+	+	CCONJ
ejpam-3279	29	55	η	η	PROPN
ejpam-3279	29	56	⊗	⊗	PROPN
ejpam-3279	29	57	ξ	ξ	PROPN
ejpam-3279	29	58	,	,	PUNCT
ejpam-3279	29	59	where	where	SCONJ
ejpam-3279	29	60	η	η	PROPN
ejpam-3279	29	61	is	be	AUX
ejpam-3279	29	62	differential	differential	ADJ
ejpam-3279	29	63	1	1	NUM
ejpam-3279	29	64	-	-	PUNCT
ejpam-3279	29	65	form	form	NOUN
ejpam-3279	29	66	called	call	VERB
ejpam-3279	29	67	a	a	DET
ejpam-3279	29	68	contact	contact	NOUN
ejpam-3279	29	69	form	form	NOUN
ejpam-3279	29	70	,	,	PUNCT
ejpam-3279	29	71	ξ	ξ	X
ejpam-3279	29	72	be	be	VERB
ejpam-3279	29	73	a	a	DET
ejpam-3279	29	74	vector	vector	NOUN
ejpam-3279	29	75	field	field	NOUN
ejpam-3279	29	76	called	call	VERB
ejpam-3279	29	77	a	a	DET
ejpam-3279	29	78	characteristic	characteristic	NOUN
ejpam-3279	29	79	,	,	PUNCT
ejpam-3279	29	80	φ	φ	PROPN
ejpam-3279	29	81	endomorphism	endomorphism	PROPN
ejpam-3279	29	82	of	of	ADP
ejpam-3279	29	83	x(m	x(m	PROPN
ejpam-3279	29	84	)	)	PUNCT
ejpam-3279	29	85	called	call	VERB
ejpam-3279	29	86	a	a	DET
ejpam-3279	29	87	structure	structure	NOUN
ejpam-3279	29	88	endomorphisim	endomorphisim	ADJ
ejpam-3279	29	89	and	and	CCONJ
ejpam-3279	29	90	there	there	PRON
ejpam-3279	29	91	is	be	VERB
ejpam-3279	29	92	a	a	DET
ejpam-3279	29	93	riemannian	riemannian	ADJ
ejpam-3279	29	94	structure	structure	NOUN
ejpam-3279	29	95	g	g	PROPN
ejpam-3279	29	96	=	=	SYM
ejpam-3279	29	97	〈	〈	PROPN
ejpam-3279	29	98	.	.	PROPN
ejpam-3279	29	99	,	,	PUNCT
ejpam-3279	29	100	.	.	PUNCT
ejpam-3279	30	1	〉	〉	NOUN
ejpam-3279	30	2	on	on	ADP
ejpam-3279	30	3	m	m	PRON
ejpam-3279	30	4	such	such	ADJ
ejpam-3279	30	5	that	that	SCONJ
ejpam-3279	30	6	:	:	PUNCT
ejpam-3279	31	1	〈	〈	X
ejpam-3279	31	2	φx	φx	NOUN
ejpam-3279	31	3	,	,	PUNCT
ejpam-3279	31	4	φy	φy	ADP
ejpam-3279	31	5	〉	〉	NOUN
ejpam-3279	31	6	=	=	SYM
ejpam-3279	31	7	〈	〈	PROPN
ejpam-3279	31	8	x	x	X
ejpam-3279	31	9	,	,	PUNCT
ejpam-3279	31	10	y	y	PROPN
ejpam-3279	31	11	〉	〉	PROPN
ejpam-3279	31	12	−	−	PROPN
ejpam-3279	31	13	η(x)η(y	η(x)η(y	PROPN
ejpam-3279	31	14	)	)	PUNCT
ejpam-3279	31	15	,	,	PUNCT
ejpam-3279	31	16	x	x	X
ejpam-3279	31	17	,	,	PUNCT
ejpam-3279	31	18	y	y	PROPN
ejpam-3279	31	19	∈	∈	PROPN
ejpam-3279	31	20	x(m	x(m	PROPN
ejpam-3279	31	21	)	)	PUNCT
ejpam-3279	31	22	.	.	PUNCT
ejpam-3279	32	1	definition	definition	NOUN
ejpam-3279	32	2	2.2	2.2	NUM
ejpam-3279	32	3	.	.	PUNCT
ejpam-3279	33	1	[	[	X
ejpam-3279	33	2	5	5	NUM
ejpam-3279	33	3	]	]	PUNCT
ejpam-3279	33	4	almost	almost	ADV
ejpam-3279	33	5	contact	contact	NOUN
ejpam-3279	33	6	manifold	manifold	NOUN
ejpam-3279	33	7	is	be	AUX
ejpam-3279	33	8	called	call	VERB
ejpam-3279	33	9	a	a	DET
ejpam-3279	33	10	nearly	nearly	ADV
ejpam-3279	33	11	cosymplectic	cosymplectic	ADJ
ejpam-3279	33	12	manifold	manifold	ADJ
ejpam-3279	33	13	(	(	PUNCT
ejpam-3279	33	14	nc	nc	NOUN
ejpam-3279	33	15	-	-	ADJ
ejpam-3279	33	16	manifold	manifold	ADJ
ejpam-3279	33	17	)	)	PUNCT
ejpam-3279	33	18	if	if	SCONJ
ejpam-3279	33	19	the	the	DET
ejpam-3279	33	20	equality	equality	NOUN
ejpam-3279	33	21	∇x(φ)y	∇x(φ)y	VERB
ejpam-3279	34	1	+	+	PROPN
ejpam-3279	34	2	∇y	∇y	PROPN
ejpam-3279	34	3	(	(	PUNCT
ejpam-3279	34	4	φ)x	φ)x	ADJ
ejpam-3279	34	5	=	=	SYM
ejpam-3279	34	6	0	0	NUM
ejpam-3279	34	7	,	,	PUNCT
ejpam-3279	34	8	x	x	PRON
ejpam-3279	34	9	,	,	PUNCT
ejpam-3279	34	10	y	y	PROPN
ejpam-3279	34	11	∈	∈	PROPN
ejpam-3279	34	12	x(m	x(m	PROPN
ejpam-3279	34	13	)	)	PUNCT
ejpam-3279	34	14	,	,	PUNCT
ejpam-3279	34	15	holds	hold	VERB
ejpam-3279	34	16	.	.	PUNCT
ejpam-3279	35	1	definition	definition	NOUN
ejpam-3279	35	2	2.3	2.3	NUM
ejpam-3279	35	3	.	.	PUNCT
ejpam-3279	36	1	[	[	X
ejpam-3279	36	2	12	12	NUM
ejpam-3279	36	3	]	]	X
ejpam-3279	36	4	let	let	VERB
ejpam-3279	36	5	(	(	PUNCT
ejpam-3279	36	6	m	m	PROPN
ejpam-3279	36	7	,	,	PUNCT
ejpam-3279	36	8	η	η	PROPN
ejpam-3279	36	9	,	,	PUNCT
ejpam-3279	36	10	φ	φ	NOUN
ejpam-3279	36	11	,	,	PUNCT
ejpam-3279	36	12	g	g	NOUN
ejpam-3279	36	13	)	)	PUNCT
ejpam-3279	36	14	be	be	AUX
ejpam-3279	36	15	an	an	DET
ejpam-3279	36	16	almost	almost	ADV
ejpam-3279	36	17	contact	contact	NOUN
ejpam-3279	36	18	metric	metric	ADJ
ejpam-3279	36	19	manifold	manifold	ADJ
ejpam-3279	36	20	(	(	PUNCT
ejpam-3279	36	21	ac	ac	ADJ
ejpam-3279	36	22	-	-	ADJ
ejpam-3279	36	23	manifold	manifold	ADJ
ejpam-3279	36	24	)	)	PUNCT
ejpam-3279	36	25	.	.	PUNCT
ejpam-3279	37	1	in	in	ADP
ejpam-3279	37	2	the	the	DET
ejpam-3279	37	3	module	module	NOUN
ejpam-3279	37	4	xc(m	xc(m	PUNCT
ejpam-3279	37	5	)	)	PUNCT
ejpam-3279	37	6	(	(	PUNCT
ejpam-3279	37	7	complexification	complexification	NOUN
ejpam-3279	37	8	of	of	ADP
ejpam-3279	37	9	the	the	DET
ejpam-3279	37	10	module	module	NOUN
ejpam-3279	37	11	x(m	x(m	PROPN
ejpam-3279	37	12	)	)	PUNCT
ejpam-3279	37	13	)	)	PUNCT
ejpam-3279	37	14	define	define	VERB
ejpam-3279	37	15	two	two	NUM
ejpam-3279	37	16	endomorphisms	endomorphism	NOUN
ejpam-3279	37	17	σ	σ	NOUN
ejpam-3279	37	18	and	and	CCONJ
ejpam-3279	37	19	σ̄	σ̄	PROPN
ejpam-3279	37	20	as	as	SCONJ
ejpam-3279	37	21	follows	follow	VERB
ejpam-3279	37	22	:	:	PUNCT
ejpam-3279	37	23	σ	σ	NOUN
ejpam-3279	37	24	=	=	SYM
ejpam-3279	37	25	1	1	NUM
ejpam-3279	37	26	2(id−	2(id−	NUM
ejpam-3279	37	27	√	√	NUM
ejpam-3279	37	28	−1φ	−1φ	PROPN
ejpam-3279	37	29	)	)	PUNCT
ejpam-3279	37	30	and	and	CCONJ
ejpam-3279	37	31	σ̄	σ̄	PRON
ejpam-3279	37	32	=	=	SYM
ejpam-3279	37	33	−1	−1	NOUN
ejpam-3279	37	34	2(id+	2(id+	NUM
ejpam-3279	37	35	√	√	PROPN
ejpam-3279	37	36	−1φ	−1φ	PROPN
ejpam-3279	37	37	)	)	PUNCT
ejpam-3279	37	38	.	.	PUNCT
ejpam-3279	38	1	further	far	ADV
ejpam-3279	38	2	,	,	PUNCT
ejpam-3279	38	3	depending	depend	VERB
ejpam-3279	38	4	on	on	ADP
ejpam-3279	38	5	σ	σ	PROPN
ejpam-3279	38	6	,	,	PUNCT
ejpam-3279	38	7	we	we	PRON
ejpam-3279	38	8	can	can	AUX
ejpam-3279	38	9	define	define	VERB
ejpam-3279	38	10	two	two	NUM
ejpam-3279	38	11	projections	projection	NOUN
ejpam-3279	38	12	as	as	SCONJ
ejpam-3279	38	13	follows	follow	VERB
ejpam-3279	38	14	:	:	PUNCT
ejpam-3279	38	15	π	π	PROPN
ejpam-3279	38	16	=	=	PUNCT
ejpam-3279	38	17	σ	σ	PROPN
ejpam-3279	38	18	◦	◦	NOUN
ejpam-3279	38	19	`	`	PUNCT
ejpam-3279	38	20	=	=	SYM
ejpam-3279	38	21	−1	−1	NOUN
ejpam-3279	38	22	2	2	NUM
ejpam-3279	38	23	(	(	PUNCT
ejpam-3279	38	24	φ2	φ2	NOUN
ejpam-3279	38	25	−	−	PROPN
ejpam-3279	38	26	√	√	PROPN
ejpam-3279	38	27	−1φ	−1φ	PROPN
ejpam-3279	38	28	)	)	PUNCT
ejpam-3279	38	29	and	and	CCONJ
ejpam-3279	38	30	π̄	π̄	VERB
ejpam-3279	38	31	=	=	NOUN
ejpam-3279	38	32	σ̄	σ̄	X
ejpam-3279	38	33	◦	◦	NOUN
ejpam-3279	38	34	`	`	PUNCT
ejpam-3279	38	35	=	=	SYM
ejpam-3279	38	36	1	1	NUM
ejpam-3279	38	37	2	2	NUM
ejpam-3279	38	38	(	(	PUNCT
ejpam-3279	38	39	φ2	φ2	NOUN
ejpam-3279	38	40	+	+	CCONJ
ejpam-3279	38	41	√	√	PROPN
ejpam-3279	38	42	−1φ	−1φ	PROPN
ejpam-3279	38	43	)	)	PUNCT
ejpam-3279	38	44	,	,	PUNCT
ejpam-3279	38	45	where	where	SCONJ
ejpam-3279	38	46	σ	σ	PROPN
ejpam-3279	38	47	◦	◦	PROPN
ejpam-3279	38	48	φ	φ	PROPN
ejpam-3279	38	49	=	=	SYM
ejpam-3279	38	50	φ	φ	PROPN
ejpam-3279	38	51	◦	◦	PROPN
ejpam-3279	38	52	σ	σ	PROPN
ejpam-3279	38	53	=	=	VERB
ejpam-3279	38	54	iσ	iσ	NOUN
ejpam-3279	38	55	and	and	CCONJ
ejpam-3279	38	56	σ̄	σ̄	PRON
ejpam-3279	38	57	◦	◦	NOUN
ejpam-3279	38	58	φ	φ	PROPN
ejpam-3279	38	59	=	=	SYM
ejpam-3279	38	60	φ	φ	PROPN
ejpam-3279	38	61	◦	◦	NOUN
ejpam-3279	38	62	σ̄	σ̄	X
ejpam-3279	38	63	=	=	NOUN
ejpam-3279	38	64	−iσ̄.	−iσ̄.	NOUN
ejpam-3279	38	65	therefore	therefore	ADV
ejpam-3279	38	66	,	,	PUNCT
ejpam-3279	38	67	if	if	SCONJ
ejpam-3279	38	68	we	we	PRON
ejpam-3279	38	69	denote	denote	VERB
ejpam-3279	38	70	imπ	imπ	VERB
ejpam-3279	38	71	=	=	SYM
ejpam-3279	38	72	d	d	NOUN
ejpam-3279	38	73	√	√	NUM
ejpam-3279	38	74	−1	−1	NOUN
ejpam-3279	38	75	φ	φ	PROPN
ejpam-3279	38	76	and	and	CCONJ
ejpam-3279	38	77	imπ̄	imπ̄	NOUN
ejpam-3279	38	78	=	=	PUNCT
ejpam-3279	38	79	d−	d−	PROPN
ejpam-3279	38	80	√	√	NUM
ejpam-3279	38	81	−1	−1	NOUN
ejpam-3279	38	82	φ	φ	PROPN
ejpam-3279	38	83	,	,	PUNCT
ejpam-3279	38	84	then	then	ADV
ejpam-3279	38	85	xc(m	xc(m	PUNCT
ejpam-3279	38	86	)	)	PUNCT
ejpam-3279	39	1	=	=	PUNCT
ejpam-3279	40	1	d	d	NOUN
ejpam-3279	40	2	√	√	NUM
ejpam-3279	40	3	−1	−1	NOUN
ejpam-3279	40	4	φ	φ	NOUN
ejpam-3279	40	5	⊕d−	⊕d−	VERB
ejpam-3279	40	6	√	√	NUM
ejpam-3279	40	7	−1	−1	NOUN
ejpam-3279	40	8	φ	φ	PROPN
ejpam-3279	40	9	⊕d0	⊕d0	PROPN
ejpam-3279	40	10	φ	φ	PROPN
ejpam-3279	40	11	,	,	PUNCT
ejpam-3279	40	12	where	where	SCONJ
ejpam-3279	40	13	d	d	NOUN
ejpam-3279	40	14	√	√	NUM
ejpam-3279	40	15	−1	−1	NOUN
ejpam-3279	40	16	φ	φ	PROPN
ejpam-3279	40	17	,	,	PUNCT
ejpam-3279	40	18	d−	d−	PROPN
ejpam-3279	40	19	√	√	NUM
ejpam-3279	40	20	−1	−1	NOUN
ejpam-3279	40	21	φ	φ	PROPN
ejpam-3279	40	22	and	and	CCONJ
ejpam-3279	40	23	d0	d0	PROPN
ejpam-3279	40	24	φ	φ	PROPN
ejpam-3279	40	25	are	be	AUX
ejpam-3279	40	26	proper	proper	ADJ
ejpam-3279	40	27	submodules	submodule	NOUN
ejpam-3279	40	28	of	of	ADP
ejpam-3279	40	29	endomorphism	endomorphism	PROPN
ejpam-3279	40	30	φ	φ	PROPN
ejpam-3279	40	31	with	with	ADP
ejpam-3279	40	32	proper	proper	ADJ
ejpam-3279	40	33	values√	values√	NOUN
ejpam-3279	40	34	−1,−	−1,−	NOUN
ejpam-3279	40	35	√	√	VERB
ejpam-3279	40	36	−1	−1	NOUN
ejpam-3279	40	37	and	and	CCONJ
ejpam-3279	40	38	0	0	NUM
ejpam-3279	40	39	respectively	respectively	ADV
ejpam-3279	40	40	.	.	PUNCT
ejpam-3279	41	1	definition	definition	NOUN
ejpam-3279	41	2	2.4	2.4	NUM
ejpam-3279	41	3	.	.	PUNCT
ejpam-3279	42	1	[	[	X
ejpam-3279	42	2	15	15	NUM
ejpam-3279	42	3	]	]	X
ejpam-3279	42	4	at	at	ADP
ejpam-3279	42	5	each	each	DET
ejpam-3279	42	6	point	point	NOUN
ejpam-3279	42	7	p	p	X
ejpam-3279	42	8	∈	∈	PROPN
ejpam-3279	42	9	m	m	NOUN
ejpam-3279	42	10	,	,	PUNCT
ejpam-3279	42	11	we	we	PRON
ejpam-3279	42	12	can	can	AUX
ejpam-3279	42	13	construct	construct	VERB
ejpam-3279	42	14	a	a	DET
ejpam-3279	42	15	frame	frame	NOUN
ejpam-3279	42	16	in	in	ADP
ejpam-3279	42	17	t	t	PROPN
ejpam-3279	42	18	cp	cp	INTJ
ejpam-3279	42	19	(	(	PUNCT
ejpam-3279	42	20	m	m	VERB
ejpam-3279	42	21	)	)	PUNCT
ejpam-3279	42	22	by	by	ADP
ejpam-3279	42	23	the	the	DET
ejpam-3279	42	24	form	form	NOUN
ejpam-3279	42	25	(	(	PUNCT
ejpam-3279	42	26	p	p	X
ejpam-3279	42	27	,	,	PUNCT
ejpam-3279	42	28	ε0	ε0	PROPN
ejpam-3279	42	29	,	,	PUNCT
ejpam-3279	42	30	ε1	ε1	PROPN
ejpam-3279	42	31	,	,	PUNCT
ejpam-3279	42	32	...	...	PUNCT
ejpam-3279	42	33	,	,	PUNCT
ejpam-3279	42	34	εn	εn	ADJ
ejpam-3279	42	35	,	,	PUNCT
ejpam-3279	42	36	ε1̂	ε1̂	NOUN
ejpam-3279	42	37	,	,	PUNCT
ejpam-3279	42	38	...	...	PUNCT
ejpam-3279	42	39	,	,	PUNCT
ejpam-3279	42	40	εn̂	εn̂	PROPN
ejpam-3279	42	41	)	)	PUNCT
ejpam-3279	42	42	,	,	PUNCT
ejpam-3279	42	43	where	where	SCONJ
ejpam-3279	42	44	εa	εa	NOUN
ejpam-3279	42	45	=	=	PUNCT
ejpam-3279	42	46	√	√	PROPN
ejpam-3279	42	47	2σp(ep	2σp(ep	NUM
ejpam-3279	42	48	)	)	PUNCT
ejpam-3279	42	49	,	,	PUNCT
ejpam-3279	42	50	εâ	εâ	PROPN
ejpam-3279	42	51	=	=	SYM
ejpam-3279	42	52	√	√	NUM
ejpam-3279	42	53	2σ̄(ep	2σ̄(ep	PROPN
ejpam-3279	42	54	)	)	PUNCT
ejpam-3279	42	55	and	and	CCONJ
ejpam-3279	42	56	ε0	ε0	PROPN
ejpam-3279	42	57	=	=	PUNCT
ejpam-3279	42	58	ξp	ξp	PROPN
ejpam-3279	42	59	.	.	PUNCT
ejpam-3279	43	1	the	the	DET
ejpam-3279	43	2	frame	frame	NOUN
ejpam-3279	43	3	(	(	PUNCT
ejpam-3279	43	4	p	p	X
ejpam-3279	43	5	,	,	PUNCT
ejpam-3279	43	6	ε0	ε0	PROPN
ejpam-3279	43	7	,	,	PUNCT
ejpam-3279	43	8	ε1	ε1	PROPN
ejpam-3279	43	9	,	,	PUNCT
ejpam-3279	43	10	...	...	PUNCT
ejpam-3279	43	11	,	,	PUNCT
ejpam-3279	43	12	εn	εn	ADJ
ejpam-3279	43	13	,	,	PUNCT
ejpam-3279	43	14	ε1̂	ε1̂	NOUN
ejpam-3279	43	15	,	,	PUNCT
ejpam-3279	43	16	...	...	PUNCT
ejpam-3279	43	17	,	,	PUNCT
ejpam-3279	43	18	εn̂	εn̂	PROPN
ejpam-3279	43	19	)	)	PUNCT
ejpam-3279	43	20	is	be	AUX
ejpam-3279	43	21	called	call	VERB
ejpam-3279	43	22	an	an	DET
ejpam-3279	43	23	a	a	DET
ejpam-3279	43	24	-	-	PUNCT
ejpam-3279	43	25	frame	frame	NOUN
ejpam-3279	43	26	.	.	PUNCT
ejpam-3279	44	1	the	the	DET
ejpam-3279	44	2	principle	principle	ADJ
ejpam-3279	44	3	fiber	fiber	NOUN
ejpam-3279	44	4	bundle	bundle	NOUN
ejpam-3279	44	5	of	of	ADP
ejpam-3279	44	6	all	all	DET
ejpam-3279	44	7	a	a	DET
ejpam-3279	44	8	-	-	PUNCT
ejpam-3279	44	9	frames	frame	NOUN
ejpam-3279	44	10	with	with	ADP
ejpam-3279	44	11	structure	structure	NOUN
ejpam-3279	44	12	group	group	NOUN
ejpam-3279	44	13	{	{	PUNCT
ejpam-3279	44	14	1	1	NUM
ejpam-3279	44	15	}	}	PUNCT
ejpam-3279	44	16	×	×	PROPN
ejpam-3279	44	17	u(n	u(n	PROPN
ejpam-3279	44	18	)	)	PUNCT
ejpam-3279	44	19	is	be	AUX
ejpam-3279	44	20	called	call	VERB
ejpam-3279	44	21	an	an	DET
ejpam-3279	44	22	g	g	NOUN
ejpam-3279	44	23	-	-	PUNCT
ejpam-3279	44	24	adjoined	adjoin	VERB
ejpam-3279	44	25	structure	structure	NOUN
ejpam-3279	44	26	space	space	NOUN
ejpam-3279	44	27	.	.	PUNCT
ejpam-3279	45	1	lemma	lemma	PROPN
ejpam-3279	45	2	2.1	2.1	NUM
ejpam-3279	45	3	.	.	PUNCT
ejpam-3279	46	1	[	[	X
ejpam-3279	46	2	13	13	NUM
ejpam-3279	46	3	]	]	PUNCT
ejpam-3279	46	4	given	give	VERB
ejpam-3279	46	5	an	an	DET
ejpam-3279	46	6	ac	ac	ADJ
ejpam-3279	46	7	-	-	ADJ
ejpam-3279	46	8	manifold	manifold	ADJ
ejpam-3279	46	9	.	.	PUNCT
ejpam-3279	47	1	then	then	ADV
ejpam-3279	47	2	the	the	DET
ejpam-3279	47	3	matrices	matrix	NOUN
ejpam-3279	47	4	of	of	ADP
ejpam-3279	47	5	the	the	DET
ejpam-3279	47	6	tensors	tensor	NOUN
ejpam-3279	47	7	φ	φ	X
ejpam-3279	47	8	and	and	CCONJ
ejpam-3279	47	9	riemannian	riemannian	ADJ
ejpam-3279	47	10	metric	metric	ADJ
ejpam-3279	47	11	g	g	NOUN
ejpam-3279	47	12	in	in	ADP
ejpam-3279	47	13	a	a	DET
ejpam-3279	47	14	-	-	PUNCT
ejpam-3279	47	15	frame	frame	NOUN
ejpam-3279	47	16	are	be	AUX
ejpam-3279	47	17	given	give	VERB
ejpam-3279	47	18	by	by	ADP
ejpam-3279	47	19	the	the	DET
ejpam-3279	47	20	following	follow	VERB
ejpam-3279	47	21	forms	form	NOUN
ejpam-3279	47	22	:	:	PUNCT
ejpam-3279	47	23	(	(	PUNCT
ejpam-3279	47	24	φij	φij	NOUN
ejpam-3279	47	25	)	)	PUNCT
ejpam-3279	47	26	=	=	SYM
ejpam-3279	48	1			PROPN
ejpam-3279	48	2	0	0	NUM
ejpam-3279	48	3	0	0	NUM
ejpam-3279	48	4	0	0	NUM
ejpam-3279	48	5	0	0	NUM
ejpam-3279	48	6	√	√	NUM
ejpam-3279	48	7	−1	−1	NOUN
ejpam-3279	48	8	in	in	ADP
ejpam-3279	48	9	o	o	PROPN
ejpam-3279	48	10	0	0	NUM
ejpam-3279	48	11	0	0	NUM
ejpam-3279	48	12	−	−	NOUN
ejpam-3279	48	13	√	√	NUM
ejpam-3279	48	14	−1	−1	NOUN
ejpam-3279	48	15	in	in	ADP
ejpam-3279	48	16			PROPN
ejpam-3279	48	17	,	,	PUNCT
ejpam-3279	48	18	(	(	PUNCT
ejpam-3279	48	19	gij	gij	NOUN
ejpam-3279	48	20	)	)	PUNCT
ejpam-3279	48	21	=	=	SYM
ejpam-3279	49	1			PROPN
ejpam-3279	49	2	1	1	NUM
ejpam-3279	49	3	0	0	NUM
ejpam-3279	49	4	0	0	NUM
ejpam-3279	49	5	0	0	NUM
ejpam-3279	49	6	0	0	NUM
ejpam-3279	50	1	−in	−in	NOUN
ejpam-3279	50	2	0	0	NUM
ejpam-3279	50	3	in	in	ADP
ejpam-3279	50	4	0	0	NUM
ejpam-3279	50	5			PROPN
ejpam-3279	50	6	,	,	PUNCT
ejpam-3279	50	7	where	where	SCONJ
ejpam-3279	50	8	in	in	ADP
ejpam-3279	50	9	is	be	AUX
ejpam-3279	50	10	the	the	DET
ejpam-3279	50	11	identity	identity	NOUN
ejpam-3279	50	12	matrix	matrix	NOUN
ejpam-3279	50	13	of	of	ADP
ejpam-3279	50	14	order	order	NOUN
ejpam-3279	50	15	n.	n.	PROPN
ejpam-3279	50	16	n.	n.	PROPN
ejpam-3279	50	17	j.	j.	PROPN
ejpam-3279	50	18	mohammed	mohammed	PROPN
ejpam-3279	50	19	,	,	PUNCT
ejpam-3279	50	20	h.	h.	PROPN
ejpam-3279	50	21	m.	m.	PROPN
ejpam-3279	50	22	abood	abood	PROPN
ejpam-3279	50	23	/	/	SYM
ejpam-3279	50	24	eur	eur	PROPN
ejpam-3279	50	25	.	.	PUNCT
ejpam-3279	51	1	j.	j.	PROPN
ejpam-3279	51	2	pure	pure	PROPN
ejpam-3279	51	3	appl	appl	PROPN
ejpam-3279	51	4	.	.	PROPN
ejpam-3279	51	5	math	math	PROPN
ejpam-3279	51	6	,	,	PUNCT
ejpam-3279	51	7	11	11	NUM
ejpam-3279	51	8	(	(	PUNCT
ejpam-3279	51	9	3	3	NUM
ejpam-3279	51	10	)	)	PUNCT
ejpam-3279	51	11	(	(	PUNCT
ejpam-3279	51	12	2018	2018	NUM
ejpam-3279	51	13	)	)	PUNCT
ejpam-3279	51	14	,	,	PUNCT
ejpam-3279	51	15	823	823	NUM
ejpam-3279	51	16	-	-	SYM
ejpam-3279	51	17	833	833	NUM
ejpam-3279	51	18	825	825	NUM
ejpam-3279	51	19	the	the	DET
ejpam-3279	51	20	following	follow	VERB
ejpam-3279	51	21	theorem	theorem	NOUN
ejpam-3279	51	22	describes	describe	VERB
ejpam-3279	51	23	the	the	DET
ejpam-3279	51	24	structure	structure	NOUN
ejpam-3279	51	25	equations	equation	NOUN
ejpam-3279	51	26	of	of	ADP
ejpam-3279	51	27	nc	nc	PROPN
ejpam-3279	51	28	-	-	ADJ
ejpam-3279	51	29	manifold	manifold	ADJ
ejpam-3279	51	30	in	in	ADP
ejpam-3279	51	31	the	the	DET
ejpam-3279	51	32	gadjoined	gadjoined	ADJ
ejpam-3279	51	33	structure	structure	NOUN
ejpam-3279	51	34	space	space	NOUN
ejpam-3279	51	35	.	.	PUNCT
ejpam-3279	52	1	theorem	theorem	VERB
ejpam-3279	52	2	2.1	2.1	NUM
ejpam-3279	52	3	.	.	PUNCT
ejpam-3279	53	1	[	[	X
ejpam-3279	53	2	14	14	NUM
ejpam-3279	53	3	]	]	PUNCT
ejpam-3279	53	4	in	in	ADP
ejpam-3279	53	5	g	g	NOUN
ejpam-3279	53	6	-	-	PUNCT
ejpam-3279	53	7	adjoined	adjoin	VERB
ejpam-3279	53	8	structure	structure	NOUN
ejpam-3279	53	9	space	space	NOUN
ejpam-3279	53	10	,	,	PUNCT
ejpam-3279	53	11	the	the	DET
ejpam-3279	53	12	structure	structure	NOUN
ejpam-3279	53	13	equations	equation	NOUN
ejpam-3279	53	14	of	of	ADP
ejpam-3279	53	15	nc	nc	PROPN
ejpam-3279	53	16	-	-	ADJ
ejpam-3279	53	17	manifold	manifold	NOUN
ejpam-3279	53	18	are	be	AUX
ejpam-3279	53	19	given	give	VERB
ejpam-3279	53	20	by	by	ADP
ejpam-3279	53	21	the	the	DET
ejpam-3279	53	22	following	follow	VERB
ejpam-3279	53	23	forms	form	NOUN
ejpam-3279	53	24	:	:	PUNCT
ejpam-3279	53	25	(	(	PUNCT
ejpam-3279	53	26	i	i	NOUN
ejpam-3279	53	27	)	)	PUNCT
ejpam-3279	53	28	dωa	dωa	PROPN
ejpam-3279	53	29	=	=	PUNCT
ejpam-3279	53	30	ωab	ωab	X
ejpam-3279	53	31	∧	∧	PROPN
ejpam-3279	53	32	ωb	ωb	PROPN
ejpam-3279	54	1	+	+	NOUN
ejpam-3279	54	2	babcωb	babcωb	PROPN
ejpam-3279	54	3	∧	∧	PROPN
ejpam-3279	54	4	ωc	ωc	INTJ
ejpam-3279	54	5	+	+	CCONJ
ejpam-3279	54	6	3	3	NUM
ejpam-3279	54	7	2c	2c	NUM
ejpam-3279	54	8	abωb	abωb	NOUN
ejpam-3279	54	9	∧	∧	PROPN
ejpam-3279	54	10	ω	ω	PROPN
ejpam-3279	54	11	;	;	PUNCT
ejpam-3279	54	12	(	(	PUNCT
ejpam-3279	54	13	ii	ii	NOUN
ejpam-3279	54	14	)	)	PUNCT
ejpam-3279	54	15	dωa	dωa	NOUN
ejpam-3279	54	16	=	=	SYM
ejpam-3279	54	17	−ωba	−ωba	NOUN
ejpam-3279	54	18	∧	∧	PROPN
ejpam-3279	54	19	ωb	ωb	ADP
ejpam-3279	54	20	+	+	NOUN
ejpam-3279	54	21	babcω	babcω	NOUN
ejpam-3279	54	22	b	b	X
ejpam-3279	54	23	∧	∧	PROPN
ejpam-3279	54	24	ωc	ωc	INTJ
ejpam-3279	54	25	+	+	NOUN
ejpam-3279	54	26	3	3	NUM
ejpam-3279	54	27	2cabω	2cabω	NUM
ejpam-3279	54	28	b	b	PROPN
ejpam-3279	54	29	∧	∧	PROPN
ejpam-3279	54	30	ω	ω	PROPN
ejpam-3279	54	31	;	;	PUNCT
ejpam-3279	54	32	(	(	PUNCT
ejpam-3279	54	33	iii	iii	X
ejpam-3279	54	34	)	)	PUNCT
ejpam-3279	54	35	dω	dω	NOUN
ejpam-3279	54	36	=	=	PUNCT
ejpam-3279	54	37	cbcωb	cbcωb	PROPN
ejpam-3279	54	38	∧	∧	PROPN
ejpam-3279	54	39	ωc	ωc	ADP
ejpam-3279	54	40	+	+	CCONJ
ejpam-3279	54	41	cbcω	cbcω	ADJ
ejpam-3279	54	42	b	b	X
ejpam-3279	54	43	∧	∧	PROPN
ejpam-3279	54	44	ωc	ωc	X
ejpam-3279	54	45	;	;	PUNCT
ejpam-3279	54	46	(	(	PUNCT
ejpam-3279	54	47	iv	iv	X
ejpam-3279	54	48	)	)	PUNCT
ejpam-3279	54	49	dωab	dωab	NOUN
ejpam-3279	54	50	=	=	SYM
ejpam-3279	54	51	ωac	ωac	NOUN
ejpam-3279	54	52	∧	∧	NOUN
ejpam-3279	54	53	ωcb	ωcb	VERB
ejpam-3279	54	54	+	+	CCONJ
ejpam-3279	55	1	[	[	X
ejpam-3279	55	2	aadbc	aadbc	NOUN
ejpam-3279	55	3	−	−	PROPN
ejpam-3279	55	4	2badhbhbc	2badhbhbc	NUM
ejpam-3279	55	5	+	+	CCONJ
ejpam-3279	55	6	3	3	NUM
ejpam-3279	55	7	2c	2c	NUM
ejpam-3279	55	8	adcbc]ω	adcbc]ω	NOUN
ejpam-3279	55	9	c	c	NOUN
ejpam-3279	55	10	∧	∧	NOUN
ejpam-3279	55	11	ωd	ωd	INTJ
ejpam-3279	55	12	,	,	PUNCT
ejpam-3279	55	13	where	where	SCONJ
ejpam-3279	55	14	babc	babc	PROPN
ejpam-3279	55	15	=	=	NOUN
ejpam-3279	55	16	√	√	NUM
ejpam-3279	55	17	−1	−1	NOUN
ejpam-3279	55	18	2	2	NUM
ejpam-3279	55	19	φa	φa	ADP
ejpam-3279	55	20	b̂,ĉ	b̂,ĉ	PROPN
ejpam-3279	55	21	,	,	PUNCT
ejpam-3279	55	22	cab	cab	NOUN
ejpam-3279	55	23	=	=	SYM
ejpam-3279	55	24	√	√	PROPN
ejpam-3279	55	25	−1φa	−1φa	PROPN
ejpam-3279	55	26	0,b̂	0,b̂	NOUN
ejpam-3279	55	27	,	,	PUNCT
ejpam-3279	55	28	cab	cab	NOUN
ejpam-3279	55	29	=	=	SYM
ejpam-3279	55	30	−	−	NOUN
ejpam-3279	55	31	√	√	PROPN
ejpam-3279	55	32	−1φâb,0	−1φâb,0	NOUN
ejpam-3279	55	33	and	and	CCONJ
ejpam-3279	55	34	babc	babc	PROPN
ejpam-3279	55	35	=	=	SYM
ejpam-3279	56	1	−	−	PROPN
ejpam-3279	56	2	√	√	NUM
ejpam-3279	56	3	−1	−1	NOUN
ejpam-3279	56	4	2	2	NUM
ejpam-3279	56	5	φâb	φâb	PROPN
ejpam-3279	56	6	,	,	PUNCT
ejpam-3279	56	7	c.	c.	NOUN
ejpam-3279	56	8	the	the	DET
ejpam-3279	56	9	tensors	tensor	NOUN
ejpam-3279	56	10	b	b	NUM
ejpam-3279	56	11	,	,	PUNCT
ejpam-3279	56	12	c	c	PROPN
ejpam-3279	56	13	and	and	CCONJ
ejpam-3279	56	14	a	a	PRON
ejpam-3279	56	15	are	be	AUX
ejpam-3279	56	16	called	call	VERB
ejpam-3279	56	17	the	the	DET
ejpam-3279	56	18	first	first	ADJ
ejpam-3279	56	19	,	,	PUNCT
ejpam-3279	56	20	second	second	ADJ
ejpam-3279	56	21	and	and	CCONJ
ejpam-3279	56	22	third	third	ADJ
ejpam-3279	56	23	structure	structure	NOUN
ejpam-3279	56	24	tensors	tensor	NOUN
ejpam-3279	56	25	respectively	respectively	ADV
ejpam-3279	56	26	.	.	PUNCT
ejpam-3279	57	1	definition	definition	NOUN
ejpam-3279	57	2	2.5	2.5	NUM
ejpam-3279	57	3	.	.	PUNCT
ejpam-3279	58	1	[	[	X
ejpam-3279	58	2	16	16	NUM
ejpam-3279	58	3	]	]	PUNCT
ejpam-3279	58	4	a	a	DET
ejpam-3279	58	5	riemann	riemann	PROPN
ejpam-3279	58	6	-	-	PUNCT
ejpam-3279	58	7	christoffel	christoffel	NOUN
ejpam-3279	58	8	tensor	tensor	NOUN
ejpam-3279	58	9	of	of	ADP
ejpam-3279	58	10	a	a	DET
ejpam-3279	58	11	smooth	smooth	ADJ
ejpam-3279	58	12	manifold	manifold	NOUN
ejpam-3279	58	13	m	m	VERB
ejpam-3279	58	14	is	be	AUX
ejpam-3279	58	15	a	a	DET
ejpam-3279	58	16	tensor	tensor	NOUN
ejpam-3279	58	17	of	of	ADP
ejpam-3279	58	18	type	type	NOUN
ejpam-3279	58	19	(	(	PUNCT
ejpam-3279	58	20	4	4	NUM
ejpam-3279	58	21	,	,	PUNCT
ejpam-3279	58	22	0	0	NUM
ejpam-3279	58	23	)	)	PUNCT
ejpam-3279	58	24	which	which	PRON
ejpam-3279	58	25	is	be	AUX
ejpam-3279	58	26	defined	define	VERB
ejpam-3279	58	27	by	by	ADP
ejpam-3279	58	28	r(x	r(x	PROPN
ejpam-3279	58	29	,	,	PUNCT
ejpam-3279	58	30	y	y	PROPN
ejpam-3279	58	31	,	,	PUNCT
ejpam-3279	58	32	z	z	PROPN
ejpam-3279	58	33	,	,	PUNCT
ejpam-3279	58	34	w	w	PROPN
ejpam-3279	58	35	)	)	PUNCT
ejpam-3279	58	36	=	=	SYM
ejpam-3279	58	37	g(r(z	g(r(z	PROPN
ejpam-3279	58	38	,	,	PUNCT
ejpam-3279	58	39	w	w	NOUN
ejpam-3279	58	40	)	)	PUNCT
ejpam-3279	58	41	y	y	PROPN
ejpam-3279	58	42	,	,	PUNCT
ejpam-3279	58	43	x	x	NOUN
ejpam-3279	58	44	)	)	PUNCT
ejpam-3279	58	45	,	,	PUNCT
ejpam-3279	58	46	where	where	SCONJ
ejpam-3279	58	47	r(x	r(x	PROPN
ejpam-3279	58	48	,	,	PUNCT
ejpam-3279	58	49	y	y	NOUN
ejpam-3279	58	50	)	)	PUNCT
ejpam-3279	58	51	z	z	NOUN
ejpam-3279	59	1	=	=	SYM
ejpam-3279	59	2	(	(	PUNCT
ejpam-3279	59	3	[	[	X
ejpam-3279	59	4	∇x	∇x	NOUN
ejpam-3279	59	5	,	,	PUNCT
ejpam-3279	59	6	∇y	∇y	PROPN
ejpam-3279	59	7	]	]	X
ejpam-3279	59	8	−∇[x	−∇[x	PROPN
ejpam-3279	59	9	,	,	PUNCT
ejpam-3279	59	10	y	y	PROPN
ejpam-3279	59	11	]	]	X
ejpam-3279	59	12	)	)	PUNCT
ejpam-3279	59	13	z	z	NOUN
ejpam-3279	59	14	,	,	PUNCT
ejpam-3279	59	15	and	and	CCONJ
ejpam-3279	59	16	satisfies	satisfy	VERB
ejpam-3279	59	17	the	the	DET
ejpam-3279	59	18	following	follow	VERB
ejpam-3279	59	19	properties	property	NOUN
ejpam-3279	59	20	:	:	PUNCT
ejpam-3279	59	21	(	(	PUNCT
ejpam-3279	59	22	i	i	NOUN
ejpam-3279	59	23	)	)	PUNCT
ejpam-3279	59	24	r(x	r(x	PROPN
ejpam-3279	59	25	,	,	PUNCT
ejpam-3279	59	26	y	y	PROPN
ejpam-3279	59	27	,	,	PUNCT
ejpam-3279	59	28	z	z	PROPN
ejpam-3279	59	29	,	,	PUNCT
ejpam-3279	59	30	w	w	NOUN
ejpam-3279	59	31	)	)	PUNCT
ejpam-3279	59	32	=	=	SYM
ejpam-3279	60	1	−r(y	−r(y	VERB
ejpam-3279	60	2	,	,	PUNCT
ejpam-3279	60	3	x	x	NOUN
ejpam-3279	60	4	,	,	PUNCT
ejpam-3279	60	5	z	z	PROPN
ejpam-3279	60	6	,	,	PUNCT
ejpam-3279	60	7	w	w	PROPN
ejpam-3279	60	8	)	)	PUNCT
ejpam-3279	60	9	(	(	PUNCT
ejpam-3279	60	10	ii	ii	NOUN
ejpam-3279	60	11	)	)	PUNCT
ejpam-3279	60	12	r(x	r(x	PROPN
ejpam-3279	60	13	,	,	PUNCT
ejpam-3279	60	14	y	y	PROPN
ejpam-3279	60	15	,	,	PUNCT
ejpam-3279	60	16	z	z	PROPN
ejpam-3279	60	17	,	,	PUNCT
ejpam-3279	60	18	w	w	NOUN
ejpam-3279	60	19	)	)	PUNCT
ejpam-3279	60	20	=	=	SYM
ejpam-3279	60	21	−r(x	−r(x	PROPN
ejpam-3279	60	22	,	,	PUNCT
ejpam-3279	60	23	y	y	PROPN
ejpam-3279	60	24	,	,	PUNCT
ejpam-3279	60	25	w	w	PROPN
ejpam-3279	60	26	,	,	PUNCT
ejpam-3279	60	27	z	z	NOUN
ejpam-3279	60	28	)	)	PUNCT
ejpam-3279	60	29	(	(	PUNCT
ejpam-3279	60	30	iii	iii	X
ejpam-3279	60	31	)	)	PUNCT
ejpam-3279	60	32	r(x	r(x	PROPN
ejpam-3279	60	33	,	,	PUNCT
ejpam-3279	60	34	y	y	PROPN
ejpam-3279	60	35	,	,	PUNCT
ejpam-3279	60	36	z	z	PROPN
ejpam-3279	60	37	,	,	PUNCT
ejpam-3279	60	38	w	w	NOUN
ejpam-3279	60	39	)	)	PUNCT
ejpam-3279	60	40	=	=	SYM
ejpam-3279	60	41	r(z	r(z	PROPN
ejpam-3279	60	42	,	,	PUNCT
ejpam-3279	60	43	w	w	PROPN
ejpam-3279	60	44	,	,	PUNCT
ejpam-3279	60	45	x	x	NOUN
ejpam-3279	60	46	,	,	PUNCT
ejpam-3279	60	47	y	y	PROPN
ejpam-3279	60	48	)	)	PUNCT
ejpam-3279	60	49	(	(	PUNCT
ejpam-3279	60	50	iv	iv	X
ejpam-3279	60	51	)	)	PUNCT
ejpam-3279	60	52	r(x	r(x	PROPN
ejpam-3279	60	53	,	,	PUNCT
ejpam-3279	60	54	y	y	PROPN
ejpam-3279	60	55	,	,	PUNCT
ejpam-3279	60	56	z	z	PROPN
ejpam-3279	60	57	,	,	PUNCT
ejpam-3279	60	58	w	w	PROPN
ejpam-3279	60	59	)	)	PUNCT
ejpam-3279	61	1	+	+	PROPN
ejpam-3279	61	2	r(x	r(x	PROPN
ejpam-3279	61	3	,	,	PUNCT
ejpam-3279	61	4	z	z	PROPN
ejpam-3279	61	5	,	,	PUNCT
ejpam-3279	61	6	w	w	PROPN
ejpam-3279	61	7	,	,	PUNCT
ejpam-3279	61	8	y	y	PROPN
ejpam-3279	61	9	)	)	PUNCT
ejpam-3279	61	10	+	+	PUNCT
ejpam-3279	61	11	r(x	r(x	PROPN
ejpam-3279	61	12	,	,	PUNCT
ejpam-3279	61	13	w	w	PROPN
ejpam-3279	61	14	,	,	PUNCT
ejpam-3279	61	15	y	y	PROPN
ejpam-3279	61	16	,	,	PUNCT
ejpam-3279	61	17	z	z	NOUN
ejpam-3279	61	18	)	)	PUNCT
ejpam-3279	61	19	=	=	SYM
ejpam-3279	61	20	0	0	X
ejpam-3279	61	21	.	.	PUNCT
ejpam-3279	62	1	the	the	DET
ejpam-3279	62	2	components	component	NOUN
ejpam-3279	62	3	of	of	ADP
ejpam-3279	62	4	riemann	riemann	PROPN
ejpam-3279	62	5	-	-	PUNCT
ejpam-3279	62	6	christoffel	christoffel	NOUN
ejpam-3279	62	7	tensor	tensor	NOUN
ejpam-3279	62	8	of	of	ADP
ejpam-3279	62	9	nc	nc	PROPN
ejpam-3279	62	10	-	-	ADJ
ejpam-3279	62	11	manifold	manifold	NOUN
ejpam-3279	62	12	are	be	AUX
ejpam-3279	62	13	given	give	VERB
ejpam-3279	62	14	in	in	ADP
ejpam-3279	62	15	theorem	theorem	ADJ
ejpam-3279	62	16	below	below	ADV
ejpam-3279	62	17	.	.	PUNCT
ejpam-3279	63	1	theorem	theorem	VERB
ejpam-3279	63	2	2.2	2.2	NUM
ejpam-3279	63	3	.	.	PUNCT
ejpam-3279	64	1	[	[	X
ejpam-3279	64	2	14	14	NUM
ejpam-3279	64	3	]	]	PUNCT
ejpam-3279	64	4	in	in	ADP
ejpam-3279	64	5	the	the	DET
ejpam-3279	64	6	g	g	NOUN
ejpam-3279	64	7	-	-	PUNCT
ejpam-3279	64	8	adjoined	adjoin	VERB
ejpam-3279	64	9	structure	structure	NOUN
ejpam-3279	64	10	space	space	NOUN
ejpam-3279	64	11	,	,	PUNCT
ejpam-3279	64	12	the	the	DET
ejpam-3279	64	13	components	component	NOUN
ejpam-3279	64	14	of	of	ADP
ejpam-3279	64	15	riemannchristoffel	riemannchristoffel	PROPN
ejpam-3279	64	16	tensor	tensor	NOUN
ejpam-3279	64	17	of	of	ADP
ejpam-3279	64	18	nc	nc	PROPN
ejpam-3279	64	19	-	-	ADJ
ejpam-3279	64	20	manifold	manifold	NOUN
ejpam-3279	64	21	have	have	VERB
ejpam-3279	64	22	the	the	DET
ejpam-3279	64	23	following	follow	VERB
ejpam-3279	64	24	forms	form	NOUN
ejpam-3279	64	25	:	:	PUNCT
ejpam-3279	64	26	(	(	PUNCT
ejpam-3279	64	27	i	i	NOUN
ejpam-3279	64	28	)	)	PUNCT
ejpam-3279	64	29	râbcd	râbcd	VERB
ejpam-3279	64	30	=	=	SYM
ejpam-3279	64	31	0	0	NUM
ejpam-3279	64	32	;	;	PUNCT
ejpam-3279	64	33	(	(	PUNCT
ejpam-3279	64	34	ii	ii	NOUN
ejpam-3279	64	35	)	)	PUNCT
ejpam-3279	64	36	rabcd	rabcd	VERB
ejpam-3279	64	37	=	=	PUNCT
ejpam-3279	64	38	−2bab[cd	−2bab[cd	PROPN
ejpam-3279	64	39	]	]	X
ejpam-3279	64	40	;	;	PUNCT
ejpam-3279	64	41	(	(	PUNCT
ejpam-3279	64	42	iii	iii	X
ejpam-3279	64	43	)	)	PUNCT
ejpam-3279	64	44	râb̂cd	râb̂cd	NOUN
ejpam-3279	64	45	=	=	SYM
ejpam-3279	64	46	−2babhbhcd	−2babhbhcd	NOUN
ejpam-3279	64	47	;	;	PUNCT
ejpam-3279	64	48	(	(	PUNCT
ejpam-3279	64	49	iv	iv	X
ejpam-3279	64	50	)	)	PUNCT
ejpam-3279	64	51	râ0b0	râ0b0	PROPN
ejpam-3279	64	52	=	=	SYM
ejpam-3279	64	53	caccbc	caccbc	NOUN
ejpam-3279	64	54	;	;	PUNCT
ejpam-3279	64	55	(	(	PUNCT
ejpam-3279	64	56	v	v	NOUN
ejpam-3279	64	57	)	)	PUNCT
ejpam-3279	64	58	râbcd̂	râbcd̂	NOUN
ejpam-3279	64	59	=	=	SYM
ejpam-3279	64	60	aadbc	aadbc	NOUN
ejpam-3279	64	61	−badhbhbc	−badhbhbc	PROPN
ejpam-3279	64	62	−	−	PROPN
ejpam-3279	64	63	5	5	NUM
ejpam-3279	64	64	3c	3c	NUM
ejpam-3279	64	65	adcbc	adcbc	VERB
ejpam-3279	64	66	.	.	PUNCT
ejpam-3279	65	1	n.	n.	PROPN
ejpam-3279	65	2	j.	j.	PROPN
ejpam-3279	65	3	mohammed	mohammed	PROPN
ejpam-3279	65	4	,	,	PUNCT
ejpam-3279	65	5	h.	h.	PROPN
ejpam-3279	65	6	m.	m.	PROPN
ejpam-3279	65	7	abood	abood	PROPN
ejpam-3279	65	8	/	/	SYM
ejpam-3279	65	9	eur	eur	PROPN
ejpam-3279	65	10	.	.	PUNCT
ejpam-3279	66	1	j.	j.	PROPN
ejpam-3279	66	2	pure	pure	PROPN
ejpam-3279	66	3	appl	appl	PROPN
ejpam-3279	66	4	.	.	PROPN
ejpam-3279	66	5	math	math	PROPN
ejpam-3279	66	6	,	,	PUNCT
ejpam-3279	66	7	11	11	NUM
ejpam-3279	66	8	(	(	PUNCT
ejpam-3279	66	9	3	3	NUM
ejpam-3279	66	10	)	)	PUNCT
ejpam-3279	66	11	(	(	PUNCT
ejpam-3279	66	12	2018	2018	NUM
ejpam-3279	66	13	)	)	PUNCT
ejpam-3279	66	14	,	,	PUNCT
ejpam-3279	66	15	823	823	NUM
ejpam-3279	66	16	-	-	SYM
ejpam-3279	66	17	833	833	NUM
ejpam-3279	66	18	826	826	NUM
ejpam-3279	66	19	the	the	DET
ejpam-3279	66	20	other	other	ADJ
ejpam-3279	66	21	components	component	NOUN
ejpam-3279	66	22	of	of	ADP
ejpam-3279	66	23	riemann	riemann	PROPN
ejpam-3279	66	24	-	-	PUNCT
ejpam-3279	66	25	christoffel	christoffel	NOUN
ejpam-3279	66	26	tensor	tensor	NOUN
ejpam-3279	66	27	r	r	NOUN
ejpam-3279	66	28	can	can	AUX
ejpam-3279	66	29	be	be	AUX
ejpam-3279	66	30	obtained	obtain	VERB
ejpam-3279	66	31	by	by	ADP
ejpam-3279	66	32	the	the	DET
ejpam-3279	66	33	property	property	NOUN
ejpam-3279	66	34	of	of	ADP
ejpam-3279	66	35	symmetry	symmetry	NOUN
ejpam-3279	66	36	for	for	ADP
ejpam-3279	66	37	r	r	NOUN
ejpam-3279	66	38	or	or	CCONJ
ejpam-3279	66	39	equal	equal	ADJ
ejpam-3279	66	40	to	to	ADP
ejpam-3279	66	41	zero	zero	NUM
ejpam-3279	66	42	.	.	PUNCT
ejpam-3279	67	1	definition	definition	NOUN
ejpam-3279	67	2	2.6	2.6	NUM
ejpam-3279	67	3	.	.	PUNCT
ejpam-3279	68	1	[	[	X
ejpam-3279	68	2	18	18	NUM
ejpam-3279	68	3	]	]	PUNCT
ejpam-3279	68	4	a	a	DET
ejpam-3279	68	5	tensor	tensor	NOUN
ejpam-3279	68	6	of	of	ADP
ejpam-3279	68	7	type	type	NOUN
ejpam-3279	68	8	(	(	PUNCT
ejpam-3279	68	9	2	2	NUM
ejpam-3279	68	10	,	,	PUNCT
ejpam-3279	68	11	0	0	NUM
ejpam-3279	68	12	)	)	PUNCT
ejpam-3279	68	13	which	which	PRON
ejpam-3279	68	14	is	be	AUX
ejpam-3279	68	15	a	a	DET
ejpam-3279	68	16	contracting	contracting	NOUN
ejpam-3279	68	17	of	of	ADP
ejpam-3279	68	18	riemann	riemann	PROPN
ejpam-3279	68	19	-	-	PUNCT
ejpam-3279	68	20	christoffel	christoffel	NOUN
ejpam-3279	68	21	tensor	tensor	NOUN
ejpam-3279	68	22	and	and	CCONJ
ejpam-3279	68	23	defined	define	VERB
ejpam-3279	68	24	as	as	ADP
ejpam-3279	68	25	rij	rij	ADJ
ejpam-3279	68	26	=	=	SYM
ejpam-3279	68	27	rkijk	rkijk	NOUN
ejpam-3279	68	28	=	=	PUNCT
ejpam-3279	68	29	gklrkijl	gklrkijl	PROPN
ejpam-3279	68	30	is	be	AUX
ejpam-3279	68	31	called	call	VERB
ejpam-3279	68	32	a	a	DET
ejpam-3279	68	33	ricci	ricci	PROPN
ejpam-3279	68	34	tensor	tensor	NOUN
ejpam-3279	68	35	.	.	PUNCT
ejpam-3279	69	1	lemma	lemma	PROPN
ejpam-3279	69	2	2.2	2.2	NUM
ejpam-3279	69	3	.	.	PUNCT
ejpam-3279	70	1	[	[	X
ejpam-3279	70	2	14	14	NUM
ejpam-3279	70	3	]	]	PUNCT
ejpam-3279	70	4	in	in	ADP
ejpam-3279	70	5	the	the	DET
ejpam-3279	70	6	g	g	NOUN
ejpam-3279	70	7	-	-	PUNCT
ejpam-3279	70	8	adjoined	adjoin	VERB
ejpam-3279	70	9	structure	structure	NOUN
ejpam-3279	70	10	space	space	NOUN
ejpam-3279	70	11	,	,	PUNCT
ejpam-3279	70	12	the	the	DET
ejpam-3279	70	13	components	component	NOUN
ejpam-3279	70	14	of	of	ADP
ejpam-3279	70	15	ricci	ricci	PROPN
ejpam-3279	70	16	tensor	tensor	NOUN
ejpam-3279	70	17	of	of	ADP
ejpam-3279	70	18	nc	nc	PROPN
ejpam-3279	70	19	-	-	ADJ
ejpam-3279	70	20	manifold	manifold	NOUN
ejpam-3279	70	21	are	be	AUX
ejpam-3279	70	22	given	give	VERB
ejpam-3279	70	23	by	by	ADP
ejpam-3279	70	24	the	the	DET
ejpam-3279	70	25	following	follow	VERB
ejpam-3279	70	26	forms	form	NOUN
ejpam-3279	70	27	:	:	PUNCT
ejpam-3279	70	28	(	(	PUNCT
ejpam-3279	70	29	i	i	NOUN
ejpam-3279	70	30	)	)	PUNCT
ejpam-3279	70	31	rab	rab	PROPN
ejpam-3279	70	32	=	=	SYM
ejpam-3279	70	33	0	0	NUM
ejpam-3279	71	1	;	;	PUNCT
ejpam-3279	71	2	(	(	PUNCT
ejpam-3279	71	3	ii	ii	NOUN
ejpam-3279	71	4	)	)	PUNCT
ejpam-3279	71	5	rab̂	rab̂	PROPN
ejpam-3279	71	6	=	=	SYM
ejpam-3279	71	7	−acbac	−acbac	NOUN
ejpam-3279	71	8	+	+	CCONJ
ejpam-3279	72	1	3bcbhbhac	3bcbhbhac	NUM
ejpam-3279	72	2	+	+	NUM
ejpam-3279	72	3	2	2	NUM
ejpam-3279	72	4	3c	3c	NUM
ejpam-3279	72	5	bccac	bccac	NOUN
ejpam-3279	72	6	;	;	PUNCT
ejpam-3279	72	7	(	(	PUNCT
ejpam-3279	72	8	iii	iii	X
ejpam-3279	72	9	)	)	PUNCT
ejpam-3279	72	10	ra0	ra0	NOUN
ejpam-3279	72	11	=	=	SYM
ejpam-3279	72	12	0	0	NUM
ejpam-3279	72	13	;	;	PUNCT
ejpam-3279	72	14	(	(	PUNCT
ejpam-3279	72	15	iv	iv	X
ejpam-3279	72	16	)	)	PUNCT
ejpam-3279	72	17	roo	roo	PROPN
ejpam-3279	72	18	=	=	SYM
ejpam-3279	72	19	−2ccdccd	−2ccdccd	PROPN
ejpam-3279	72	20	.	.	PROPN
ejpam-3279	73	1	and	and	CCONJ
ejpam-3279	73	2	the	the	DET
ejpam-3279	73	3	others	other	NOUN
ejpam-3279	73	4	are	be	AUX
ejpam-3279	73	5	conjugate	conjugate	ADJ
ejpam-3279	73	6	to	to	ADP
ejpam-3279	73	7	the	the	DET
ejpam-3279	73	8	above	above	ADJ
ejpam-3279	73	9	components	component	NOUN
ejpam-3279	73	10	or	or	CCONJ
ejpam-3279	73	11	equal	equal	ADJ
ejpam-3279	73	12	to	to	ADP
ejpam-3279	73	13	zero	zero	NUM
ejpam-3279	73	14	.	.	PUNCT
ejpam-3279	74	1	the	the	DET
ejpam-3279	74	2	previous	previous	ADJ
ejpam-3279	74	3	definitions	definition	NOUN
ejpam-3279	74	4	of	of	ADP
ejpam-3279	74	5	riemann	riemann	PROPN
ejpam-3279	74	6	-	-	PUNCT
ejpam-3279	74	7	christoffel	christoffel	PROPN
ejpam-3279	74	8	and	and	CCONJ
ejpam-3279	74	9	ricci	ricci	PROPN
ejpam-3279	74	10	tensors	tensor	NOUN
ejpam-3279	74	11	completed	complete	VERB
ejpam-3279	74	12	the	the	DET
ejpam-3279	74	13	requirements	requirement	NOUN
ejpam-3279	74	14	of	of	ADP
ejpam-3279	74	15	the	the	DET
ejpam-3279	74	16	projective	projective	ADJ
ejpam-3279	74	17	tensor	tensor	NOUN
ejpam-3279	74	18	which	which	PRON
ejpam-3279	74	19	is	be	AUX
ejpam-3279	74	20	embodied	embody	VERB
ejpam-3279	74	21	in	in	ADP
ejpam-3279	74	22	the	the	DET
ejpam-3279	74	23	next	next	ADJ
ejpam-3279	74	24	definition	definition	NOUN
ejpam-3279	74	25	.	.	PUNCT
ejpam-3279	75	1	definition	definition	NOUN
ejpam-3279	75	2	2.7	2.7	NUM
ejpam-3279	75	3	.	.	PUNCT
ejpam-3279	76	1	[	[	X
ejpam-3279	76	2	10	10	NUM
ejpam-3279	76	3	]	]	PUNCT
ejpam-3279	76	4	let	let	AUX
ejpam-3279	76	5	m	m	PRON
ejpam-3279	76	6	be	be	AUX
ejpam-3279	76	7	an	an	DET
ejpam-3279	76	8	ac	ac	ADJ
ejpam-3279	76	9	-	-	ADJ
ejpam-3279	76	10	manifold	manifold	ADJ
ejpam-3279	76	11	.	.	PUNCT
ejpam-3279	77	1	a	a	DET
ejpam-3279	77	2	tensor	tensor	NOUN
ejpam-3279	77	3	of	of	ADP
ejpam-3279	77	4	type	type	NOUN
ejpam-3279	77	5	(	(	PUNCT
ejpam-3279	77	6	4	4	NUM
ejpam-3279	77	7	,	,	PUNCT
ejpam-3279	77	8	0	0	NUM
ejpam-3279	77	9	)	)	PUNCT
ejpam-3279	77	10	which	which	PRON
ejpam-3279	77	11	is	be	AUX
ejpam-3279	77	12	defined	define	VERB
ejpam-3279	77	13	as	as	ADP
ejpam-3279	77	14	pijkl	pijkl	NOUN
ejpam-3279	78	1	=	=	PRON
ejpam-3279	78	2	rijkl	rijkl	NOUN
ejpam-3279	78	3	−	−	NUM
ejpam-3279	78	4	1	1	NUM
ejpam-3279	78	5	2n	2n	NUM
ejpam-3279	79	1	[	[	X
ejpam-3279	79	2	rikgjl	rikgjl	NOUN
ejpam-3279	79	3	−	−	NOUN
ejpam-3279	79	4	rjkgil	rjkgil	NOUN
ejpam-3279	79	5	]	]	PUNCT
ejpam-3279	79	6	is	be	AUX
ejpam-3279	79	7	called	call	VERB
ejpam-3279	79	8	a	a	DET
ejpam-3279	79	9	projective	projective	ADJ
ejpam-3279	79	10	curvature	curvature	NOUN
ejpam-3279	79	11	tensor	tensor	NOUN
ejpam-3279	79	12	,	,	PUNCT
ejpam-3279	79	13	where	where	SCONJ
ejpam-3279	79	14	pijkl	pijkl	NOUN
ejpam-3279	79	15	=	=	NOUN
ejpam-3279	79	16	−pjikl	−pjikl	PROPN
ejpam-3279	79	17	=	=	SYM
ejpam-3279	79	18	−pijlk	−pijlk	NOUN
ejpam-3279	79	19	=	=	PUNCT
ejpam-3279	79	20	pklij	pklij	NOUN
ejpam-3279	79	21	.	.	PUNCT
ejpam-3279	80	1	we	we	PRON
ejpam-3279	80	2	will	will	AUX
ejpam-3279	80	3	demonstrate	demonstrate	VERB
ejpam-3279	80	4	the	the	DET
ejpam-3279	80	5	projective	projective	ADJ
ejpam-3279	80	6	tensor	tensor	NOUN
ejpam-3279	80	7	on	on	ADP
ejpam-3279	80	8	one	one	NUM
ejpam-3279	80	9	of	of	ADP
ejpam-3279	80	10	the	the	DET
ejpam-3279	80	11	ac	ac	PROPN
ejpam-3279	80	12	-manifolds	-manifold	NOUN
ejpam-3279	80	13	which	which	PRON
ejpam-3279	80	14	is	be	AUX
ejpam-3279	80	15	nc	nc	PROPN
ejpam-3279	80	16	manifold	manifold	PROPN
ejpam-3279	80	17	.	.	PUNCT
ejpam-3279	81	1	definition	definition	NOUN
ejpam-3279	81	2	2.8	2.8	NUM
ejpam-3279	81	3	.	.	PUNCT
ejpam-3279	82	1	[	[	X
ejpam-3279	82	2	12	12	NUM
ejpam-3279	82	3	]	]	X
ejpam-3279	82	4	an	an	DET
ejpam-3279	82	5	ac	ac	ADJ
ejpam-3279	82	6	-	-	ADJ
ejpam-3279	82	7	manifold	manifold	ADJ
ejpam-3279	82	8	m	m	VERB
ejpam-3279	82	9	is	be	AUX
ejpam-3279	82	10	called	call	VERB
ejpam-3279	82	11	vanishing	vanish	VERB
ejpam-3279	82	12	projective	projective	ADJ
ejpam-3279	82	13	tensor	tensor	NOUN
ejpam-3279	82	14	,	,	PUNCT
ejpam-3279	82	15	if	if	SCONJ
ejpam-3279	82	16	the	the	DET
ejpam-3279	82	17	projective	projective	ADJ
ejpam-3279	82	18	tensor	tensor	NOUN
ejpam-3279	82	19	is	be	AUX
ejpam-3279	82	20	vanishes	vanish	VERB
ejpam-3279	82	21	.	.	PUNCT
ejpam-3279	83	1	definition	definition	NOUN
ejpam-3279	83	2	2.9	2.9	NUM
ejpam-3279	83	3	.	.	PUNCT
ejpam-3279	84	1	an	an	DET
ejpam-3279	84	2	nc	nc	PROPN
ejpam-3279	84	3	-	-	ADJ
ejpam-3279	84	4	manifold	manifold	NOUN
ejpam-3279	84	5	has	have	VERB
ejpam-3279	84	6	φ	φ	VERB
ejpam-3279	84	7	-	-	PUNCT
ejpam-3279	84	8	invariant	invariant	ADJ
ejpam-3279	84	9	ricci	ricci	PROPN
ejpam-3279	84	10	tensor	tensor	NOUN
ejpam-3279	84	11	,	,	PUNCT
ejpam-3279	84	12	if	if	SCONJ
ejpam-3279	84	13	φ	φ	NUM
ejpam-3279	84	14	◦	◦	NOUN
ejpam-3279	84	15	r	r	NOUN
ejpam-3279	84	16	=	=	SYM
ejpam-3279	84	17	r	r	NOUN
ejpam-3279	84	18	◦	◦	NOUN
ejpam-3279	84	19	φ	φ	NOUN
ejpam-3279	84	20	.	.	PUNCT
ejpam-3279	85	1	lemma	lemma	PROPN
ejpam-3279	85	2	2.3	2.3	NUM
ejpam-3279	85	3	.	.	PUNCT
ejpam-3279	86	1	an	an	DET
ejpam-3279	86	2	nc	nc	PROPN
ejpam-3279	86	3	-	-	ADJ
ejpam-3279	86	4	manifold	manifold	NOUN
ejpam-3279	86	5	has	have	VERB
ejpam-3279	86	6	φ	φ	VERB
ejpam-3279	86	7	-	-	PUNCT
ejpam-3279	86	8	invariant	invariant	ADJ
ejpam-3279	86	9	ricci	ricci	PROPN
ejpam-3279	86	10	tensor	tensor	NOUN
ejpam-3279	86	11	if	if	SCONJ
ejpam-3279	86	12	and	and	CCONJ
ejpam-3279	86	13	only	only	ADV
ejpam-3279	86	14	if	if	SCONJ
ejpam-3279	86	15	,	,	PUNCT
ejpam-3279	86	16	in	in	ADP
ejpam-3279	86	17	the	the	DET
ejpam-3279	86	18	gadjoined	gadjoined	ADJ
ejpam-3279	86	19	structure	structure	NOUN
ejpam-3279	86	20	space	space	NOUN
ejpam-3279	86	21	the	the	DET
ejpam-3279	86	22	following	follow	VERB
ejpam-3279	86	23	condition	condition	NOUN
ejpam-3279	86	24	râb	râb	PROPN
ejpam-3279	86	25	=	=	SYM
ejpam-3279	86	26	rab	rab	PROPN
ejpam-3279	86	27	=	=	SYM
ejpam-3279	86	28	0	0	NUM
ejpam-3279	86	29	holds	hold	NOUN
ejpam-3279	86	30	.	.	PUNCT
ejpam-3279	87	1	definition	definition	NOUN
ejpam-3279	87	2	2.10	2.10	NUM
ejpam-3279	87	3	.	.	PUNCT
ejpam-3279	88	1	[	[	X
ejpam-3279	88	2	11	11	NUM
ejpam-3279	88	3	]	]	PUNCT
ejpam-3279	88	4	let	let	VERB
ejpam-3279	88	5	m	m	PRON
ejpam-3279	88	6	be	be	AUX
ejpam-3279	88	7	a	a	DET
ejpam-3279	88	8	riemannian	riemannian	ADJ
ejpam-3279	88	9	manifold	manifold	NOUN
ejpam-3279	88	10	,	,	PUNCT
ejpam-3279	88	11	t	t	PROPN
ejpam-3279	88	12	be	be	AUX
ejpam-3279	88	13	a	a	DET
ejpam-3279	88	14	non	non	ADJ
ejpam-3279	88	15	-	-	ADJ
ejpam-3279	88	16	zero	zero	NUM
ejpam-3279	88	17	tensor	tensor	NOUN
ejpam-3279	88	18	field	field	NOUN
ejpam-3279	88	19	of	of	ADP
ejpam-3279	88	20	the	the	DET
ejpam-3279	88	21	type	type	NOUN
ejpam-3279	88	22	(	(	PUNCT
ejpam-3279	88	23	r	r	NOUN
ejpam-3279	88	24	,	,	PUNCT
ejpam-3279	88	25	s	s	PART
ejpam-3279	88	26	)	)	PUNCT
ejpam-3279	88	27	on	on	ADP
ejpam-3279	88	28	m.	m.	NOUN
ejpam-3279	88	29	a	a	DET
ejpam-3279	88	30	tensor	tensor	NOUN
ejpam-3279	88	31	t	t	NOUN
ejpam-3279	88	32	is	be	AUX
ejpam-3279	88	33	said	say	VERB
ejpam-3279	88	34	to	to	PART
ejpam-3279	88	35	be	be	AUX
ejpam-3279	88	36	a	a	DET
ejpam-3279	88	37	recurrent	recurrent	NOUN
ejpam-3279	88	38	if	if	SCONJ
ejpam-3279	88	39	there	there	PRON
ejpam-3279	88	40	is	be	VERB
ejpam-3279	88	41	1	1	NUM
ejpam-3279	88	42	-	-	PUNCT
ejpam-3279	88	43	form	form	NOUN
ejpam-3279	88	44	ρ	ρ	NOUN
ejpam-3279	88	45	on	on	ADP
ejpam-3279	88	46	m	m	PRON
ejpam-3279	88	47	such	such	ADJ
ejpam-3279	88	48	that	that	PRON
ejpam-3279	88	49	∇t	∇t	PROPN
ejpam-3279	88	50	=	=	SYM
ejpam-3279	88	51	ρ	ρ	PROPN
ejpam-3279	88	52	⊗	⊗	PROPN
ejpam-3279	88	53	t	t	PROPN
ejpam-3279	88	54	,	,	PUNCT
ejpam-3279	88	55	where	where	SCONJ
ejpam-3279	88	56	∇	∇	PROPN
ejpam-3279	88	57	is	be	AUX
ejpam-3279	88	58	the	the	DET
ejpam-3279	88	59	riemannian	riemannian	ADJ
ejpam-3279	88	60	connection	connection	NOUN
ejpam-3279	88	61	on	on	ADP
ejpam-3279	88	62	m.	m.	NOUN
ejpam-3279	88	63	the	the	DET
ejpam-3279	88	64	1	1	NUM
ejpam-3279	88	65	-	-	PUNCT
ejpam-3279	88	66	form	form	NOUN
ejpam-3279	88	67	ρ	ρ	NOUN
ejpam-3279	88	68	is	be	AUX
ejpam-3279	88	69	called	call	VERB
ejpam-3279	88	70	a	a	DET
ejpam-3279	88	71	recurrence	recurrence	NOUN
ejpam-3279	88	72	covector	covector	NOUN
ejpam-3279	88	73	.	.	PUNCT
ejpam-3279	89	1	an	an	DET
ejpam-3279	89	2	nc	nc	PROPN
ejpam-3279	89	3	-	-	ADJ
ejpam-3279	89	4	manifold	manifold	NOUN
ejpam-3279	89	5	which	which	PRON
ejpam-3279	89	6	allows	allow	VERB
ejpam-3279	89	7	a	a	DET
ejpam-3279	89	8	field	field	NOUN
ejpam-3279	89	9	of	of	ADP
ejpam-3279	89	10	the	the	DET
ejpam-3279	89	11	recurrent	recurrent	ADJ
ejpam-3279	89	12	tensor	tensor	NOUN
ejpam-3279	89	13	t	t	PROPN
ejpam-3279	89	14	is	be	AUX
ejpam-3279	89	15	called	call	VERB
ejpam-3279	89	16	t	t	NOUN
ejpam-3279	89	17	-	-	PUNCT
ejpam-3279	89	18	recurrent	recurrent	NOUN
ejpam-3279	89	19	.	.	PUNCT
ejpam-3279	90	1	n.	n.	PROPN
ejpam-3279	90	2	j.	j.	PROPN
ejpam-3279	90	3	mohammed	mohammed	PROPN
ejpam-3279	90	4	,	,	PUNCT
ejpam-3279	90	5	h.	h.	PROPN
ejpam-3279	90	6	m.	m.	PROPN
ejpam-3279	90	7	abood	abood	PROPN
ejpam-3279	90	8	/	/	SYM
ejpam-3279	90	9	eur	eur	PROPN
ejpam-3279	90	10	.	.	PUNCT
ejpam-3279	91	1	j.	j.	PROPN
ejpam-3279	91	2	pure	pure	PROPN
ejpam-3279	91	3	appl	appl	PROPN
ejpam-3279	91	4	.	.	PROPN
ejpam-3279	91	5	math	math	PROPN
ejpam-3279	91	6	,	,	PUNCT
ejpam-3279	91	7	11	11	NUM
ejpam-3279	91	8	(	(	PUNCT
ejpam-3279	91	9	3	3	NUM
ejpam-3279	91	10	)	)	PUNCT
ejpam-3279	91	11	(	(	PUNCT
ejpam-3279	91	12	2018	2018	NUM
ejpam-3279	91	13	)	)	PUNCT
ejpam-3279	91	14	,	,	PUNCT
ejpam-3279	91	15	823	823	NUM
ejpam-3279	91	16	-	-	SYM
ejpam-3279	91	17	833	833	NUM
ejpam-3279	91	18	827	827	NUM
ejpam-3279	91	19	lemma	lemma	PROPN
ejpam-3279	91	20	2.4	2.4	NUM
ejpam-3279	91	21	.	.	PUNCT
ejpam-3279	92	1	[	[	X
ejpam-3279	92	2	11	11	NUM
ejpam-3279	92	3	]	]	PUNCT
ejpam-3279	92	4	if	if	SCONJ
ejpam-3279	92	5	ρ	ρ	PROPN
ejpam-3279	92	6	=	=	SYM
ejpam-3279	92	7	0	0	NUM
ejpam-3279	92	8	,	,	PUNCT
ejpam-3279	92	9	then	then	ADV
ejpam-3279	92	10	the	the	DET
ejpam-3279	92	11	manifold	manifold	NOUN
ejpam-3279	92	12	is	be	AUX
ejpam-3279	92	13	called	call	VERB
ejpam-3279	92	14	t	t	NOUN
ejpam-3279	92	15	-	-	PUNCT
ejpam-3279	92	16	symmetrical	symmetrical	ADJ
ejpam-3279	92	17	,	,	PUNCT
ejpam-3279	92	18	and	and	CCONJ
ejpam-3279	92	19	if	if	SCONJ
ejpam-3279	92	20	ρ	ρ	PROPN
ejpam-3279	92	21	6=	6=	NOUN
ejpam-3279	92	22	0	0	NUM
ejpam-3279	93	1	then	then	ADV
ejpam-3279	93	2	it	it	PRON
ejpam-3279	93	3	is	be	AUX
ejpam-3279	93	4	called	call	VERB
ejpam-3279	93	5	nontrivially	nontrivially	ADV
ejpam-3279	93	6	t	t	NOUN
ejpam-3279	93	7	-	-	PUNCT
ejpam-3279	93	8	symmetrical	symmetrical	ADJ
ejpam-3279	93	9	.	.	PUNCT
ejpam-3279	94	1	now	now	ADV
ejpam-3279	94	2	,	,	PUNCT
ejpam-3279	94	3	we	we	PRON
ejpam-3279	94	4	are	be	AUX
ejpam-3279	94	5	in	in	ADP
ejpam-3279	94	6	position	position	NOUN
ejpam-3279	94	7	to	to	PART
ejpam-3279	94	8	introduce	introduce	VERB
ejpam-3279	94	9	the	the	DET
ejpam-3279	94	10	next	next	ADJ
ejpam-3279	94	11	definition	definition	NOUN
ejpam-3279	94	12	.	.	PUNCT
ejpam-3279	95	1	definition	definition	NOUN
ejpam-3279	95	2	2.11	2.11	NUM
ejpam-3279	95	3	.	.	PUNCT
ejpam-3279	96	1	let	let	VERB
ejpam-3279	96	2	m	m	PRON
ejpam-3279	96	3	be	be	AUX
ejpam-3279	96	4	nc	nc	ADJ
ejpam-3279	96	5	-	-	ADJ
ejpam-3279	96	6	manifold	manifold	ADJ
ejpam-3279	96	7	,	,	PUNCT
ejpam-3279	96	8	m	m	VERB
ejpam-3279	96	9	is	be	AUX
ejpam-3279	96	10	called	call	VERB
ejpam-3279	96	11	pr	pr	NOUN
ejpam-3279	96	12	-	-	NOUN
ejpam-3279	96	13	recurrent	recurrent	NOUN
ejpam-3279	96	14	if	if	SCONJ
ejpam-3279	96	15	m	m	NOUN
ejpam-3279	96	16	is	be	AUX
ejpam-3279	96	17	p	p	ADJ
ejpam-3279	96	18	-	-	PUNCT
ejpam-3279	96	19	recurrent	recurrent	NOUN
ejpam-3279	96	20	and	and	CCONJ
ejpam-3279	96	21	r	r	NOUN
ejpam-3279	96	22	-	-	NOUN
ejpam-3279	96	23	recurrent	recurrent	NOUN
ejpam-3279	96	24	with	with	ADP
ejpam-3279	96	25	the	the	DET
ejpam-3279	96	26	same	same	ADJ
ejpam-3279	96	27	recurrence	recurrence	NOUN
ejpam-3279	96	28	convector	convector	NOUN
ejpam-3279	96	29	.	.	PUNCT
ejpam-3279	97	1	definition	definition	NOUN
ejpam-3279	97	2	2.12	2.12	NUM
ejpam-3279	97	3	.	.	PUNCT
ejpam-3279	98	1	[	[	X
ejpam-3279	98	2	17	17	NUM
ejpam-3279	98	3	]	]	PUNCT
ejpam-3279	98	4	a	a	DET
ejpam-3279	98	5	riemannian	riemannian	ADJ
ejpam-3279	98	6	manifold	manifold	NOUN
ejpam-3279	98	7	is	be	AUX
ejpam-3279	98	8	called	call	VERB
ejpam-3279	98	9	an	an	DET
ejpam-3279	98	10	einstein	einstein	NOUN
ejpam-3279	98	11	manifold	manifold	NOUN
ejpam-3279	98	12	,	,	PUNCT
ejpam-3279	98	13	if	if	SCONJ
ejpam-3279	98	14	the	the	DET
ejpam-3279	98	15	ricci	ricci	PROPN
ejpam-3279	98	16	tensor	tensor	NOUN
ejpam-3279	98	17	satisfies	satisfy	VERB
ejpam-3279	98	18	the	the	DET
ejpam-3279	98	19	equation	equation	NOUN
ejpam-3279	98	20	rij	rij	X
ejpam-3279	98	21	=	=	SYM
ejpam-3279	98	22	egij	egij	NOUN
ejpam-3279	98	23	,	,	PUNCT
ejpam-3279	98	24	where	where	SCONJ
ejpam-3279	98	25	,	,	PUNCT
ejpam-3279	98	26	e	e	PROPN
ejpam-3279	98	27	is	be	AUX
ejpam-3279	98	28	an	an	DET
ejpam-3279	98	29	einstein	einstein	ADJ
ejpam-3279	98	30	constant	constant	NOUN
ejpam-3279	98	31	.	.	PUNCT
ejpam-3279	99	1	lemma	lemma	PROPN
ejpam-3279	99	2	2.5	2.5	NUM
ejpam-3279	99	3	.	.	PUNCT
ejpam-3279	100	1	[	[	X
ejpam-3279	100	2	12	12	NUM
ejpam-3279	100	3	]	]	PUNCT
ejpam-3279	100	4	in	in	ADP
ejpam-3279	100	5	the	the	DET
ejpam-3279	100	6	g	g	NOUN
ejpam-3279	100	7	-	-	PUNCT
ejpam-3279	100	8	adjoined	adjoin	VERB
ejpam-3279	100	9	structure	structure	NOUN
ejpam-3279	100	10	space	space	NOUN
ejpam-3279	100	11	,	,	PUNCT
ejpam-3279	100	12	an	an	DET
ejpam-3279	100	13	nc	nc	PROPN
ejpam-3279	100	14	-	-	ADJ
ejpam-3279	100	15	manifold	manifold	NOUN
ejpam-3279	100	16	is	be	AUX
ejpam-3279	100	17	a	a	DET
ejpam-3279	100	18	manifold	manifold	NOUN
ejpam-3279	100	19	of	of	ADP
ejpam-3279	100	20	class	class	NOUN
ejpam-3279	100	21	(	(	PUNCT
ejpam-3279	100	22	i	i	NOUN
ejpam-3279	100	23	)	)	PUNCT
ejpam-3279	100	24	cr1	cr1	PROPN
ejpam-3279	100	25	if	if	SCONJ
ejpam-3279	100	26	and	and	CCONJ
ejpam-3279	100	27	only	only	ADV
ejpam-3279	100	28	if	if	SCONJ
ejpam-3279	100	29	,	,	PUNCT
ejpam-3279	100	30	rabcd	rabcd	VERB
ejpam-3279	100	31	=	=	SYM
ejpam-3279	100	32	râbcd	râbcd	NOUN
ejpam-3279	100	33	=	=	PUNCT
ejpam-3279	100	34	râb̂cd	râb̂cd	NOUN
ejpam-3279	100	35	=	=	SYM
ejpam-3279	100	36	0	0	NUM
ejpam-3279	100	37	;	;	PUNCT
ejpam-3279	100	38	(	(	PUNCT
ejpam-3279	100	39	ii	ii	NOUN
ejpam-3279	100	40	)	)	PUNCT
ejpam-3279	100	41	cr2	cr2	PROPN
ejpam-3279	100	42	if	if	SCONJ
ejpam-3279	100	43	and	and	CCONJ
ejpam-3279	100	44	only	only	ADV
ejpam-3279	100	45	if	if	SCONJ
ejpam-3279	100	46	,	,	PUNCT
ejpam-3279	100	47	rabcd	rabcd	VERB
ejpam-3279	100	48	=	=	SYM
ejpam-3279	100	49	râbcd	râbcd	X
ejpam-3279	100	50	=	=	SYM
ejpam-3279	100	51	0	0	NUM
ejpam-3279	100	52	;	;	PUNCT
ejpam-3279	100	53	(	(	PUNCT
ejpam-3279	100	54	iii	iii	X
ejpam-3279	100	55	)	)	PUNCT
ejpam-3279	100	56	cr3	cr3	NOUN
ejpam-3279	101	1	if	if	SCONJ
ejpam-3279	101	2	and	and	CCONJ
ejpam-3279	101	3	only	only	ADV
ejpam-3279	101	4	if	if	SCONJ
ejpam-3279	101	5	,	,	PUNCT
ejpam-3279	101	6	râbcd	râbcd	VERB
ejpam-3279	101	7	=	=	SYM
ejpam-3279	101	8	0	0	X
ejpam-3279	101	9	.	.	PUNCT
ejpam-3279	102	1	it	it	PRON
ejpam-3279	102	2	easy	easy	ADJ
ejpam-3279	102	3	to	to	PART
ejpam-3279	102	4	see	see	VERB
ejpam-3279	102	5	that	that	SCONJ
ejpam-3279	102	6	cr1	cr1	PROPN
ejpam-3279	102	7	⊂	⊂	PROPN
ejpam-3279	102	8	cr2	cr2	PROPN
ejpam-3279	102	9	⊂	⊂	PROPN
ejpam-3279	102	10	cr3	cr3	PROPN
ejpam-3279	102	11	concerning	concern	VERB
ejpam-3279	102	12	the	the	DET
ejpam-3279	102	13	projective	projective	ADJ
ejpam-3279	102	14	tensor	tensor	NOUN
ejpam-3279	102	15	,	,	PUNCT
ejpam-3279	102	16	we	we	PRON
ejpam-3279	102	17	defined	define	VERB
ejpam-3279	102	18	three	three	NUM
ejpam-3279	102	19	special	special	ADJ
ejpam-3279	102	20	classes	class	NOUN
ejpam-3279	102	21	of	of	ADP
ejpam-3279	102	22	nc	nc	PROPN
ejpam-3279	102	23	-	-	ADJ
ejpam-3279	102	24	manifold	manifold	NOUN
ejpam-3279	102	25	which	which	PRON
ejpam-3279	102	26	are	be	AUX
ejpam-3279	102	27	given	give	VERB
ejpam-3279	102	28	in	in	ADP
ejpam-3279	102	29	the	the	DET
ejpam-3279	102	30	definition	definition	NOUN
ejpam-3279	102	31	below	below	ADV
ejpam-3279	102	32	.	.	PUNCT
ejpam-3279	103	1	definition	definition	NOUN
ejpam-3279	103	2	2.13	2.13	NUM
ejpam-3279	103	3	.	.	PUNCT
ejpam-3279	104	1	in	in	ADP
ejpam-3279	104	2	the	the	DET
ejpam-3279	104	3	g	g	NOUN
ejpam-3279	104	4	-	-	PUNCT
ejpam-3279	104	5	adjoined	adjoin	VERB
ejpam-3279	104	6	structure	structure	NOUN
ejpam-3279	104	7	space	space	NOUN
ejpam-3279	104	8	,	,	PUNCT
ejpam-3279	104	9	an	an	DET
ejpam-3279	104	10	nc	nc	PROPN
ejpam-3279	104	11	-	-	ADJ
ejpam-3279	104	12	manifold	manifold	NOUN
ejpam-3279	104	13	is	be	AUX
ejpam-3279	104	14	a	a	DET
ejpam-3279	104	15	manifold	manifold	NOUN
ejpam-3279	104	16	of	of	ADP
ejpam-3279	104	17	class	class	NOUN
ejpam-3279	104	18	(	(	PUNCT
ejpam-3279	104	19	i	i	NOUN
ejpam-3279	104	20	)	)	PUNCT
ejpam-3279	104	21	pr1	pr1	NOUN
ejpam-3279	104	22	if	if	SCONJ
ejpam-3279	105	1	and	and	CCONJ
ejpam-3279	105	2	only	only	ADV
ejpam-3279	105	3	if	if	SCONJ
ejpam-3279	105	4	,	,	PUNCT
ejpam-3279	105	5	pabcd	pabcd	NOUN
ejpam-3279	105	6	=	=	PUNCT
ejpam-3279	105	7	pâbcd	pâbcd	X
ejpam-3279	105	8	=	=	PUNCT
ejpam-3279	105	9	pâb̂cd	pâb̂cd	X
ejpam-3279	105	10	=	=	PUNCT
ejpam-3279	105	11	0	0	NUM
ejpam-3279	105	12	;	;	PUNCT
ejpam-3279	105	13	(	(	PUNCT
ejpam-3279	105	14	ii	ii	NOUN
ejpam-3279	105	15	)	)	PUNCT
ejpam-3279	105	16	pr2	pr2	NOUN
ejpam-3279	105	17	if	if	SCONJ
ejpam-3279	105	18	and	and	CCONJ
ejpam-3279	105	19	only	only	ADV
ejpam-3279	105	20	if	if	SCONJ
ejpam-3279	105	21	,	,	PUNCT
ejpam-3279	105	22	pabcd	pabcd	NOUN
ejpam-3279	105	23	=	=	PUNCT
ejpam-3279	105	24	pâbcd	pâbcd	X
ejpam-3279	105	25	=	=	SYM
ejpam-3279	105	26	0	0	NUM
ejpam-3279	105	27	;	;	PUNCT
ejpam-3279	105	28	(	(	PUNCT
ejpam-3279	105	29	iii	iii	X
ejpam-3279	105	30	)	)	PUNCT
ejpam-3279	105	31	pr3	pr3	NOUN
ejpam-3279	105	32	if	if	SCONJ
ejpam-3279	105	33	and	and	CCONJ
ejpam-3279	105	34	only	only	ADV
ejpam-3279	105	35	if	if	SCONJ
ejpam-3279	105	36	,	,	PUNCT
ejpam-3279	105	37	pâbcd	pâbcd	PRON
ejpam-3279	105	38	=	=	SYM
ejpam-3279	105	39	0	0	NUM
ejpam-3279	105	40	.	.	NOUN
ejpam-3279	105	41	3	3	X
ejpam-3279	105	42	.	.	X
ejpam-3279	106	1	the	the	DET
ejpam-3279	106	2	main	main	ADJ
ejpam-3279	106	3	results	result	NOUN
ejpam-3279	106	4	in	in	ADP
ejpam-3279	106	5	the	the	DET
ejpam-3279	106	6	present	present	ADJ
ejpam-3279	106	7	section	section	NOUN
ejpam-3279	106	8	,	,	PUNCT
ejpam-3279	106	9	we	we	PRON
ejpam-3279	106	10	concentrate	concentrate	VERB
ejpam-3279	106	11	our	our	PRON
ejpam-3279	106	12	attention	attention	NOUN
ejpam-3279	106	13	on	on	ADP
ejpam-3279	106	14	projective	projective	ADJ
ejpam-3279	106	15	tensor	tensor	NOUN
ejpam-3279	106	16	of	of	ADP
ejpam-3279	106	17	ncmanifold	ncmanifold	PROPN
ejpam-3279	106	18	,	,	PUNCT
ejpam-3279	106	19	and	and	CCONJ
ejpam-3279	106	20	study	study	VERB
ejpam-3279	106	21	the	the	DET
ejpam-3279	106	22	notion	notion	NOUN
ejpam-3279	106	23	of	of	ADP
ejpam-3279	106	24	projective	projective	ADJ
ejpam-3279	106	25	-	-	PUNCT
ejpam-3279	106	26	recurrent	recurrent	NOUN
ejpam-3279	106	27	nc	nc	NOUN
ejpam-3279	106	28	-	-	ADJ
ejpam-3279	106	29	manifold	manifold	NOUN
ejpam-3279	106	30	.	.	PUNCT
ejpam-3279	107	1	lemma	lemma	PROPN
ejpam-3279	107	2	3.1	3.1	NUM
ejpam-3279	107	3	.	.	PUNCT
ejpam-3279	108	1	in	in	ADP
ejpam-3279	108	2	the	the	DET
ejpam-3279	108	3	g	g	NOUN
ejpam-3279	108	4	-	-	PUNCT
ejpam-3279	108	5	adjoined	adjoin	VERB
ejpam-3279	108	6	structure	structure	NOUN
ejpam-3279	108	7	space	space	NOUN
ejpam-3279	108	8	,	,	PUNCT
ejpam-3279	108	9	the	the	DET
ejpam-3279	108	10	components	component	NOUN
ejpam-3279	108	11	of	of	ADP
ejpam-3279	108	12	projective	projective	ADJ
ejpam-3279	108	13	curvature	curvature	NOUN
ejpam-3279	108	14	tensor	tensor	NOUN
ejpam-3279	108	15	of	of	ADP
ejpam-3279	108	16	nc	nc	PROPN
ejpam-3279	108	17	-	-	ADJ
ejpam-3279	108	18	manifold	manifold	NOUN
ejpam-3279	108	19	are	be	AUX
ejpam-3279	108	20	given	give	VERB
ejpam-3279	108	21	by	by	ADP
ejpam-3279	108	22	the	the	DET
ejpam-3279	108	23	following	follow	VERB
ejpam-3279	108	24	forms	form	NOUN
ejpam-3279	108	25	:	:	PUNCT
ejpam-3279	108	26	(	(	PUNCT
ejpam-3279	108	27	i	i	NOUN
ejpam-3279	108	28	)	)	PUNCT
ejpam-3279	108	29	pabcd	pabcd	NOUN
ejpam-3279	108	30	=	=	PUNCT
ejpam-3279	109	1	−2bab[cd	−2bab[cd	PROPN
ejpam-3279	109	2	]	]	PUNCT
ejpam-3279	109	3	;	;	PUNCT
ejpam-3279	109	4	(	(	PUNCT
ejpam-3279	109	5	ii	ii	NOUN
ejpam-3279	109	6	)	)	PUNCT
ejpam-3279	109	7	pâb̂cd	pâb̂cd	PROPN
ejpam-3279	109	8	=	=	PUNCT
ejpam-3279	109	9	−2babhbhcd	−2babhbhcd	NOUN
ejpam-3279	109	10	−	−	NUM
ejpam-3279	109	11	1	1	NUM
ejpam-3279	109	12	2n	2n	NUM
ejpam-3279	110	1	[	[	X
ejpam-3279	110	2	rac	rac	PROPN
ejpam-3279	110	3	δ	δ	PROPN
ejpam-3279	110	4	b	b	PROPN
ejpam-3279	110	5	d	d	NOUN
ejpam-3279	110	6	−	−	PROPN
ejpam-3279	110	7	rbcδad	rbcδad	NOUN
ejpam-3279	110	8	]	]	X
ejpam-3279	110	9	;	;	PUNCT
ejpam-3279	110	10	(	(	PUNCT
ejpam-3279	110	11	iii	iii	X
ejpam-3279	110	12	)	)	PUNCT
ejpam-3279	110	13	pâbcd̂	pâbcd̂	NOUN
ejpam-3279	110	14	=	=	SYM
ejpam-3279	110	15	aadbc	aadbc	NOUN
ejpam-3279	110	16	−badhbhac	−badhbhac	X
ejpam-3279	111	1	−	−	NOUN
ejpam-3279	111	2	5	5	NUM
ejpam-3279	111	3	3c	3c	NUM
ejpam-3279	111	4	ad	ad	NOUN
ejpam-3279	111	5	ac	ac	NOUN
ejpam-3279	111	6	−	−	PROPN
ejpam-3279	111	7	1	1	NUM
ejpam-3279	111	8	2nr	2nr	NOUN
ejpam-3279	111	9	a	a	DET
ejpam-3279	111	10	c	c	NOUN
ejpam-3279	111	11	δ	δ	PROPN
ejpam-3279	111	12	d	d	NOUN
ejpam-3279	111	13	a	a	X
ejpam-3279	111	14	;	;	PUNCT
ejpam-3279	111	15	(	(	PUNCT
ejpam-3279	111	16	iv	iv	X
ejpam-3279	111	17	)	)	PUNCT
ejpam-3279	111	18	pâ0b0	pâ0b0	PROPN
ejpam-3279	111	19	=	=	NOUN
ejpam-3279	111	20	caccbc	caccbc	NOUN
ejpam-3279	111	21	−	−	PROPN
ejpam-3279	111	22	1	1	NUM
ejpam-3279	111	23	2nr	2nr	NOUN
ejpam-3279	111	24	a	a	DET
ejpam-3279	111	25	b	b	PROPN
ejpam-3279	111	26	.	.	PUNCT
ejpam-3279	112	1	n.	n.	PROPN
ejpam-3279	112	2	j.	j.	PROPN
ejpam-3279	112	3	mohammed	mohammed	PROPN
ejpam-3279	112	4	,	,	PUNCT
ejpam-3279	112	5	h.	h.	PROPN
ejpam-3279	112	6	m.	m.	PROPN
ejpam-3279	112	7	abood	abood	PROPN
ejpam-3279	112	8	/	/	SYM
ejpam-3279	112	9	eur	eur	PROPN
ejpam-3279	112	10	.	.	PUNCT
ejpam-3279	113	1	j.	j.	PROPN
ejpam-3279	113	2	pure	pure	PROPN
ejpam-3279	113	3	appl	appl	PROPN
ejpam-3279	113	4	.	.	PROPN
ejpam-3279	113	5	math	math	PROPN
ejpam-3279	113	6	,	,	PUNCT
ejpam-3279	113	7	11	11	NUM
ejpam-3279	113	8	(	(	PUNCT
ejpam-3279	113	9	3	3	NUM
ejpam-3279	113	10	)	)	PUNCT
ejpam-3279	113	11	(	(	PUNCT
ejpam-3279	113	12	2018	2018	NUM
ejpam-3279	113	13	)	)	PUNCT
ejpam-3279	113	14	,	,	PUNCT
ejpam-3279	113	15	823	823	NUM
ejpam-3279	113	16	-	-	SYM
ejpam-3279	113	17	833	833	NUM
ejpam-3279	113	18	828	828	NUM
ejpam-3279	113	19	and	and	CCONJ
ejpam-3279	113	20	the	the	DET
ejpam-3279	113	21	others	other	NOUN
ejpam-3279	113	22	are	be	AUX
ejpam-3279	113	23	conjugate	conjugate	ADJ
ejpam-3279	113	24	to	to	ADP
ejpam-3279	113	25	the	the	DET
ejpam-3279	113	26	above	above	ADJ
ejpam-3279	113	27	components	component	NOUN
ejpam-3279	113	28	or	or	CCONJ
ejpam-3279	113	29	equal	equal	ADJ
ejpam-3279	113	30	to	to	ADP
ejpam-3279	113	31	zero	zero	NUM
ejpam-3279	113	32	.	.	PUNCT
ejpam-3279	114	1	proof	proof	NOUN
ejpam-3279	114	2	:	:	PUNCT
ejpam-3279	114	3	by	by	ADP
ejpam-3279	114	4	using	use	VERB
ejpam-3279	114	5	the	the	DET
ejpam-3279	114	6	theorem	theorem	ADJ
ejpam-3279	114	7	2.2	2.2	NUM
ejpam-3279	114	8	,	,	PUNCT
ejpam-3279	114	9	lemma	lemma	PROPN
ejpam-3279	114	10	2.2	2.2	NUM
ejpam-3279	114	11	and	and	CCONJ
ejpam-3279	114	12	definition	definition	NOUN
ejpam-3279	114	13	2.7	2.7	NUM
ejpam-3279	114	14	,	,	PUNCT
ejpam-3279	114	15	directly	directly	ADV
ejpam-3279	114	16	we	we	PRON
ejpam-3279	114	17	obtain	obtain	VERB
ejpam-3279	114	18	the	the	DET
ejpam-3279	114	19	above	above	ADJ
ejpam-3279	114	20	components	component	NOUN
ejpam-3279	114	21	.	.	PUNCT
ejpam-3279	115	1	theorem	theorem	VERB
ejpam-3279	115	2	3.1	3.1	NUM
ejpam-3279	115	3	.	.	PUNCT
ejpam-3279	116	1	let	let	VERB
ejpam-3279	116	2	m	m	PRON
ejpam-3279	116	3	be	be	AUX
ejpam-3279	116	4	nc	nc	ADJ
ejpam-3279	116	5	-	-	ADJ
ejpam-3279	116	6	manifold	manifold	ADJ
ejpam-3279	116	7	with	with	ADP
ejpam-3279	116	8	vanishing	vanish	VERB
ejpam-3279	116	9	projective	projective	ADJ
ejpam-3279	116	10	tensor	tensor	NOUN
ejpam-3279	116	11	.	.	PUNCT
ejpam-3279	117	1	if	if	SCONJ
ejpam-3279	117	2	m	m	NOUN
ejpam-3279	117	3	is	be	AUX
ejpam-3279	117	4	a	a	DET
ejpam-3279	117	5	manifold	manifold	NOUN
ejpam-3279	117	6	of	of	ADP
ejpam-3279	117	7	vanishing	vanish	VERB
ejpam-3279	117	8	ricci	ricci	PROPN
ejpam-3279	117	9	tensor	tensor	NOUN
ejpam-3279	117	10	,	,	PUNCT
ejpam-3279	117	11	then	then	ADV
ejpam-3279	117	12	the	the	DET
ejpam-3279	117	13	fist	fist	ADJ
ejpam-3279	117	14	structure	structure	NOUN
ejpam-3279	117	15	tensor	tensor	NOUN
ejpam-3279	117	16	is	be	AUX
ejpam-3279	117	17	vanishing	vanish	VERB
ejpam-3279	117	18	in	in	ADP
ejpam-3279	117	19	the	the	DET
ejpam-3279	117	20	first	first	ADJ
ejpam-3279	117	21	canonical	canonical	ADJ
ejpam-3279	117	22	connection	connection	NOUN
ejpam-3279	117	23	.	.	PUNCT
ejpam-3279	118	1	proof	proof	NOUN
ejpam-3279	118	2	:	:	PUNCT
ejpam-3279	118	3	suppose	suppose	VERB
ejpam-3279	118	4	that	that	SCONJ
ejpam-3279	118	5	m	m	NOUN
ejpam-3279	118	6	is	be	AUX
ejpam-3279	118	7	projectively	projectively	ADV
ejpam-3279	118	8	vanishing	vanish	VERB
ejpam-3279	118	9	nc	nc	NOUN
ejpam-3279	118	10	-	-	ADJ
ejpam-3279	118	11	manifold	manifold	ADJ
ejpam-3279	118	12	.	.	PUNCT
ejpam-3279	119	1	making	make	VERB
ejpam-3279	119	2	use	use	NOUN
ejpam-3279	119	3	of	of	ADP
ejpam-3279	119	4	definition	definition	NOUN
ejpam-3279	119	5	2.8	2.8	NUM
ejpam-3279	119	6	and	and	CCONJ
ejpam-3279	119	7	lemma	lemma	PROPN
ejpam-3279	119	8	3.1	3.1	NUM
ejpam-3279	119	9	,	,	PUNCT
ejpam-3279	119	10	we	we	PRON
ejpam-3279	119	11	have	have	VERB
ejpam-3279	119	12	−2babhbhcd	−2babhbhcd	VERB
ejpam-3279	119	13	−	−	NUM
ejpam-3279	119	14	1	1	NUM
ejpam-3279	119	15	2n	2n	NUM
ejpam-3279	120	1	[	[	X
ejpam-3279	120	2	rac	rac	PROPN
ejpam-3279	120	3	δ	δ	PROPN
ejpam-3279	120	4	b	b	PROPN
ejpam-3279	120	5	d	d	NOUN
ejpam-3279	120	6	−	−	PROPN
ejpam-3279	120	7	rbcδad	rbcδad	NOUN
ejpam-3279	120	8	]	]	PUNCT
ejpam-3279	120	9	=	=	SYM
ejpam-3279	120	10	0	0	PUNCT
ejpam-3279	120	11	(	(	PUNCT
ejpam-3279	120	12	3.1	3.1	NUM
ejpam-3279	120	13	)	)	PUNCT
ejpam-3279	120	14	since	since	SCONJ
ejpam-3279	120	15	m	m	PROPN
ejpam-3279	120	16	has	have	AUX
ejpam-3279	120	17	vanishing	vanish	VERB
ejpam-3279	120	18	ricci	ricci	PROPN
ejpam-3279	120	19	tensor	tensor	NOUN
ejpam-3279	120	20	,	,	PUNCT
ejpam-3279	120	21	so	so	CCONJ
ejpam-3279	120	22	(	(	PUNCT
ejpam-3279	120	23	3.1	3.1	NUM
ejpam-3279	120	24	)	)	PUNCT
ejpam-3279	120	25	becomes	become	VERB
ejpam-3279	120	26	−2badhbhcd	−2badhbhcd	ADJ
ejpam-3279	120	27	=	=	SYM
ejpam-3279	120	28	0	0	NUM
ejpam-3279	120	29	(	(	PUNCT
ejpam-3279	120	30	3.2	3.2	NUM
ejpam-3279	120	31	)	)	PUNCT
ejpam-3279	120	32	contracting	contract	VERB
ejpam-3279	120	33	the	the	DET
ejpam-3279	120	34	equation	equation	NOUN
ejpam-3279	120	35	(	(	PUNCT
ejpam-3279	120	36	3.2	3.2	NUM
ejpam-3279	120	37	)	)	PUNCT
ejpam-3279	120	38	by	by	ADP
ejpam-3279	120	39	the	the	DET
ejpam-3279	120	40	induces	induce	NOUN
ejpam-3279	120	41	(	(	PUNCT
ejpam-3279	120	42	a	a	DET
ejpam-3279	120	43	,	,	PUNCT
ejpam-3279	120	44	c	c	NOUN
ejpam-3279	120	45	)	)	PUNCT
ejpam-3279	120	46	and	and	CCONJ
ejpam-3279	120	47	(	(	PUNCT
ejpam-3279	120	48	b	b	X
ejpam-3279	120	49	,	,	PUNCT
ejpam-3279	120	50	d	d	PROPN
ejpam-3279	120	51	)	)	PUNCT
ejpam-3279	120	52	,	,	PUNCT
ejpam-3279	120	53	it	it	PRON
ejpam-3279	120	54	follows	follow	VERB
ejpam-3279	120	55	that	that	SCONJ
ejpam-3279	120	56	−2babhbhab	−2babhbhab	PROPN
ejpam-3279	120	57	=	=	PUNCT
ejpam-3279	120	58	0	0	PUNCT
ejpam-3279	121	1	since	since	SCONJ
ejpam-3279	121	2	b	b	PROPN
ejpam-3279	121	3	abh	abh	PROPN
ejpam-3279	121	4	and	and	CCONJ
ejpam-3279	121	5	bhab	bhab	PROPN
ejpam-3279	121	6	are	be	AUX
ejpam-3279	121	7	antisymmetric	antisymmetric	ADJ
ejpam-3279	121	8	tensors	tensor	NOUN
ejpam-3279	121	9	,	,	PUNCT
ejpam-3279	121	10	then	then	ADV
ejpam-3279	121	11	we	we	PRON
ejpam-3279	121	12	get∑	get∑	VERB
ejpam-3279	121	13	a	a	DET
ejpam-3279	121	14	,	,	PUNCT
ejpam-3279	121	15	b	b	NOUN
ejpam-3279	121	16	,	,	PUNCT
ejpam-3279	121	17	h	h	NOUN
ejpam-3279	122	1	|babh|2	|babh|2	NOUN
ejpam-3279	122	2	=	=	NOUN
ejpam-3279	122	3	0	0	PUNCT
ejpam-3279	123	1	consequently	consequently	ADV
ejpam-3279	123	2	,	,	PUNCT
ejpam-3279	123	3	we	we	PRON
ejpam-3279	123	4	deduce	deduce	VERB
ejpam-3279	123	5	that	that	DET
ejpam-3279	123	6	babh	babh	NOUN
ejpam-3279	123	7	=	=	SYM
ejpam-3279	123	8	0	0	X
ejpam-3279	123	9	.	.	PUNCT
ejpam-3279	123	10	theorem	theorem	VERB
ejpam-3279	123	11	3.2	3.2	NUM
ejpam-3279	123	12	.	.	PUNCT
ejpam-3279	124	1	if	if	SCONJ
ejpam-3279	124	2	m	m	NOUN
ejpam-3279	124	3	is	be	AUX
ejpam-3279	124	4	a	a	DET
ejpam-3279	124	5	projectively	projectively	ADV
ejpam-3279	124	6	vanishing	vanish	VERB
ejpam-3279	124	7	nc	nc	NOUN
ejpam-3279	124	8	-	-	ADJ
ejpam-3279	124	9	manifold	manifold	ADJ
ejpam-3279	124	10	and	and	CCONJ
ejpam-3279	124	11	φ	φ	VERB
ejpam-3279	124	12	-	-	PUNCT
ejpam-3279	124	13	invariant	invariant	ADJ
ejpam-3279	124	14	ricci	ricci	PROPN
ejpam-3279	124	15	tensor	tensor	NOUN
ejpam-3279	124	16	,	,	PUNCT
ejpam-3279	124	17	then	then	ADV
ejpam-3279	124	18	the	the	DET
ejpam-3279	124	19	necessary	necessary	ADJ
ejpam-3279	124	20	and	and	CCONJ
ejpam-3279	124	21	sufficient	sufficient	ADJ
ejpam-3279	124	22	condition	condition	NOUN
ejpam-3279	124	23	that	that	SCONJ
ejpam-3279	124	24	m	m	NOUN
ejpam-3279	124	25	is	be	AUX
ejpam-3279	124	26	an	an	DET
ejpam-3279	124	27	einstein	einstein	ADJ
ejpam-3279	124	28	manifold	manifold	NOUN
ejpam-3279	124	29	is	be	AUX
ejpam-3279	124	30	aadac	aadac	NOUN
ejpam-3279	124	31	=	=	SYM
ejpam-3279	124	32	5	5	NUM
ejpam-3279	124	33	3c	3c	NUM
ejpam-3279	124	34	ad	ad	NOUN
ejpam-3279	124	35	ac	ac	ADP
ejpam-3279	124	36	+	+	CCONJ
ejpam-3279	124	37	c0δ	c0δ	PROPN
ejpam-3279	124	38	d	d	PROPN
ejpam-3279	124	39	c	c	PROPN
ejpam-3279	124	40	,	,	PUNCT
ejpam-3279	124	41	where	where	SCONJ
ejpam-3279	124	42	c0	c0	PROPN
ejpam-3279	124	43	=	=	SYM
ejpam-3279	124	44	e	e	X
ejpam-3279	124	45	2n	2n	NUM
ejpam-3279	124	46	.	.	PUNCT
ejpam-3279	125	1	proof	proof	NOUN
ejpam-3279	125	2	:	:	PUNCT
ejpam-3279	125	3	let	let	VERB
ejpam-3279	125	4	m	m	PRON
ejpam-3279	125	5	be	be	AUX
ejpam-3279	125	6	projectively	projectively	ADV
ejpam-3279	125	7	vanishing	vanish	VERB
ejpam-3279	125	8	nc	nc	PROPN
ejpam-3279	125	9	-manifold	-manifold	PROPN
ejpam-3279	125	10	.	.	PUNCT
ejpam-3279	126	1	according	accord	VERB
ejpam-3279	126	2	to	to	ADP
ejpam-3279	126	3	the	the	DET
ejpam-3279	126	4	definition	definition	NOUN
ejpam-3279	126	5	2.8	2.8	NUM
ejpam-3279	126	6	and	and	CCONJ
ejpam-3279	126	7	theorem	theorem	VERB
ejpam-3279	126	8	3.1	3.1	NUM
ejpam-3279	126	9	,	,	PUNCT
ejpam-3279	126	10	we	we	PRON
ejpam-3279	126	11	have	have	VERB
ejpam-3279	126	12	aadbc	aadbc	NOUN
ejpam-3279	126	13	−badhbhbc	−badhbhbc	PROPN
ejpam-3279	126	14	−	−	PROPN
ejpam-3279	126	15	5	5	NUM
ejpam-3279	126	16	3	3	NUM
ejpam-3279	126	17	cadbc	cadbc	NOUN
ejpam-3279	126	18	−	−	NOUN
ejpam-3279	126	19	1	1	NUM
ejpam-3279	126	20	2n	2n	NUM
ejpam-3279	126	21	rac	rac	PROPN
ejpam-3279	126	22	δ	δ	PROPN
ejpam-3279	126	23	d	d	PROPN
ejpam-3279	126	24	b	b	X
ejpam-3279	126	25	=	=	SYM
ejpam-3279	126	26	0	0	NUM
ejpam-3279	126	27	(	(	PUNCT
ejpam-3279	126	28	3.3	3.3	NUM
ejpam-3279	126	29	)	)	PUNCT
ejpam-3279	126	30	symmetrizing	symmetrize	VERB
ejpam-3279	126	31	and	and	CCONJ
ejpam-3279	126	32	antisymmetrizing	antisymmetrize	VERB
ejpam-3279	126	33	the	the	DET
ejpam-3279	126	34	equation	equation	NOUN
ejpam-3279	126	35	(	(	PUNCT
ejpam-3279	126	36	3.3	3.3	NUM
ejpam-3279	126	37	)	)	PUNCT
ejpam-3279	126	38	by	by	ADP
ejpam-3279	126	39	the	the	DET
ejpam-3279	126	40	induces	induce	NOUN
ejpam-3279	126	41	(	(	PUNCT
ejpam-3279	126	42	h	h	NOUN
ejpam-3279	126	43	,	,	PUNCT
ejpam-3279	126	44	d	d	NOUN
ejpam-3279	126	45	)	)	PUNCT
ejpam-3279	126	46	,	,	PUNCT
ejpam-3279	126	47	we	we	PRON
ejpam-3279	126	48	deduce	deduce	VERB
ejpam-3279	126	49	aadbc	aadbc	NOUN
ejpam-3279	127	1	−	−	PROPN
ejpam-3279	127	2	5	5	NUM
ejpam-3279	127	3	3	3	NUM
ejpam-3279	127	4	cadbc	cadbc	NOUN
ejpam-3279	127	5	−	−	NOUN
ejpam-3279	127	6	1	1	NUM
ejpam-3279	127	7	2n	2n	NUM
ejpam-3279	127	8	rac	rac	PROPN
ejpam-3279	127	9	δ	δ	PROPN
ejpam-3279	127	10	d	d	PROPN
ejpam-3279	127	11	b	b	X
ejpam-3279	127	12	=	=	SYM
ejpam-3279	127	13	0	0	NUM
ejpam-3279	127	14	(	(	PUNCT
ejpam-3279	127	15	3.4	3.4	NUM
ejpam-3279	127	16	)	)	PUNCT
ejpam-3279	127	17	suppose	suppose	VERB
ejpam-3279	127	18	that	that	SCONJ
ejpam-3279	127	19	m	m	PROPN
ejpam-3279	127	20	is	be	AUX
ejpam-3279	127	21	einstein	einstein	PROPN
ejpam-3279	127	22	manifold	manifold	PROPN
ejpam-3279	127	23	.	.	PUNCT
ejpam-3279	128	1	using	use	VERB
ejpam-3279	128	2	the	the	DET
ejpam-3279	128	3	definition	definition	NOUN
ejpam-3279	128	4	3.2	3.2	NUM
ejpam-3279	128	5	,	,	PUNCT
ejpam-3279	128	6	so	so	CCONJ
ejpam-3279	128	7	the	the	DET
ejpam-3279	128	8	equation	equation	NOUN
ejpam-3279	128	9	(	(	PUNCT
ejpam-3279	128	10	3.4	3.4	NUM
ejpam-3279	128	11	)	)	PUNCT
ejpam-3279	128	12	becomes	become	VERB
ejpam-3279	128	13	aadbc	aadbc	NOUN
ejpam-3279	128	14	−	−	PROPN
ejpam-3279	128	15	5	5	NUM
ejpam-3279	128	16	3	3	NUM
ejpam-3279	128	17	cadbc	cadbc	NOUN
ejpam-3279	129	1	−	−	NUM
ejpam-3279	129	2	e	e	NOUN
ejpam-3279	129	3	2n	2n	NUM
ejpam-3279	129	4	δac	δac	PROPN
ejpam-3279	129	5	δ	δ	PROPN
ejpam-3279	129	6	d	d	PROPN
ejpam-3279	129	7	b	b	PROPN
ejpam-3279	129	8	=	=	SYM
ejpam-3279	129	9	0	0	NUM
ejpam-3279	129	10	(	(	PUNCT
ejpam-3279	129	11	3.5	3.5	NUM
ejpam-3279	129	12	)	)	PUNCT
ejpam-3279	129	13	n.	n.	PROPN
ejpam-3279	129	14	j.	j.	PROPN
ejpam-3279	129	15	mohammed	mohammed	PROPN
ejpam-3279	129	16	,	,	PUNCT
ejpam-3279	129	17	h.	h.	PROPN
ejpam-3279	129	18	m.	m.	PROPN
ejpam-3279	129	19	abood	abood	PROPN
ejpam-3279	129	20	/	/	SYM
ejpam-3279	129	21	eur	eur	PROPN
ejpam-3279	129	22	.	.	PUNCT
ejpam-3279	130	1	j.	j.	PROPN
ejpam-3279	130	2	pure	pure	PROPN
ejpam-3279	130	3	appl	appl	PROPN
ejpam-3279	130	4	.	.	PROPN
ejpam-3279	130	5	math	math	PROPN
ejpam-3279	130	6	,	,	PUNCT
ejpam-3279	130	7	11	11	NUM
ejpam-3279	130	8	(	(	PUNCT
ejpam-3279	130	9	3	3	NUM
ejpam-3279	130	10	)	)	PUNCT
ejpam-3279	130	11	(	(	PUNCT
ejpam-3279	130	12	2018	2018	NUM
ejpam-3279	130	13	)	)	PUNCT
ejpam-3279	130	14	,	,	PUNCT
ejpam-3279	130	15	823	823	NUM
ejpam-3279	130	16	-	-	SYM
ejpam-3279	130	17	833	833	NUM
ejpam-3279	130	18	829	829	NUM
ejpam-3279	130	19	contracting	contracting	NOUN
ejpam-3279	130	20	(	(	PUNCT
ejpam-3279	130	21	3.5	3.5	NUM
ejpam-3279	130	22	)	)	PUNCT
ejpam-3279	130	23	by	by	ADP
ejpam-3279	130	24	induces	induce	NOUN
ejpam-3279	130	25	(	(	PUNCT
ejpam-3279	130	26	a	a	DET
ejpam-3279	130	27	,	,	PUNCT
ejpam-3279	130	28	b	b	NOUN
ejpam-3279	130	29	)	)	PUNCT
ejpam-3279	131	1	,	,	PUNCT
ejpam-3279	131	2	it	it	PRON
ejpam-3279	131	3	follows	follow	VERB
ejpam-3279	131	4	that	that	SCONJ
ejpam-3279	131	5	aadac	aadac	NOUN
ejpam-3279	131	6	=	=	SYM
ejpam-3279	131	7	5	5	NUM
ejpam-3279	131	8	3	3	NUM
ejpam-3279	131	9	cadac	cadac	NOUN
ejpam-3279	131	10	+	+	CCONJ
ejpam-3279	131	11	c0δ	c0δ	PROPN
ejpam-3279	131	12	d	d	X
ejpam-3279	131	13	c	c	X
ejpam-3279	131	14	(	(	PUNCT
ejpam-3279	131	15	3.6	3.6	NUM
ejpam-3279	131	16	)	)	PUNCT
ejpam-3279	131	17	conversely	conversely	ADV
ejpam-3279	131	18	,	,	PUNCT
ejpam-3279	131	19	let	let	VERB
ejpam-3279	131	20	the	the	DET
ejpam-3279	131	21	equation	equation	NOUN
ejpam-3279	131	22	(	(	PUNCT
ejpam-3279	131	23	3.6	3.6	NUM
ejpam-3279	131	24	)	)	PUNCT
ejpam-3279	131	25	holds	hold	VERB
ejpam-3279	131	26	.	.	PUNCT
ejpam-3279	132	1	contracting	contract	VERB
ejpam-3279	132	2	the	the	DET
ejpam-3279	132	3	equation	equation	NOUN
ejpam-3279	132	4	(	(	PUNCT
ejpam-3279	132	5	3.4	3.4	NUM
ejpam-3279	132	6	)	)	PUNCT
ejpam-3279	132	7	by	by	ADP
ejpam-3279	132	8	indices	index	NOUN
ejpam-3279	132	9	(	(	PUNCT
ejpam-3279	132	10	a	a	DET
ejpam-3279	132	11	,	,	PUNCT
ejpam-3279	132	12	b	b	NOUN
ejpam-3279	132	13	)	)	PUNCT
ejpam-3279	132	14	,	,	PUNCT
ejpam-3279	132	15	we	we	PRON
ejpam-3279	132	16	deduce	deduce	VERB
ejpam-3279	132	17	aadac	aadac	VERB
ejpam-3279	133	1	−	−	ADP
ejpam-3279	133	2	5	5	NUM
ejpam-3279	133	3	3	3	NUM
ejpam-3279	133	4	cadac	cadac	NOUN
ejpam-3279	133	5	−	−	PROPN
ejpam-3279	133	6	1	1	NUM
ejpam-3279	133	7	2n	2n	NUM
ejpam-3279	133	8	rdc	rdc	X
ejpam-3279	133	9	=	=	SYM
ejpam-3279	133	10	0	0	NUM
ejpam-3279	133	11	(	(	PUNCT
ejpam-3279	133	12	3.7	3.7	NUM
ejpam-3279	133	13	)	)	PUNCT
ejpam-3279	133	14	making	make	VERB
ejpam-3279	133	15	use	use	NOUN
ejpam-3279	133	16	of	of	ADP
ejpam-3279	133	17	the	the	DET
ejpam-3279	133	18	equations	equation	NOUN
ejpam-3279	133	19	(	(	PUNCT
ejpam-3279	133	20	3.6	3.6	NUM
ejpam-3279	133	21	)	)	PUNCT
ejpam-3279	133	22	and	and	CCONJ
ejpam-3279	133	23	(	(	PUNCT
ejpam-3279	133	24	3.7	3.7	NUM
ejpam-3279	133	25	)	)	PUNCT
ejpam-3279	133	26	,	,	PUNCT
ejpam-3279	133	27	it	it	PRON
ejpam-3279	133	28	follows	follow	VERB
ejpam-3279	133	29	that	that	DET
ejpam-3279	133	30	rac	rac	NOUN
ejpam-3279	133	31	=	=	PUNCT
ejpam-3279	133	32	eδac	eδac	NOUN
ejpam-3279	133	33	according	accord	VERB
ejpam-3279	133	34	to	to	ADP
ejpam-3279	133	35	the	the	DET
ejpam-3279	133	36	φ	φ	ADJ
ejpam-3279	133	37	-	-	PUNCT
ejpam-3279	133	38	invariant	invariant	ADJ
ejpam-3279	133	39	ricci	ricci	PROPN
ejpam-3279	133	40	tensor	tensor	NOUN
ejpam-3279	133	41	,	,	PUNCT
ejpam-3279	133	42	we	we	PRON
ejpam-3279	133	43	get	get	VERB
ejpam-3279	133	44	that	that	SCONJ
ejpam-3279	133	45	m	m	NOUN
ejpam-3279	133	46	is	be	AUX
ejpam-3279	133	47	einstein	einstein	PROPN
ejpam-3279	133	48	manifold	manifold	PROPN
ejpam-3279	133	49	.	.	PUNCT
ejpam-3279	134	1	theorem	theorem	VERB
ejpam-3279	134	2	3.3	3.3	NUM
ejpam-3279	134	3	.	.	PUNCT
ejpam-3279	135	1	suppose	suppose	VERB
ejpam-3279	135	2	that	that	SCONJ
ejpam-3279	135	3	m	m	PROPN
ejpam-3279	135	4	is	be	AUX
ejpam-3279	135	5	a	a	DET
ejpam-3279	135	6	projectively	projectively	ADV
ejpam-3279	135	7	vanishing	vanish	VERB
ejpam-3279	135	8	nc	nc	NOUN
ejpam-3279	135	9	-	-	ADJ
ejpam-3279	135	10	manifold	manifold	ADJ
ejpam-3279	135	11	and	and	CCONJ
ejpam-3279	135	12	φ	φ	VERB
ejpam-3279	135	13	-	-	PUNCT
ejpam-3279	135	14	invariant	invariant	ADJ
ejpam-3279	135	15	ricci	ricci	PROPN
ejpam-3279	135	16	tensor	tensor	NOUN
ejpam-3279	135	17	.	.	PUNCT
ejpam-3279	136	1	if	if	SCONJ
ejpam-3279	136	2	m	m	NOUN
ejpam-3279	136	3	is	be	AUX
ejpam-3279	136	4	an	an	DET
ejpam-3279	136	5	einstein	einstein	NOUN
ejpam-3279	136	6	manifold	manifold	NOUN
ejpam-3279	136	7	then	then	ADV
ejpam-3279	136	8	the	the	DET
ejpam-3279	136	9	first	first	ADJ
ejpam-3279	136	10	structure	structure	NOUN
ejpam-3279	136	11	tensor	tensor	NOUN
ejpam-3279	136	12	is	be	AUX
ejpam-3279	136	13	vanishing	vanish	VERB
ejpam-3279	136	14	in	in	ADP
ejpam-3279	136	15	the	the	DET
ejpam-3279	136	16	first	first	ADJ
ejpam-3279	136	17	canonical	canonical	ADJ
ejpam-3279	136	18	connection	connection	NOUN
ejpam-3279	136	19	.	.	PUNCT
ejpam-3279	137	1	proof	proof	NOUN
ejpam-3279	137	2	:	:	PUNCT
ejpam-3279	137	3	let	let	VERB
ejpam-3279	137	4	m	m	PRON
ejpam-3279	137	5	be	be	AUX
ejpam-3279	137	6	nc	nc	ADJ
ejpam-3279	137	7	-	-	ADJ
ejpam-3279	137	8	manifold	manifold	ADJ
ejpam-3279	137	9	with	with	ADP
ejpam-3279	137	10	vanishing	vanish	VERB
ejpam-3279	137	11	projective	projective	ADJ
ejpam-3279	137	12	tensor	tensor	NOUN
ejpam-3279	137	13	.	.	PUNCT
ejpam-3279	138	1	making	make	VERB
ejpam-3279	138	2	use	use	NOUN
ejpam-3279	138	3	of	of	ADP
ejpam-3279	138	4	the	the	DET
ejpam-3279	138	5	definition	definition	NOUN
ejpam-3279	138	6	2.8	2.8	NUM
ejpam-3279	138	7	and	and	CCONJ
ejpam-3279	138	8	lemma	lemma	PROPN
ejpam-3279	138	9	3.1	3.1	NUM
ejpam-3279	138	10	,	,	PUNCT
ejpam-3279	138	11	then	then	ADV
ejpam-3279	138	12	we	we	PRON
ejpam-3279	138	13	have	have	VERB
ejpam-3279	138	14	aadbc	aadbc	NOUN
ejpam-3279	138	15	−badhbhbc	−badhbhbc	PROPN
ejpam-3279	138	16	−	−	PROPN
ejpam-3279	138	17	5	5	NUM
ejpam-3279	138	18	3	3	NUM
ejpam-3279	138	19	cadbc	cadbc	NOUN
ejpam-3279	138	20	−	−	NOUN
ejpam-3279	138	21	1	1	NUM
ejpam-3279	138	22	2n	2n	NUM
ejpam-3279	138	23	rac	rac	PROPN
ejpam-3279	138	24	δ	δ	PROPN
ejpam-3279	138	25	d	d	PROPN
ejpam-3279	138	26	b	b	X
ejpam-3279	138	27	=	=	SYM
ejpam-3279	138	28	0	0	PROPN
ejpam-3279	138	29	(	(	PUNCT
ejpam-3279	138	30	3.8	3.8	NUM
ejpam-3279	138	31	)	)	PUNCT
ejpam-3279	138	32	contracting	contracting	NOUN
ejpam-3279	138	33	(	(	PUNCT
ejpam-3279	138	34	3.8	3.8	NUM
ejpam-3279	138	35	)	)	PUNCT
ejpam-3279	138	36	with	with	ADP
ejpam-3279	138	37	respect	respect	NOUN
ejpam-3279	138	38	to	to	ADP
ejpam-3279	138	39	the	the	DET
ejpam-3279	138	40	induces	induce	NOUN
ejpam-3279	138	41	(	(	PUNCT
ejpam-3279	138	42	a	a	DET
ejpam-3279	138	43	,	,	PUNCT
ejpam-3279	138	44	b	b	NOUN
ejpam-3279	138	45	)	)	PUNCT
ejpam-3279	138	46	,	,	PUNCT
ejpam-3279	138	47	it	it	PRON
ejpam-3279	138	48	follows	follow	VERB
ejpam-3279	138	49	that	that	SCONJ
ejpam-3279	138	50	aadac	aadac	NOUN
ejpam-3279	138	51	−badhbhac	−badhbhac	PUNCT
ejpam-3279	139	1	−	−	NOUN
ejpam-3279	139	2	5	5	NUM
ejpam-3279	139	3	3	3	NUM
ejpam-3279	139	4	cadac	cadac	NOUN
ejpam-3279	139	5	−	−	PROPN
ejpam-3279	139	6	1	1	NUM
ejpam-3279	139	7	2n	2n	NUM
ejpam-3279	139	8	rac	rac	PROPN
ejpam-3279	139	9	δ	δ	PROPN
ejpam-3279	140	1	d	d	PROPN
ejpam-3279	140	2	a	a	PROPN
ejpam-3279	140	3	=	=	SYM
ejpam-3279	140	4	0	0	NUM
ejpam-3279	140	5	(	(	PUNCT
ejpam-3279	140	6	3.9	3.9	NUM
ejpam-3279	140	7	)	)	PUNCT
ejpam-3279	140	8	since	since	SCONJ
ejpam-3279	140	9	m	m	PROPN
ejpam-3279	140	10	is	be	AUX
ejpam-3279	140	11	an	an	DET
ejpam-3279	140	12	einstein	einstein	ADJ
ejpam-3279	140	13	manifold	manifold	NOUN
ejpam-3279	140	14	.	.	PUNCT
ejpam-3279	141	1	so	so	ADV
ejpam-3279	141	2	according	accord	VERB
ejpam-3279	141	3	to	to	ADP
ejpam-3279	141	4	the	the	DET
ejpam-3279	141	5	theorem	theorem	NOUN
ejpam-3279	141	6	3.2	3.2	NUM
ejpam-3279	141	7	,	,	PUNCT
ejpam-3279	141	8	the	the	DET
ejpam-3279	141	9	equation	equation	NOUN
ejpam-3279	141	10	(	(	PUNCT
ejpam-3279	141	11	3.9	3.9	NUM
ejpam-3279	141	12	)	)	PUNCT
ejpam-3279	141	13	reduced	reduce	VERB
ejpam-3279	141	14	to	to	ADP
ejpam-3279	141	15	−badhbhac	−badhbhac	NOUN
ejpam-3279	142	1	=	=	SYM
ejpam-3279	142	2	0	0	PUNCT
ejpam-3279	142	3	(	(	PUNCT
ejpam-3279	142	4	3.10	3.10	NUM
ejpam-3279	142	5	)	)	PUNCT
ejpam-3279	142	6	contracting	contract	VERB
ejpam-3279	142	7	the	the	DET
ejpam-3279	142	8	equation	equation	NOUN
ejpam-3279	142	9	(	(	PUNCT
ejpam-3279	142	10	3.10	3.10	NUM
ejpam-3279	142	11	)	)	PUNCT
ejpam-3279	142	12	by	by	ADP
ejpam-3279	142	13	the	the	DET
ejpam-3279	142	14	induces	induce	NOUN
ejpam-3279	142	15	(	(	PUNCT
ejpam-3279	142	16	d	d	NOUN
ejpam-3279	142	17	,	,	PUNCT
ejpam-3279	142	18	c	c	NOUN
ejpam-3279	142	19	)	)	PUNCT
ejpam-3279	142	20	,	,	PUNCT
ejpam-3279	142	21	it	it	PRON
ejpam-3279	142	22	follows	follow	VERB
ejpam-3279	142	23	that	that	SCONJ
ejpam-3279	142	24	−badhbhad	−badhbhad	VERB
ejpam-3279	142	25	=	=	SYM
ejpam-3279	142	26	0	0	PUNCT
ejpam-3279	142	27	since	since	SCONJ
ejpam-3279	142	28	b	b	PROPN
ejpam-3279	142	29	abh	abh	PROPN
ejpam-3279	142	30	and	and	CCONJ
ejpam-3279	142	31	bhab	bhab	PROPN
ejpam-3279	142	32	are	be	AUX
ejpam-3279	142	33	antisymmetric	antisymmetric	ADJ
ejpam-3279	142	34	tensors	tensor	NOUN
ejpam-3279	142	35	,	,	PUNCT
ejpam-3279	142	36	then	then	ADV
ejpam-3279	142	37	we	we	PRON
ejpam-3279	142	38	get∑	get∑	VERB
ejpam-3279	142	39	a	a	DET
ejpam-3279	142	40	,	,	PUNCT
ejpam-3279	142	41	d	d	PROPN
ejpam-3279	142	42	,	,	PUNCT
ejpam-3279	142	43	h	h	NOUN
ejpam-3279	142	44	|bhad|2	|bhad|2	X
ejpam-3279	143	1	=	=	NOUN
ejpam-3279	143	2	0	0	PUNCT
ejpam-3279	143	3	consequently	consequently	ADV
ejpam-3279	143	4	,	,	PUNCT
ejpam-3279	143	5	we	we	PRON
ejpam-3279	143	6	deduce	deduce	VERB
ejpam-3279	143	7	that	that	SCONJ
ejpam-3279	143	8	bhad	bhad	VERB
ejpam-3279	143	9	=	=	SYM
ejpam-3279	143	10	0	0	X
ejpam-3279	143	11	.	.	PUNCT
ejpam-3279	144	1	n.	n.	PROPN
ejpam-3279	144	2	j.	j.	PROPN
ejpam-3279	144	3	mohammed	mohammed	PROPN
ejpam-3279	144	4	,	,	PUNCT
ejpam-3279	144	5	h.	h.	PROPN
ejpam-3279	144	6	m.	m.	PROPN
ejpam-3279	144	7	abood	abood	PROPN
ejpam-3279	144	8	/	/	SYM
ejpam-3279	144	9	eur	eur	PROPN
ejpam-3279	144	10	.	.	PUNCT
ejpam-3279	145	1	j.	j.	PROPN
ejpam-3279	145	2	pure	pure	PROPN
ejpam-3279	145	3	appl	appl	PROPN
ejpam-3279	145	4	.	.	PROPN
ejpam-3279	145	5	math	math	PROPN
ejpam-3279	145	6	,	,	PUNCT
ejpam-3279	145	7	11	11	NUM
ejpam-3279	145	8	(	(	PUNCT
ejpam-3279	145	9	3	3	NUM
ejpam-3279	145	10	)	)	PUNCT
ejpam-3279	145	11	(	(	PUNCT
ejpam-3279	145	12	2018	2018	NUM
ejpam-3279	145	13	)	)	PUNCT
ejpam-3279	145	14	,	,	PUNCT
ejpam-3279	145	15	823	823	NUM
ejpam-3279	145	16	-	-	SYM
ejpam-3279	145	17	833	833	NUM
ejpam-3279	145	18	830	830	NUM
ejpam-3279	145	19	theorem	theorem	VERB
ejpam-3279	145	20	3.4	3.4	NUM
ejpam-3279	145	21	.	.	PUNCT
ejpam-3279	146	1	let	let	VERB
ejpam-3279	146	2	m	m	PRON
ejpam-3279	146	3	be	be	AUX
ejpam-3279	146	4	nc	nc	ADJ
ejpam-3279	146	5	-	-	ADJ
ejpam-3279	146	6	manifold	manifold	ADJ
ejpam-3279	146	7	,	,	PUNCT
ejpam-3279	146	8	then	then	ADV
ejpam-3279	146	9	the	the	DET
ejpam-3279	146	10	classes	class	NOUN
ejpam-3279	146	11	cr3	cr3	NOUN
ejpam-3279	146	12	and	and	CCONJ
ejpam-3279	146	13	pr3	pr3	NOUN
ejpam-3279	146	14	are	be	AUX
ejpam-3279	146	15	coincide	coincide	ADJ
ejpam-3279	146	16	if	if	SCONJ
ejpam-3279	146	17	and	and	CCONJ
ejpam-3279	146	18	only	only	ADV
ejpam-3279	146	19	if	if	SCONJ
ejpam-3279	146	20	,	,	PUNCT
ejpam-3279	146	21	m	m	PROPN
ejpam-3279	146	22	is	be	AUX
ejpam-3279	146	23	φ	φ	ADJ
ejpam-3279	146	24	-	-	PUNCT
ejpam-3279	146	25	invariant	invariant	ADJ
ejpam-3279	146	26	ricci	ricci	PROPN
ejpam-3279	146	27	tensor	tensor	NOUN
ejpam-3279	146	28	.	.	PUNCT
ejpam-3279	147	1	proof	proof	NOUN
ejpam-3279	147	2	:	:	PUNCT
ejpam-3279	147	3	suppose	suppose	VERB
ejpam-3279	147	4	that	that	SCONJ
ejpam-3279	147	5	cr3	cr3	PROPN
ejpam-3279	147	6	and	and	CCONJ
ejpam-3279	147	7	pr3	pr3	NOUN
ejpam-3279	147	8	are	be	AUX
ejpam-3279	147	9	coincide	coincide	ADJ
ejpam-3279	147	10	,	,	PUNCT
ejpam-3279	147	11	then	then	ADV
ejpam-3279	147	12	we	we	PRON
ejpam-3279	147	13	have	have	VERB
ejpam-3279	147	14	1	1	NUM
ejpam-3279	147	15	2n	2n	NUM
ejpam-3279	147	16	rbcδ	rbcδ	NOUN
ejpam-3279	147	17	a	a	DET
ejpam-3279	147	18	d	d	X
ejpam-3279	147	19	(	(	PUNCT
ejpam-3279	147	20	3.11	3.11	NUM
ejpam-3279	147	21	)	)	PUNCT
ejpam-3279	147	22	contracting	contract	VERB
ejpam-3279	147	23	the	the	DET
ejpam-3279	147	24	equation	equation	NOUN
ejpam-3279	147	25	(	(	PUNCT
ejpam-3279	147	26	3.11	3.11	NUM
ejpam-3279	147	27	)	)	PUNCT
ejpam-3279	147	28	by	by	ADP
ejpam-3279	147	29	the	the	DET
ejpam-3279	147	30	induces	induce	NOUN
ejpam-3279	147	31	(	(	PUNCT
ejpam-3279	147	32	a	a	DET
ejpam-3279	147	33	,	,	PUNCT
ejpam-3279	147	34	b	b	NOUN
ejpam-3279	147	35	)	)	PUNCT
ejpam-3279	147	36	,	,	PUNCT
ejpam-3279	147	37	we	we	PRON
ejpam-3279	147	38	get	get	VERB
ejpam-3279	147	39	rdc	rdc	NOUN
ejpam-3279	147	40	=	=	SYM
ejpam-3279	147	41	0	0	PUNCT
ejpam-3279	147	42	suppose	suppose	VERB
ejpam-3279	147	43	that	that	SCONJ
ejpam-3279	147	44	m	m	PROPN
ejpam-3279	147	45	is	be	AUX
ejpam-3279	147	46	φ	φ	ADJ
ejpam-3279	147	47	-	-	PUNCT
ejpam-3279	147	48	invariant	invariant	ADJ
ejpam-3279	147	49	ricci	ricci	PROPN
ejpam-3279	147	50	tensor	tensor	NOUN
ejpam-3279	147	51	.	.	PUNCT
ejpam-3279	148	1	making	make	VERB
ejpam-3279	148	2	use	use	NOUN
ejpam-3279	148	3	of	of	ADP
ejpam-3279	148	4	lemmas	lemmas	PROPN
ejpam-3279	148	5	3.1	3.1	NUM
ejpam-3279	148	6	and	and	CCONJ
ejpam-3279	148	7	2.2	2.2	NUM
ejpam-3279	148	8	,	,	PUNCT
ejpam-3279	148	9	it	it	PRON
ejpam-3279	148	10	follows	follow	VERB
ejpam-3279	148	11	that	that	SCONJ
ejpam-3279	148	12	pȧbcd	pȧbcd	NOUN
ejpam-3279	148	13	=	=	PUNCT
ejpam-3279	148	14	rȧbcd	rȧbcd	VERB
ejpam-3279	148	15	therefore	therefore	ADV
ejpam-3279	148	16	,	,	PUNCT
ejpam-3279	148	17	cr3	cr3	PROPN
ejpam-3279	148	18	and	and	CCONJ
ejpam-3279	148	19	pr3	pr3	NOUN
ejpam-3279	148	20	are	be	AUX
ejpam-3279	148	21	coincide	coincide	ADJ
ejpam-3279	148	22	.	.	PUNCT
ejpam-3279	149	1	theorem	theorem	VERB
ejpam-3279	149	2	3.5	3.5	NUM
ejpam-3279	149	3	.	.	PUNCT
ejpam-3279	150	1	suppose	suppose	VERB
ejpam-3279	150	2	that	that	SCONJ
ejpam-3279	150	3	m	m	PROPN
ejpam-3279	150	4	is	be	AUX
ejpam-3279	150	5	pr	pr	NOUN
ejpam-3279	150	6	-	-	PUNCT
ejpam-3279	150	7	recurrent	recurrent	ADJ
ejpam-3279	150	8	nc	nc	NOUN
ejpam-3279	150	9	-	-	ADJ
ejpam-3279	150	10	manifold	manifold	ADJ
ejpam-3279	150	11	.	.	PUNCT
ejpam-3279	151	1	then	then	ADV
ejpam-3279	151	2	m	m	PROPN
ejpam-3279	151	3	is	be	AUX
ejpam-3279	151	4	either	either	CCONJ
ejpam-3279	151	5	projective	projective	ADJ
ejpam-3279	151	6	symmetrical	symmetrical	ADJ
ejpam-3279	151	7	manifold	manifold	NOUN
ejpam-3279	151	8	or	or	CCONJ
ejpam-3279	151	9	vanishing	vanish	VERB
ejpam-3279	151	10	first	first	ADJ
ejpam-3279	151	11	structure	structure	NOUN
ejpam-3279	151	12	tensor	tensor	NOUN
ejpam-3279	151	13	.	.	PUNCT
ejpam-3279	152	1	proof	proof	NOUN
ejpam-3279	152	2	:	:	PUNCT
ejpam-3279	152	3	let	let	VERB
ejpam-3279	152	4	m	m	PRON
ejpam-3279	152	5	be	be	AUX
ejpam-3279	152	6	pr	pr	NOUN
ejpam-3279	152	7	-	-	PUNCT
ejpam-3279	152	8	recurrent	recurrent	NOUN
ejpam-3279	152	9	nc	nc	PROPN
ejpam-3279	152	10	-manifold	-manifold	PROPN
ejpam-3279	152	11	.	.	PUNCT
ejpam-3279	153	1	according	accord	VERB
ejpam-3279	153	2	to	to	ADP
ejpam-3279	153	3	the	the	DET
ejpam-3279	153	4	definition	definition	NOUN
ejpam-3279	153	5	2.11	2.11	NUM
ejpam-3279	153	6	,	,	PUNCT
ejpam-3279	153	7	m	m	VERB
ejpam-3279	153	8	is	be	AUX
ejpam-3279	153	9	p	p	PROPN
ejpam-3279	153	10	-recurrent	-recurrent	PROPN
ejpam-3279	153	11	and	and	CCONJ
ejpam-3279	153	12	r	r	NOUN
ejpam-3279	153	13	-	-	PUNCT
ejpam-3279	153	14	recurrent	recurrent	NOUN
ejpam-3279	153	15	nc	nc	PROPN
ejpam-3279	153	16	-manifold	-manifold	PROPN
ejpam-3279	153	17	.	.	PUNCT
ejpam-3279	154	1	from	from	ADP
ejpam-3279	154	2	definition	definition	NOUN
ejpam-3279	154	3	2.10	2.10	NUM
ejpam-3279	154	4	,	,	PUNCT
ejpam-3279	154	5	we	we	PRON
ejpam-3279	154	6	have	have	VERB
ejpam-3279	154	7	∇p	∇p	NOUN
ejpam-3279	154	8	=	=	SYM
ejpam-3279	154	9	ρ⊗	ρ⊗	NOUN
ejpam-3279	154	10	p	p	NOUN
ejpam-3279	154	11	which	which	PRON
ejpam-3279	154	12	has	have	VERB
ejpam-3279	154	13	the	the	DET
ejpam-3279	154	14	following	follow	VERB
ejpam-3279	154	15	coordinate	coordinate	NOUN
ejpam-3279	154	16	form	form	NOUN
ejpam-3279	154	17	pijk`,h	pijk`,h	NOUN
ejpam-3279	155	1	=	=	SYM
ejpam-3279	155	2	ρhpijk	ρhpijk	PROPN
ejpam-3279	155	3	`	`	PUNCT
ejpam-3279	155	4	(	(	PUNCT
ejpam-3279	155	5	3.12	3.12	NUM
ejpam-3279	155	6	)	)	PUNCT
ejpam-3279	155	7	consider	consider	VERB
ejpam-3279	155	8	the	the	DET
ejpam-3279	155	9	equation	equation	NOUN
ejpam-3279	155	10	(	(	PUNCT
ejpam-3279	155	11	3.12	3.12	NUM
ejpam-3279	155	12	)	)	PUNCT
ejpam-3279	155	13	in	in	ADP
ejpam-3279	155	14	the	the	DET
ejpam-3279	155	15	g	g	NOUN
ejpam-3279	155	16	-	-	PUNCT
ejpam-3279	155	17	adjoined	adjoin	VERB
ejpam-3279	155	18	structure	structure	NOUN
ejpam-3279	155	19	space	space	NOUN
ejpam-3279	155	20	,	,	PUNCT
ejpam-3279	155	21	so	so	SCONJ
ejpam-3279	155	22	we	we	PRON
ejpam-3279	155	23	have	have	AUX
ejpam-3279	155	24	pâb̂cd	pâb̂cd	NOUN
ejpam-3279	155	25	,	,	PUNCT
ejpam-3279	155	26	k	k	NOUN
ejpam-3279	155	27	=	=	PUNCT
ejpam-3279	155	28	ρkpâb̂cd	ρkpâb̂cd	NOUN
ejpam-3279	155	29	,	,	PUNCT
ejpam-3279	155	30	k	k	X
ejpam-3279	155	31	(	(	PUNCT
ejpam-3279	155	32	3.13	3.13	NUM
ejpam-3279	155	33	)	)	PUNCT
ejpam-3279	155	34	according	accord	VERB
ejpam-3279	155	35	to	to	ADP
ejpam-3279	155	36	the	the	DET
ejpam-3279	155	37	lemma	lemma	PROPN
ejpam-3279	155	38	3.1	3.1	NUM
ejpam-3279	155	39	,	,	PUNCT
ejpam-3279	155	40	the	the	DET
ejpam-3279	155	41	equation	equation	NOUN
ejpam-3279	155	42	(	(	PUNCT
ejpam-3279	155	43	3.13	3.13	NUM
ejpam-3279	155	44	)	)	PUNCT
ejpam-3279	155	45	becomes	become	VERB
ejpam-3279	155	46	−2babhbhcd	−2babhbhcd	NOUN
ejpam-3279	155	47	,	,	PUNCT
ejpam-3279	155	48	k	k	PROPN
ejpam-3279	155	49	−	−	PROPN
ejpam-3279	155	50	1	1	NUM
ejpam-3279	155	51	2n	2n	NUM
ejpam-3279	155	52	[	[	X
ejpam-3279	155	53	rac	rac	NOUN
ejpam-3279	155	54	,	,	PUNCT
ejpam-3279	155	55	kδ	kδ	NOUN
ejpam-3279	155	56	b	b	PROPN
ejpam-3279	156	1	d	d	PROPN
ejpam-3279	156	2	−	−	PROPN
ejpam-3279	156	3	rbc	rbc	PROPN
ejpam-3279	156	4	,	,	PUNCT
ejpam-3279	156	5	kδad	kδad	NOUN
ejpam-3279	156	6	]	]	PUNCT
ejpam-3279	156	7	=	=	PUNCT
ejpam-3279	156	8	ρk[−2babhbhcd	ρk[−2babhbhcd	ADJ
ejpam-3279	156	9	−	−	PROPN
ejpam-3279	156	10	1	1	NUM
ejpam-3279	156	11	2n	2n	NUM
ejpam-3279	157	1	[	[	X
ejpam-3279	157	2	rac	rac	PROPN
ejpam-3279	157	3	δ	δ	PROPN
ejpam-3279	157	4	b	b	PROPN
ejpam-3279	157	5	d	d	NOUN
ejpam-3279	157	6	−	−	PROPN
ejpam-3279	157	7	rbcδad	rbcδad	NOUN
ejpam-3279	157	8	]	]	X
ejpam-3279	157	9	]	]	X
ejpam-3279	157	10	making	make	VERB
ejpam-3279	157	11	use	use	NOUN
ejpam-3279	157	12	of	of	ADP
ejpam-3279	157	13	the	the	DET
ejpam-3279	157	14	definition	definition	NOUN
ejpam-3279	157	15	2.10	2.10	NUM
ejpam-3279	157	16	,	,	PUNCT
ejpam-3279	157	17	it	it	PRON
ejpam-3279	157	18	follows	follow	VERB
ejpam-3279	157	19	that	that	SCONJ
ejpam-3279	157	20	babhbhcd	babhbhcd	NOUN
ejpam-3279	157	21	,	,	PUNCT
ejpam-3279	157	22	k	k	PROPN
ejpam-3279	157	23	=	=	PUNCT
ejpam-3279	157	24	−ρkbabhbhcd	−ρkbabhbhcd	ADJ
ejpam-3279	157	25	symmetrization	symmetrization	NOUN
ejpam-3279	157	26	and	and	CCONJ
ejpam-3279	157	27	antisymmetrization	antisymmetrization	NOUN
ejpam-3279	157	28	by	by	ADP
ejpam-3279	157	29	induces	induce	NOUN
ejpam-3279	157	30	(	(	PUNCT
ejpam-3279	157	31	a	a	DET
ejpam-3279	157	32	,	,	PUNCT
ejpam-3279	157	33	b	b	NOUN
ejpam-3279	157	34	)	)	PUNCT
ejpam-3279	157	35	,	,	PUNCT
ejpam-3279	157	36	we	we	PRON
ejpam-3279	157	37	obtain	obtain	VERB
ejpam-3279	157	38	ρkb	ρkb	ADJ
ejpam-3279	157	39	abhbhcd	abhbhcd	NOUN
ejpam-3279	157	40	=	=	SYM
ejpam-3279	157	41	0	0	NUM
ejpam-3279	157	42	contracting	contract	VERB
ejpam-3279	157	43	the	the	DET
ejpam-3279	157	44	last	last	ADJ
ejpam-3279	157	45	equation	equation	NOUN
ejpam-3279	157	46	by	by	ADP
ejpam-3279	157	47	induces	induce	NOUN
ejpam-3279	157	48	(	(	PUNCT
ejpam-3279	157	49	a	a	DET
ejpam-3279	157	50	,	,	PUNCT
ejpam-3279	157	51	c	c	NOUN
ejpam-3279	157	52	)	)	PUNCT
ejpam-3279	157	53	and	and	CCONJ
ejpam-3279	157	54	(	(	PUNCT
ejpam-3279	157	55	b	b	X
ejpam-3279	157	56	,	,	PUNCT
ejpam-3279	157	57	d),we	d),we	PROPN
ejpam-3279	157	58	get	get	VERB
ejpam-3279	157	59	ρkb	ρkb	ADJ
ejpam-3279	157	60	abhbhab	abhbhab	NOUN
ejpam-3279	157	61	=	=	SYM
ejpam-3279	157	62	0	0	NUM
ejpam-3279	157	63	n.	n.	PROPN
ejpam-3279	157	64	j.	j.	PROPN
ejpam-3279	157	65	mohammed	mohammed	PROPN
ejpam-3279	157	66	,	,	PUNCT
ejpam-3279	157	67	h.	h.	PROPN
ejpam-3279	157	68	m.	m.	PROPN
ejpam-3279	157	69	abood	abood	PROPN
ejpam-3279	157	70	/	/	SYM
ejpam-3279	157	71	eur	eur	PROPN
ejpam-3279	157	72	.	.	PUNCT
ejpam-3279	158	1	j.	j.	PROPN
ejpam-3279	158	2	pure	pure	PROPN
ejpam-3279	158	3	appl	appl	PROPN
ejpam-3279	158	4	.	.	PROPN
ejpam-3279	158	5	math	math	PROPN
ejpam-3279	158	6	,	,	PUNCT
ejpam-3279	158	7	11	11	NUM
ejpam-3279	158	8	(	(	PUNCT
ejpam-3279	158	9	3	3	NUM
ejpam-3279	158	10	)	)	PUNCT
ejpam-3279	158	11	(	(	PUNCT
ejpam-3279	158	12	2018	2018	NUM
ejpam-3279	158	13	)	)	PUNCT
ejpam-3279	158	14	,	,	PUNCT
ejpam-3279	158	15	823	823	NUM
ejpam-3279	158	16	-	-	SYM
ejpam-3279	158	17	833	833	NUM
ejpam-3279	158	18	831	831	NUM
ejpam-3279	158	19	consequently	consequently	ADV
ejpam-3279	158	20	,	,	PUNCT
ejpam-3279	158	21	either	either	CCONJ
ejpam-3279	158	22	ρk	ρk	ADP
ejpam-3279	158	23	=	=	SYM
ejpam-3279	158	24	0	0	PROPN
ejpam-3279	158	25	,	,	PUNCT
ejpam-3279	158	26	i.e	i.e	PROPN
ejpam-3279	159	1	∇p	∇p	NOUN
ejpam-3279	159	2	=	=	NOUN
ejpam-3279	159	3	0	0	NUM
ejpam-3279	159	4	which	which	PRON
ejpam-3279	159	5	means	mean	VERB
ejpam-3279	159	6	that	that	SCONJ
ejpam-3279	159	7	m	m	NOUN
ejpam-3279	159	8	is	be	AUX
ejpam-3279	159	9	projective	projective	ADJ
ejpam-3279	159	10	symmetrical	symmetrical	ADJ
ejpam-3279	159	11	manifold	manifold	NOUN
ejpam-3279	159	12	.	.	PUNCT
ejpam-3279	160	1	or	or	CCONJ
ejpam-3279	160	2	,	,	PUNCT
ejpam-3279	160	3	babhbhab	babhbhab	PROPN
ejpam-3279	160	4	=	=	SYM
ejpam-3279	160	5	0	0	NUM
ejpam-3279	161	1	so	so	CCONJ
ejpam-3279	161	2	by	by	ADP
ejpam-3279	161	3	using	use	VERB
ejpam-3279	161	4	the	the	DET
ejpam-3279	161	5	same	same	ADJ
ejpam-3279	161	6	technique	technique	NOUN
ejpam-3279	161	7	in	in	ADP
ejpam-3279	161	8	proof	proof	NOUN
ejpam-3279	161	9	of	of	ADP
ejpam-3279	161	10	the	the	DET
ejpam-3279	161	11	theorem	theorem	NOUN
ejpam-3279	161	12	3.1	3.1	NUM
ejpam-3279	161	13	,	,	PUNCT
ejpam-3279	161	14	we	we	PRON
ejpam-3279	161	15	have	have	VERB
ejpam-3279	161	16	babh	babh	NOUN
ejpam-3279	161	17	=	=	SYM
ejpam-3279	161	18	0	0	PUNCT
ejpam-3279	162	1	therefore	therefore	ADV
ejpam-3279	162	2	,	,	PUNCT
ejpam-3279	162	3	the	the	DET
ejpam-3279	162	4	first	first	ADJ
ejpam-3279	162	5	structure	structure	NOUN
ejpam-3279	162	6	tensor	tensor	NOUN
ejpam-3279	162	7	is	be	AUX
ejpam-3279	162	8	vanishing	vanish	VERB
ejpam-3279	162	9	.	.	PUNCT
ejpam-3279	163	1	theorem	theorem	ADJ
ejpam-3279	163	2	3.6	3.6	NUM
ejpam-3279	163	3	.	.	PUNCT
ejpam-3279	164	1	suppose	suppose	VERB
ejpam-3279	164	2	that	that	SCONJ
ejpam-3279	164	3	m	m	PROPN
ejpam-3279	164	4	is	be	AUX
ejpam-3279	164	5	pr	pr	NOUN
ejpam-3279	164	6	-	-	PUNCT
ejpam-3279	164	7	recurrent	recurrent	ADJ
ejpam-3279	164	8	nc	nc	NOUN
ejpam-3279	164	9	-	-	ADJ
ejpam-3279	164	10	manifold	manifold	NOUN
ejpam-3279	164	11	.	.	PUNCT
ejpam-3279	165	1	then	then	ADV
ejpam-3279	165	2	the	the	DET
ejpam-3279	165	3	sectional	sectional	ADJ
ejpam-3279	165	4	curvature	curvature	NOUN
ejpam-3279	165	5	tensor	tensor	NOUN
ejpam-3279	165	6	is	be	AUX
ejpam-3279	165	7	recurrent	recurrent	ADJ
ejpam-3279	165	8	if	if	SCONJ
ejpam-3279	165	9	and	and	CCONJ
ejpam-3279	165	10	only	only	ADV
ejpam-3279	165	11	if	if	SCONJ
ejpam-3279	165	12	,	,	PUNCT
ejpam-3279	165	13	the	the	DET
ejpam-3279	165	14	second	second	ADJ
ejpam-3279	165	15	structure	structure	NOUN
ejpam-3279	165	16	tensor	tensor	NOUN
ejpam-3279	165	17	is	be	AUX
ejpam-3279	165	18	recurrent	recurrent	ADJ
ejpam-3279	165	19	.	.	PUNCT
ejpam-3279	166	1	proof	proof	NOUN
ejpam-3279	166	2	:	:	PUNCT
ejpam-3279	166	3	let	let	VERB
ejpam-3279	166	4	m	m	PRON
ejpam-3279	166	5	be	be	AUX
ejpam-3279	166	6	pr	pr	NOUN
ejpam-3279	166	7	-	-	PUNCT
ejpam-3279	166	8	recurrent	recurrent	NOUN
ejpam-3279	166	9	nc	nc	PROPN
ejpam-3279	166	10	-manifold	-manifold	PROPN
ejpam-3279	166	11	.	.	PUNCT
ejpam-3279	167	1	according	accord	VERB
ejpam-3279	167	2	to	to	ADP
ejpam-3279	167	3	the	the	DET
ejpam-3279	167	4	definition	definition	NOUN
ejpam-3279	167	5	2.11	2.11	NUM
ejpam-3279	167	6	,	,	PUNCT
ejpam-3279	167	7	m	m	VERB
ejpam-3279	167	8	is	be	AUX
ejpam-3279	167	9	p	p	PROPN
ejpam-3279	167	10	-recurrent	-recurrent	PROPN
ejpam-3279	167	11	and	and	CCONJ
ejpam-3279	167	12	r	r	NOUN
ejpam-3279	167	13	-	-	PUNCT
ejpam-3279	167	14	recurrent	recurrent	NOUN
ejpam-3279	167	15	nc	nc	PROPN
ejpam-3279	167	16	-manifold	-manifold	PROPN
ejpam-3279	167	17	.	.	PUNCT
ejpam-3279	168	1	now	now	ADV
ejpam-3279	168	2	the	the	DET
ejpam-3279	168	3	definition	definition	NOUN
ejpam-3279	168	4	2.10	2.10	NUM
ejpam-3279	168	5	implies	imply	VERB
ejpam-3279	168	6	,	,	PUNCT
ejpam-3279	168	7	∇p	∇p	PROPN
ejpam-3279	168	8	=	=	SYM
ejpam-3279	168	9	ρ⊗	ρ⊗	NOUN
ejpam-3279	168	10	p	p	NOUN
ejpam-3279	168	11	the	the	DET
ejpam-3279	168	12	previous	previous	ADJ
ejpam-3279	168	13	tensor	tensor	NOUN
ejpam-3279	168	14	has	have	VERB
ejpam-3279	168	15	the	the	DET
ejpam-3279	168	16	following	follow	VERB
ejpam-3279	168	17	coordinate	coordinate	NOUN
ejpam-3279	168	18	form	form	NOUN
ejpam-3279	168	19	pijk`,h	pijk`,h	NOUN
ejpam-3279	168	20	=	=	SYM
ejpam-3279	168	21	ρhpijk	ρhpijk	PROPN
ejpam-3279	168	22	`	`	PUNCT
ejpam-3279	168	23	(	(	PUNCT
ejpam-3279	168	24	3.14	3.14	NUM
ejpam-3279	168	25	)	)	PUNCT
ejpam-3279	168	26	consider	consider	VERB
ejpam-3279	168	27	the	the	DET
ejpam-3279	168	28	equation	equation	NOUN
ejpam-3279	168	29	(	(	PUNCT
ejpam-3279	168	30	3.14	3.14	NUM
ejpam-3279	168	31	)	)	PUNCT
ejpam-3279	168	32	in	in	ADP
ejpam-3279	168	33	the	the	DET
ejpam-3279	168	34	g	g	NOUN
ejpam-3279	168	35	-	-	PUNCT
ejpam-3279	168	36	adjoined	adjoin	VERB
ejpam-3279	168	37	structure	structure	NOUN
ejpam-3279	168	38	space	space	NOUN
ejpam-3279	168	39	,	,	PUNCT
ejpam-3279	168	40	it	it	PRON
ejpam-3279	168	41	follows	follow	VERB
ejpam-3279	168	42	that	that	PRON
ejpam-3279	168	43	pâbcd̂,k	pâbcd̂,k	NOUN
ejpam-3279	168	44	=	=	SYM
ejpam-3279	168	45	ρkpâbcd̂,k	ρkpâbcd̂,k	PROPN
ejpam-3279	168	46	(	(	PUNCT
ejpam-3279	168	47	3.15	3.15	NUM
ejpam-3279	168	48	)	)	PUNCT
ejpam-3279	168	49	by	by	ADP
ejpam-3279	168	50	using	use	VERB
ejpam-3279	168	51	lemma	lemma	PROPN
ejpam-3279	168	52	3.1	3.1	NUM
ejpam-3279	168	53	,	,	PUNCT
ejpam-3279	168	54	then	then	ADV
ejpam-3279	168	55	the	the	DET
ejpam-3279	168	56	equation	equation	NOUN
ejpam-3279	168	57	(	(	PUNCT
ejpam-3279	168	58	3.15	3.15	NUM
ejpam-3279	168	59	)	)	PUNCT
ejpam-3279	168	60	becomes	become	VERB
ejpam-3279	168	61	aadbc	aadbc	PROPN
ejpam-3279	168	62	,	,	PUNCT
ejpam-3279	168	63	k	k	PROPN
ejpam-3279	168	64	−badhbhbc	−badhbhbc	PROPN
ejpam-3279	168	65	,	,	PUNCT
ejpam-3279	168	66	k	k	PROPN
ejpam-3279	169	1	−	−	PROPN
ejpam-3279	169	2	5	5	NUM
ejpam-3279	169	3	3	3	NUM
ejpam-3279	169	4	cadbc	cadbc	NOUN
ejpam-3279	169	5	,	,	PUNCT
ejpam-3279	169	6	k	k	PROPN
ejpam-3279	169	7	−	−	PROPN
ejpam-3279	169	8	1	1	NUM
ejpam-3279	169	9	2n	2n	NUM
ejpam-3279	169	10	rac	rac	NOUN
ejpam-3279	169	11	,	,	PUNCT
ejpam-3279	169	12	kδ	kδ	NOUN
ejpam-3279	169	13	d	d	PROPN
ejpam-3279	169	14	b	b	X
ejpam-3279	169	15	=	=	PRON
ejpam-3279	169	16	ρk[a	ρk[a	PROPN
ejpam-3279	169	17	ad	ad	NOUN
ejpam-3279	169	18	bc	bc	X
ejpam-3279	169	19	−badhbhbc	−badhbhbc	PROPN
ejpam-3279	169	20	−	−	PROPN
ejpam-3279	169	21	5	5	NUM
ejpam-3279	169	22	3	3	NUM
ejpam-3279	169	23	cadbc	cadbc	NOUN
ejpam-3279	169	24	−	−	NOUN
ejpam-3279	169	25	1	1	NUM
ejpam-3279	169	26	2n	2n	NUM
ejpam-3279	169	27	rac	rac	PROPN
ejpam-3279	169	28	δ	δ	PROPN
ejpam-3279	169	29	d	d	PROPN
ejpam-3279	169	30	b	b	PROPN
ejpam-3279	169	31	]	]	PUNCT
ejpam-3279	169	32	according	accord	VERB
ejpam-3279	169	33	to	to	ADP
ejpam-3279	169	34	the	the	DET
ejpam-3279	169	35	definition	definition	NOUN
ejpam-3279	169	36	2.10	2.10	NUM
ejpam-3279	169	37	,	,	PUNCT
ejpam-3279	169	38	we	we	PRON
ejpam-3279	169	39	have	have	VERB
ejpam-3279	169	40	aadbc	aadbc	NOUN
ejpam-3279	169	41	,	,	PUNCT
ejpam-3279	169	42	k	k	PROPN
ejpam-3279	169	43	−badhbhbc	−badhbhbc	PROPN
ejpam-3279	169	44	,	,	PUNCT
ejpam-3279	169	45	k	k	PROPN
ejpam-3279	169	46	−	−	PROPN
ejpam-3279	169	47	5	5	NUM
ejpam-3279	169	48	3	3	NUM
ejpam-3279	169	49	cadbc	cadbc	NOUN
ejpam-3279	169	50	,	,	PUNCT
ejpam-3279	169	51	k	k	NOUN
ejpam-3279	170	1	=	=	PRON
ejpam-3279	170	2	ρk[a	ρk[a	NOUN
ejpam-3279	170	3	ad	ad	NOUN
ejpam-3279	170	4	bc	bc	X
ejpam-3279	170	5	−badhbhbc	−badhbhbc	PROPN
ejpam-3279	170	6	−	−	PROPN
ejpam-3279	170	7	5	5	NUM
ejpam-3279	170	8	3	3	NUM
ejpam-3279	170	9	cadbc	cadbc	NOUN
ejpam-3279	170	10	]	]	PUNCT
ejpam-3279	170	11	(	(	PUNCT
ejpam-3279	170	12	3.16	3.16	NUM
ejpam-3279	170	13	)	)	PUNCT
ejpam-3279	170	14	symmetrization	symmetrization	NOUN
ejpam-3279	170	15	and	and	CCONJ
ejpam-3279	170	16	antisymmetrization	antisymmetrization	NOUN
ejpam-3279	170	17	the	the	DET
ejpam-3279	170	18	equation	equation	NOUN
ejpam-3279	170	19	(	(	PUNCT
ejpam-3279	170	20	3.16	3.16	NUM
ejpam-3279	170	21	)	)	PUNCT
ejpam-3279	170	22	by	by	ADP
ejpam-3279	170	23	the	the	DET
ejpam-3279	170	24	induces	induce	NOUN
ejpam-3279	170	25	(	(	PUNCT
ejpam-3279	170	26	h	h	NOUN
ejpam-3279	170	27	,	,	PUNCT
ejpam-3279	170	28	b	b	NOUN
ejpam-3279	170	29	)	)	PUNCT
ejpam-3279	170	30	,	,	PUNCT
ejpam-3279	170	31	we	we	PRON
ejpam-3279	170	32	get	get	VERB
ejpam-3279	170	33	aadbc	aadbc	NOUN
ejpam-3279	170	34	,	,	PUNCT
ejpam-3279	170	35	k	k	PROPN
ejpam-3279	170	36	−	−	PROPN
ejpam-3279	170	37	5	5	NUM
ejpam-3279	170	38	3	3	NUM
ejpam-3279	170	39	cadbc	cadbc	NOUN
ejpam-3279	170	40	,	,	PUNCT
ejpam-3279	170	41	k	k	NOUN
ejpam-3279	171	1	=	=	PUNCT
ejpam-3279	171	2	ρk[a	ρk[a	NOUN
ejpam-3279	171	3	ad	ad	NOUN
ejpam-3279	171	4	bc	bc	PROPN
ejpam-3279	171	5	−	−	PROPN
ejpam-3279	171	6	5	5	NUM
ejpam-3279	171	7	3	3	NUM
ejpam-3279	171	8	cadbc	cadbc	NOUN
ejpam-3279	171	9	]	]	PUNCT
ejpam-3279	171	10	(	(	PUNCT
ejpam-3279	171	11	3.17	3.17	NUM
ejpam-3279	171	12	)	)	PUNCT
ejpam-3279	171	13	now	now	ADV
ejpam-3279	171	14	,	,	PUNCT
ejpam-3279	171	15	if	if	SCONJ
ejpam-3279	171	16	the	the	DET
ejpam-3279	171	17	structure	structure	NOUN
ejpam-3279	171	18	tensor	tensor	NOUN
ejpam-3279	171	19	is	be	AUX
ejpam-3279	171	20	recurrent	recurrent	ADJ
ejpam-3279	171	21	so	so	ADV
ejpam-3279	171	22	(	(	PUNCT
ejpam-3279	171	23	3.17	3.17	NUM
ejpam-3279	171	24	)	)	PUNCT
ejpam-3279	171	25	becomes	become	VERB
ejpam-3279	171	26	aadbc	aadbc	NOUN
ejpam-3279	171	27	,	,	PUNCT
ejpam-3279	171	28	k	k	PROPN
ejpam-3279	171	29	=	=	PUNCT
ejpam-3279	171	30	ρka	ρka	PROPN
ejpam-3279	171	31	ad	ad	NOUN
ejpam-3279	171	32	bc	bc	VERB
ejpam-3279	171	33	conversely	conversely	ADV
ejpam-3279	171	34	,	,	PUNCT
ejpam-3279	171	35	if	if	SCONJ
ejpam-3279	171	36	the	the	DET
ejpam-3279	171	37	sectional	sectional	ADJ
ejpam-3279	171	38	curvature	curvature	NOUN
ejpam-3279	171	39	tensor	tensor	NOUN
ejpam-3279	171	40	is	be	AUX
ejpam-3279	171	41	recurrent	recurrent	ADJ
ejpam-3279	171	42	,	,	PUNCT
ejpam-3279	171	43	the	the	DET
ejpam-3279	171	44	the	the	DET
ejpam-3279	171	45	equation	equation	NOUN
ejpam-3279	171	46	(	(	PUNCT
ejpam-3279	171	47	3.17	3.17	NUM
ejpam-3279	171	48	)	)	PUNCT
ejpam-3279	171	49	gives	give	VERB
ejpam-3279	171	50	the	the	DET
ejpam-3279	171	51	following	follow	VERB
ejpam-3279	171	52	desired	desire	VERB
ejpam-3279	171	53	cadbc	cadbc	NOUN
ejpam-3279	171	54	,	,	PUNCT
ejpam-3279	172	1	k	k	PROPN
ejpam-3279	173	1	=	=	PUNCT
ejpam-3279	174	1	ρkc	ρkc	PROPN
ejpam-3279	174	2	ad	ad	NOUN
ejpam-3279	174	3	bc	bc	PROPN
ejpam-3279	174	4	.	.	PUNCT
ejpam-3279	175	1	references	reference	NOUN
ejpam-3279	175	2	832	832	NUM
ejpam-3279	175	3	references	reference	NOUN
ejpam-3279	175	4	[	[	X
ejpam-3279	175	5	1	1	NUM
ejpam-3279	175	6	]	]	PUNCT
ejpam-3279	175	7	abood	abood	PROPN
ejpam-3279	175	8	h.	h.	PROPN
ejpam-3279	175	9	m.	m.	PROPN
ejpam-3279	175	10	,	,	PUNCT
ejpam-3279	175	11	mohammed	mohammed	PROPN
ejpam-3279	175	12	n.	n.	PROPN
ejpam-3279	175	13	j.	j.	PROPN
ejpam-3279	175	14	,	,	PUNCT
ejpam-3279	175	15	locally	locally	ADV
ejpam-3279	175	16	conformal	conformal	ADJ
ejpam-3279	175	17	kahler	kahler	NOUN
ejpam-3279	175	18	manifold	manifold	ADJ
ejpam-3279	175	19	of	of	ADP
ejpam-3279	175	20	pointwise	pointwise	PROPN
ejpam-3279	175	21	holomorphic	holomorphic	ADJ
ejpam-3279	175	22	sectional	sectional	ADJ
ejpam-3279	175	23	curvature	curvature	NOUN
ejpam-3279	175	24	tensor	tensor	NOUN
ejpam-3279	175	25	,	,	PUNCT
ejpam-3279	175	26	international	international	PROPN
ejpam-3279	175	27	mathematical	mathematical	ADJ
ejpam-3279	175	28	forum	forum	PROPN
ejpam-3279	175	29	,	,	PUNCT
ejpam-3279	175	30	5	5	NUM
ejpam-3279	175	31	,	,	PUNCT
ejpam-3279	175	32	no.45	no.45	ADJ
ejpam-3279	175	33	,	,	PUNCT
ejpam-3279	175	34	p.2213	p.2213	NOUN
ejpam-3279	175	35	-	-	PUNCT
ejpam-3279	175	36	2224	2224	NUM
ejpam-3279	175	37	,	,	PUNCT
ejpam-3279	175	38	2010	2010	NUM
ejpam-3279	175	39	.	.	PUNCT
ejpam-3279	176	1	[	[	X
ejpam-3279	176	2	2	2	NUM
ejpam-3279	176	3	]	]	SYM
ejpam-3279	176	4	banaru	banaru	NOUN
ejpam-3279	176	5	m.	m.	NOUN
ejpam-3279	176	6	,	,	PUNCT
ejpam-3279	176	7	on	on	ADP
ejpam-3279	176	8	nearly	nearly	ADV
ejpam-3279	176	9	-	-	PUNCT
ejpam-3279	176	10	cosymplectic	cosymplectic	ADJ
ejpam-3279	176	11	hypersurfaces	hypersurface	NOUN
ejpam-3279	176	12	in	in	ADP
ejpam-3279	176	13	nearly	nearly	ADV
ejpam-3279	176	14	-	-	PUNCT
ejpam-3279	176	15	kahlerian	kahlerian	ADJ
ejpam-3279	176	16	manifolds	manifold	NOUN
ejpam-3279	176	17	,	,	PUNCT
ejpam-3279	176	18	studia	studia	PROPN
ejpam-3279	176	19	univ	univ	PROPN
ejpam-3279	176	20	.	.	PUNCT
ejpam-3279	177	1	babes	babe	NOUN
ejpam-3279	177	2	bolyai	bolyai	PROPN
ejpam-3279	177	3	.	.	PUNCT
ejpam-3279	178	1	math	math	NOUN
ejpam-3279	178	2	.	.	PUNCT
ejpam-3279	179	1	cluj	cluj	PROPN
ejpam-3279	179	2	napoca	napoca	PROPN
ejpam-3279	179	3	.	.	PUNCT
ejpam-3279	180	1	v.47	v.47	NOUN
ejpam-3279	180	2	.	.	PROPN
ejpam-3279	180	3	no.3	no.3	PROPN
ejpam-3279	180	4	.	.	PUNCT
ejpam-3279	180	5	2002	2002	NUM
ejpam-3279	180	6	.	.	PUNCT
ejpam-3279	181	1	[	[	X
ejpam-3279	181	2	3	3	NUM
ejpam-3279	181	3	]	]	X
ejpam-3279	181	4	blair	blair	PROPN
ejpam-3279	181	5	d.	d.	PROPN
ejpam-3279	181	6	e.	e.	PROPN
ejpam-3279	181	7	,	,	PUNCT
ejpam-3279	181	8	the	the	DET
ejpam-3279	181	9	theory	theory	NOUN
ejpam-3279	181	10	of	of	ADP
ejpam-3279	181	11	quasi	quasi	PROPN
ejpam-3279	181	12	sasakian	sasakian	PROPN
ejpam-3279	181	13	structures	structure	NOUN
ejpam-3279	181	14	,	,	PUNCT
ejpam-3279	181	15	j.	j.	PROPN
ejpam-3279	181	16	differential	differential	PROPN
ejpam-3279	181	17	geometry	geometry	NOUN
ejpam-3279	181	18	,	,	PUNCT
ejpam-3279	181	19	n.	n.	NOUN
ejpam-3279	181	20	1	1	NUM
ejpam-3279	181	21	,	,	PUNCT
ejpam-3279	181	22	p.	p.	NOUN
ejpam-3279	181	23	331	331	NUM
ejpam-3279	181	24	-	-	SYM
ejpam-3279	181	25	345	345	NUM
ejpam-3279	181	26	,	,	PUNCT
ejpam-3279	181	27	1967	1967	NUM
ejpam-3279	181	28	.	.	PUNCT
ejpam-3279	182	1	[	[	X
ejpam-3279	182	2	4	4	NUM
ejpam-3279	182	3	]	]	X
ejpam-3279	182	4	blair	blair	PROPN
ejpam-3279	182	5	d.	d.	PROPN
ejpam-3279	182	6	e.	e.	PROPN
ejpam-3279	182	7	,	,	PUNCT
ejpam-3279	182	8	showers	shower	VERB
ejpam-3279	182	9	d.	d.	PROPN
ejpam-3279	182	10	k.	k.	PROPN
ejpam-3279	182	11	,	,	PUNCT
ejpam-3279	182	12	almost	almost	ADV
ejpam-3279	182	13	contact	contact	NOUN
ejpam-3279	182	14	manifolds	manifold	NOUN
ejpam-3279	182	15	with	with	ADP
ejpam-3279	182	16	killing	kill	VERB
ejpam-3279	182	17	structure	structure	NOUN
ejpam-3279	182	18	tensors	tensor	NOUN
ejpam-3279	182	19	ii	ii	PROPN
ejpam-3279	182	20	,	,	PUNCT
ejpam-3279	182	21	j.	j.	PROPN
ejpam-3279	182	22	differential	differential	PROPN
ejpam-3279	182	23	geometry	geometry	NOUN
ejpam-3279	182	24	,	,	PUNCT
ejpam-3279	182	25	v.	v.	ADP
ejpam-3279	182	26	9	9	NUM
ejpam-3279	182	27	,	,	PUNCT
ejpam-3279	182	28	p.577	p.577	ADV
ejpam-3279	182	29	-	-	PUNCT
ejpam-3279	182	30	582	582	NUM
ejpam-3279	182	31	,	,	PUNCT
ejpam-3279	182	32	1974	1974	NUM
ejpam-3279	182	33	.	.	PUNCT
ejpam-3279	183	1	[	[	X
ejpam-3279	183	2	5	5	NUM
ejpam-3279	183	3	]	]	PUNCT
ejpam-3279	183	4	blair	blair	PROPN
ejpam-3279	183	5	d.	d.	PROPN
ejpam-3279	183	6	e.	e.	PROPN
ejpam-3279	183	7	,	,	PUNCT
ejpam-3279	183	8	showers	shower	VERB
ejpam-3279	183	9	d.	d.	PROPN
ejpam-3279	183	10	k.	k.	PROPN
ejpam-3279	183	11	,	,	PUNCT
ejpam-3279	183	12	yano	yano	PROPN
ejpam-3279	183	13	k.	k.	PROPN
ejpam-3279	183	14	,	,	PUNCT
ejpam-3279	183	15	nearly	nearly	ADV
ejpam-3279	183	16	sasakian	sasakian	ADJ
ejpam-3279	183	17	structure	structure	NOUN
ejpam-3279	183	18	,	,	PUNCT
ejpam-3279	183	19	kodoi	kodoi	PROPN
ejpam-3279	183	20	math	math	PROPN
ejpam-3279	183	21	.	.	PUNCT
ejpam-3279	184	1	sem	sem	PROPN
ejpam-3279	184	2	.	.	PUNCT
ejpam-3279	184	3	rep	rep	PROPN
ejpam-3279	184	4	.	.	PROPN
ejpam-3279	184	5	27	27	NUM
ejpam-3279	184	6	,	,	PUNCT
ejpam-3279	184	7	no	no	INTJ
ejpam-3279	184	8	.	.	NOUN
ejpam-3279	184	9	1	1	NUM
ejpam-3279	184	10	-	-	SYM
ejpam-3279	184	11	2	2	NUM
ejpam-3279	184	12	,	,	PUNCT
ejpam-3279	184	13	175	175	NUM
ejpam-3279	184	14	-	-	SYM
ejpam-3279	184	15	180	180	NUM
ejpam-3279	184	16	,	,	PUNCT
ejpam-3279	184	17	1976	1976	NUM
ejpam-3279	184	18	.	.	PUNCT
ejpam-3279	185	1	[	[	X
ejpam-3279	185	2	6	6	NUM
ejpam-3279	185	3	]	]	PUNCT
ejpam-3279	185	4	de	de	PROPN
ejpam-3279	185	5	u.	u.	PROPN
ejpam-3279	185	6	c.	c.	PROPN
ejpam-3279	185	7	and	and	CCONJ
ejpam-3279	185	8	de	de	PROPN
ejpam-3279	185	9	a.	a.	NOUN
ejpam-3279	185	10	,	,	PUNCT
ejpam-3279	185	11	on	on	ADP
ejpam-3279	185	12	some	some	DET
ejpam-3279	185	13	curvature	curvature	NOUN
ejpam-3279	185	14	properties	property	NOUN
ejpam-3279	185	15	of	of	ADP
ejpam-3279	185	16	k	k	ADJ
ejpam-3279	185	17	-contact	-contact	NOUN
ejpam-3279	185	18	manifold	manifold	ADJ
ejpam-3279	185	19	,	,	PUNCT
ejpam-3279	185	20	extracta	extracta	PROPN
ejpam-3279	185	21	mathematicae	mathematicae	PROPN
ejpam-3279	185	22	,	,	PUNCT
ejpam-3279	185	23	27	27	NUM
ejpam-3279	185	24	,	,	PUNCT
ejpam-3279	185	25	125	125	NUM
ejpam-3279	185	26	-	-	SYM
ejpam-3279	185	27	134	134	NUM
ejpam-3279	185	28	,	,	PUNCT
ejpam-3279	185	29	2012	2012	NUM
ejpam-3279	185	30	.	.	PUNCT
ejpam-3279	186	1	[	[	X
ejpam-3279	186	2	7	7	X
ejpam-3279	186	3	]	]	X
ejpam-3279	186	4	endo	endo	PROPN
ejpam-3279	186	5	h.	h.	PROPN
ejpam-3279	186	6	,	,	PUNCT
ejpam-3279	186	7	on	on	ADP
ejpam-3279	186	8	the	the	DET
ejpam-3279	186	9	curvature	curvature	NOUN
ejpam-3279	186	10	tensor	tensor	NOUN
ejpam-3279	186	11	of	of	ADP
ejpam-3279	186	12	nearly	nearly	ADV
ejpam-3279	186	13	cosymplectic	cosymplectic	ADJ
ejpam-3279	186	14	manifolds	manifold	NOUN
ejpam-3279	186	15	of	of	ADP
ejpam-3279	186	16	constant	constant	ADJ
ejpam-3279	186	17	φsection	φsection	NOUN
ejpam-3279	186	18	curvature	curvature	NOUN
ejpam-3279	186	19	,	,	PUNCT
ejpam-3279	186	20	an	an	PROPN
ejpam-3279	186	21	.	.	PUNCT
ejpam-3279	186	22	stin	stin	PROPN
ejpam-3279	186	23	.	.	PUNCT
ejpam-3279	186	24	univ	univ	PROPN
ejpam-3279	186	25	.	.	PUNCT
ejpam-3279	187	1	al	al	PROPN
ejpam-3279	187	2	.	.	PROPN
ejpam-3279	187	3	i.	i.	PROPN
ejpam-3279	187	4	cuza	cuza	PROPN
ejpam-3279	187	5	.	.	PUNCT
ejpam-3279	187	6	iasi	iasi	PROPN
ejpam-3279	187	7	.	.	PUNCT
ejpam-3279	188	1	t.	t.	PROPN
ejpam-3279	188	2	li	li	PROPN
ejpam-3279	188	3	.	.	PROPN
ejpam-3279	189	1	n.2	n.2	PROPN
ejpam-3279	189	2	,	,	PUNCT
ejpam-3279	189	3	p.439	p.439	NOUN
ejpam-3279	189	4	-	-	SYM
ejpam-3279	189	5	454	454	NUM
ejpam-3279	189	6	,	,	PUNCT
ejpam-3279	189	7	2005	2005	NUM
ejpam-3279	189	8	.	.	PUNCT
ejpam-3279	190	1	[	[	X
ejpam-3279	190	2	8	8	NUM
ejpam-3279	190	3	]	]	X
ejpam-3279	190	4	endo	endo	PROPN
ejpam-3279	190	5	h.	h.	PROPN
ejpam-3279	190	6	,	,	PUNCT
ejpam-3279	190	7	remarks	remark	VERB
ejpam-3279	190	8	on	on	ADP
ejpam-3279	190	9	nearly	nearly	ADV
ejpam-3279	190	10	cosymplectic	cosymplectic	ADJ
ejpam-3279	190	11	manifolds	manifold	NOUN
ejpam-3279	190	12	of	of	ADP
ejpam-3279	190	13	constant	constant	ADJ
ejpam-3279	190	14	φ	φ	NUM
ejpam-3279	190	15	-	-	PUNCT
ejpam-3279	190	16	section	section	NOUN
ejpam-3279	190	17	curvature	curvature	NOUN
ejpam-3279	190	18	with	with	ADP
ejpam-3279	190	19	a	a	DET
ejpam-3279	190	20	submersion	submersion	NOUN
ejpam-3279	190	21	of	of	ADP
ejpam-3279	190	22	geodesic	geodesic	ADJ
ejpam-3279	190	23	fiber	fiber	NOUN
ejpam-3279	190	24	,	,	PUNCT
ejpam-3279	190	25	tensor	tensor	NOUN
ejpam-3279	190	26	.	.	PUNCT
ejpam-3279	191	1	n.s.v.66	n.s.v.66	ADP
ejpam-3279	191	2	,	,	PUNCT
ejpam-3279	191	3	p.26	p.26	PROPN
ejpam-3279	191	4	-	-	PUNCT
ejpam-3279	191	5	39	39	NUM
ejpam-3279	191	6	,	,	PUNCT
ejpam-3279	191	7	2005	2005	NUM
ejpam-3279	191	8	.	.	PUNCT
ejpam-3279	192	1	[	[	X
ejpam-3279	192	2	9	9	X
ejpam-3279	192	3	]	]	X
ejpam-3279	192	4	ghosh	ghosh	PROPN
ejpam-3279	192	5	s.	s.	PROPN
ejpam-3279	192	6	,	,	PUNCT
ejpam-3279	192	7	on	on	ADP
ejpam-3279	192	8	a	a	DET
ejpam-3279	192	9	class	class	NOUN
ejpam-3279	192	10	of	of	ADP
ejpam-3279	192	11	(	(	PUNCT
ejpam-3279	192	12	k	k	X
ejpam-3279	192	13	,	,	PUNCT
ejpam-3279	192	14	µ)-contact	µ)-contact	NOUN
ejpam-3279	192	15	manifolds	manifold	NOUN
ejpam-3279	192	16	,	,	PUNCT
ejpam-3279	192	17	bull	bull	NOUN
ejpam-3279	192	18	.	.	PUNCT
ejpam-3279	193	1	cal	cal	PROPN
ejpam-3279	193	2	.	.	PUNCT
ejpam-3279	194	1	math	math	NOUN
ejpam-3279	194	2	.	.	PUNCT
ejpam-3279	195	1	soc	soc	PROPN
ejpam-3279	195	2	.	.	PUNCT
ejpam-3279	195	3	,	,	PUNCT
ejpam-3279	196	1	v.	v.	ADP
ejpam-3279	196	2	102	102	NUM
ejpam-3279	196	3	,	,	PUNCT
ejpam-3279	196	4	209	209	NUM
ejpam-3279	196	5	-	-	SYM
ejpam-3279	196	6	226	226	NUM
ejpam-3279	196	7	,	,	PUNCT
ejpam-3279	196	8	2010	2010	NUM
ejpam-3279	196	9	.	.	PUNCT
ejpam-3279	197	1	[	[	X
ejpam-3279	197	2	10	10	NUM
ejpam-3279	197	3	]	]	X
ejpam-3279	197	4	jawarneh	jawarneh	ADJ
ejpam-3279	197	5	m.	m.	NOUN
ejpam-3279	197	6	,	,	PUNCT
ejpam-3279	197	7	samui	samui	PROPN
ejpam-3279	197	8	s.	s.	PROPN
ejpam-3279	197	9	,	,	PUNCT
ejpam-3279	197	10	projective	projective	ADJ
ejpam-3279	197	11	curvature	curvature	NOUN
ejpam-3279	197	12	tensor	tensor	NOUN
ejpam-3279	197	13	on	on	ADP
ejpam-3279	197	14	(	(	PUNCT
ejpam-3279	197	15	k	k	NOUN
ejpam-3279	197	16	,	,	PUNCT
ejpam-3279	197	17	µ)-contact	µ)-contact	PUNCT
ejpam-3279	197	18	space	space	NOUN
ejpam-3279	197	19	forms	form	NOUN
ejpam-3279	197	20	,	,	PUNCT
ejpam-3279	197	21	journal	journal	NOUN
ejpam-3279	197	22	of	of	ADP
ejpam-3279	197	23	pure	pure	ADJ
ejpam-3279	197	24	and	and	CCONJ
ejpam-3279	197	25	applied	applied	ADJ
ejpam-3279	197	26	mathematics	mathematic	NOUN
ejpam-3279	197	27	,	,	PUNCT
ejpam-3279	197	28	v.	v.	ADP
ejpam-3279	197	29	113	113	NUM
ejpam-3279	197	30	,	,	PUNCT
ejpam-3279	197	31	no.3	no.3	VERB
ejpam-3279	197	32	,	,	PUNCT
ejpam-3279	197	33	p.	p.	NOUN
ejpam-3279	197	34	425	425	NUM
ejpam-3279	197	35	-	-	SYM
ejpam-3279	197	36	439	439	NUM
ejpam-3279	197	37	,	,	PUNCT
ejpam-3279	197	38	2017	2017	NUM
ejpam-3279	197	39	.	.	PUNCT
ejpam-3279	198	1	[	[	X
ejpam-3279	198	2	11	11	NUM
ejpam-3279	198	3	]	]	X
ejpam-3279	198	4	kirichenko	kirichenko	PROPN
ejpam-3279	198	5	v.	v.	CCONJ
ejpam-3279	198	6	f.	f.	PROPN
ejpam-3279	198	7	,	,	PUNCT
ejpam-3279	198	8	differential	differential	ADJ
ejpam-3279	198	9	geometry	geometry	NOUN
ejpam-3279	198	10	of	of	ADP
ejpam-3279	198	11	k	k	NOUN
ejpam-3279	198	12	-	-	NOUN
ejpam-3279	198	13	space	space	NOUN
ejpam-3279	198	14	,	,	PUNCT
ejpam-3279	198	15	problems	problem	NOUN
ejpam-3279	198	16	of	of	ADP
ejpam-3279	198	17	geometry	geometry	NOUN
ejpam-3279	198	18	,	,	PUNCT
ejpam-3279	198	19	v.8	v.8	NOUN
ejpam-3279	198	20	,	,	PUNCT
ejpam-3279	198	21	p.139160	p.139160	NOUN
ejpam-3279	198	22	,	,	PUNCT
ejpam-3279	198	23	1977	1977	NUM
ejpam-3279	198	24	.	.	PUNCT
ejpam-3279	199	1	[	[	X
ejpam-3279	199	2	12	12	NUM
ejpam-3279	199	3	]	]	X
ejpam-3279	199	4	kirichenko	kirichenko	PROPN
ejpam-3279	199	5	v.	v.	CCONJ
ejpam-3279	199	6	f.	f.	PROPN
ejpam-3279	199	7	,	,	PUNCT
ejpam-3279	199	8	the	the	DET
ejpam-3279	199	9	method	method	NOUN
ejpam-3279	199	10	of	of	ADP
ejpam-3279	199	11	generalization	generalization	NOUN
ejpam-3279	199	12	of	of	ADP
ejpam-3279	199	13	hermitian	hermitian	ADJ
ejpam-3279	199	14	geometry	geometry	NOUN
ejpam-3279	199	15	in	in	ADP
ejpam-3279	199	16	the	the	DET
ejpam-3279	199	17	almost	almost	ADV
ejpam-3279	199	18	hermitian	hermitian	ADJ
ejpam-3279	199	19	contact	contact	NOUN
ejpam-3279	199	20	manifold	manifold	NOUN
ejpam-3279	199	21	,	,	PUNCT
ejpam-3279	199	22	problems	problem	NOUN
ejpam-3279	199	23	of	of	ADP
ejpam-3279	199	24	geometry	geometry	NOUN
ejpam-3279	199	25	vinite	vinite	NOUN
ejpam-3279	199	26	anssr	anssr	PROPN
ejpam-3279	199	27	,	,	PUNCT
ejpam-3279	199	28	v.	v.	ADP
ejpam-3279	199	29	18	18	NUM
ejpam-3279	199	30	,	,	PUNCT
ejpam-3279	199	31	p.	p.	NOUN
ejpam-3279	199	32	25	25	NUM
ejpam-3279	199	33	-	-	SYM
ejpam-3279	199	34	71	71	NUM
ejpam-3279	199	35	,	,	PUNCT
ejpam-3279	199	36	1986	1986	NUM
ejpam-3279	199	37	.	.	PUNCT
ejpam-3279	200	1	[	[	X
ejpam-3279	200	2	13	13	NUM
ejpam-3279	200	3	]	]	X
ejpam-3279	200	4	kirichenko	kirichenko	PROPN
ejpam-3279	200	5	v.	v.	CCONJ
ejpam-3279	200	6	f.	f.	PROPN
ejpam-3279	200	7	,	,	PUNCT
ejpam-3279	200	8	differential	differential	ADJ
ejpam-3279	200	9	geometry	geometry	NOUN
ejpam-3279	200	10	structures	structure	NOUN
ejpam-3279	200	11	on	on	ADP
ejpam-3279	200	12	manifolds	manifold	NOUN
ejpam-3279	200	13	,	,	PUNCT
ejpam-3279	200	14	second	second	ADJ
ejpam-3279	200	15	edition	edition	NOUN
ejpam-3279	200	16	,	,	PUNCT
ejpam-3279	200	17	expanded	expand	VERB
ejpam-3279	200	18	.	.	PUNCT
ejpam-3279	201	1	odessa	odessa	ADJ
ejpam-3279	201	2	:	:	PUNCT
ejpam-3279	201	3	printing	printing	NOUN
ejpam-3279	201	4	house	house	NOUN
ejpam-3279	201	5	:	:	PUNCT
ejpam-3279	201	6	p.458	p.458	ADJ
ejpam-3279	201	7	,	,	PUNCT
ejpam-3279	201	8	2013	2013	NUM
ejpam-3279	201	9	.	.	PUNCT
ejpam-3279	202	1	[	[	X
ejpam-3279	202	2	14	14	NUM
ejpam-3279	202	3	]	]	X
ejpam-3279	202	4	kirichenko	kirichenko	PROPN
ejpam-3279	202	5	v.	v.	CCONJ
ejpam-3279	202	6	f.	f.	PROPN
ejpam-3279	202	7	,	,	PUNCT
ejpam-3279	202	8	kusova	kusova	PROPN
ejpam-3279	202	9	e.	e.	PROPN
ejpam-3279	202	10	v.	v.	PROPN
ejpam-3279	202	11	,	,	PUNCT
ejpam-3279	202	12	on	on	ADP
ejpam-3279	202	13	geometry	geometry	NOUN
ejpam-3279	202	14	of	of	ADP
ejpam-3279	202	15	weakly	weakly	ADJ
ejpam-3279	202	16	cosympletic	cosympletic	ADJ
ejpam-3279	202	17	manifold	manifold	ADJ
ejpam-3279	202	18	,	,	PUNCT
ejpam-3279	202	19	journal	journal	NOUN
ejpam-3279	202	20	of	of	ADP
ejpam-3279	202	21	mathematical	mathematical	ADJ
ejpam-3279	202	22	sciences	science	NOUN
ejpam-3279	202	23	,	,	PUNCT
ejpam-3279	202	24	177	177	NUM
ejpam-3279	202	25	:	:	PUNCT
ejpam-3279	202	26	668	668	NUM
ejpam-3279	202	27	,	,	PUNCT
ejpam-3279	202	28	2011	2011	NUM
ejpam-3279	202	29	.	.	PUNCT
ejpam-3279	203	1	[	[	X
ejpam-3279	203	2	15	15	NUM
ejpam-3279	203	3	]	]	X
ejpam-3279	203	4	kirichenko	kirichenko	PROPN
ejpam-3279	203	5	v.	v.	CCONJ
ejpam-3279	203	6	f.	f.	PROPN
ejpam-3279	203	7	,	,	PUNCT
ejpam-3279	203	8	rustanov	rustanov	PROPN
ejpam-3279	203	9	a.	a.	PROPN
ejpam-3279	203	10	r.	r.	PROPN
ejpam-3279	203	11	,	,	PUNCT
ejpam-3279	203	12	differential	differential	ADJ
ejpam-3279	203	13	geometry	geometry	NOUN
ejpam-3279	203	14	of	of	ADP
ejpam-3279	203	15	quasisasakian	quasisasakian	PROPN
ejpam-3279	203	16	manifolds	manifold	NOUN
ejpam-3279	203	17	,	,	PUNCT
ejpam-3279	203	18	mathematical	mathematical	ADJ
ejpam-3279	203	19	collection	collection	NOUN
ejpam-3279	203	20	.	.	PUNCT
ejpam-3279	204	1	193(8	193(8	NUM
ejpam-3279	204	2	):	):	PUNCT
ejpam-3279	204	3	71	71	NUM
ejpam-3279	204	4	-	-	SYM
ejpam-3279	204	5	100	100	NUM
ejpam-3279	204	6	,	,	PUNCT
ejpam-3279	204	7	2002	2002	NUM
ejpam-3279	204	8	.	.	PUNCT
ejpam-3279	205	1	references	reference	NOUN
ejpam-3279	205	2	833	833	NUM
ejpam-3279	206	1	[	[	X
ejpam-3279	206	2	16	16	NUM
ejpam-3279	206	3	]	]	X
ejpam-3279	206	4	kobayashi	kobayashi	PROPN
ejpam-3279	206	5	s.	s.	PROPN
ejpam-3279	206	6	,	,	PUNCT
ejpam-3279	206	7	nomizu	nomizu	PROPN
ejpam-3279	206	8	k.	k.	PROPN
ejpam-3279	206	9	,	,	PUNCT
ejpam-3279	206	10	foundations	foundation	NOUN
ejpam-3279	206	11	of	of	ADP
ejpam-3279	206	12	differential	differential	ADJ
ejpam-3279	206	13	geometry	geometry	NOUN
ejpam-3279	206	14	,	,	PUNCT
ejpam-3279	206	15	john	john	PROPN
ejpam-3279	206	16	wily	wily	PROPN
ejpam-3279	206	17	and	and	CCONJ
ejpam-3279	206	18	sons	son	NOUN
ejpam-3279	206	19	,	,	PUNCT
ejpam-3279	206	20	v.1	v.1	NUM
ejpam-3279	206	21	,	,	PUNCT
ejpam-3279	206	22	1963	1963	NUM
ejpam-3279	206	23	.	.	PUNCT
ejpam-3279	207	1	[	[	X
ejpam-3279	207	2	17	17	NUM
ejpam-3279	207	3	]	]	X
ejpam-3279	207	4	petrov	petrov	PROPN
ejpam-3279	207	5	a.	a.	PROPN
ejpam-3279	207	6	z.	z.	PROPN
ejpam-3279	207	7	,	,	PUNCT
ejpam-3279	207	8	einstein	einstein	PROPN
ejpam-3279	207	9	space	space	NOUN
ejpam-3279	207	10	,	,	PUNCT
ejpam-3279	207	11	phys	phy	NOUN
ejpam-3279	207	12	-	-	PUNCT
ejpam-3279	207	13	math	math	NOUN
ejpam-3279	207	14	.	.	PUNCT
ejpam-3279	208	1	letr	letr	PROPN
ejpam-3279	208	2	.	.	PUNCT
ejpam-3279	209	1	moscow	moscow	PROPN
ejpam-3279	209	2	,	,	PUNCT
ejpam-3279	209	3	p.	p.	NOUN
ejpam-3279	209	4	463	463	NUM
ejpam-3279	209	5	,	,	PUNCT
ejpam-3279	209	6	1961	1961	NUM
ejpam-3279	209	7	.	.	PUNCT
ejpam-3279	210	1	[	[	X
ejpam-3279	210	2	18	18	NUM
ejpam-3279	210	3	]	]	PUNCT
ejpam-3279	210	4	rachevski	rachevski	NOUN
ejpam-3279	210	5	p.	p.	PROPN
ejpam-3279	210	6	k.	k.	PROPN
ejpam-3279	210	7	,	,	PUNCT
ejpam-3279	210	8	riemmanian	riemmanian	ADJ
ejpam-3279	210	9	geometry	geometry	NOUN
ejpam-3279	210	10	and	and	CCONJ
ejpam-3279	210	11	tensor	tensor	NOUN
ejpam-3279	210	12	analysis	analysis	NOUN
ejpam-3279	210	13	,	,	PUNCT
ejpam-3279	210	14	uspekhi	uspekhi	PROPN
ejpam-3279	210	15	mat	mat	PROPN
ejpam-3279	210	16	.	.	PUNCT
ejpam-3279	211	1	nauk	nauk	PROPN
ejpam-3279	211	2	,	,	PUNCT
ejpam-3279	211	3	v.10	v.10	ADP
ejpam-3279	211	4	,	,	PUNCT
ejpam-3279	211	5	issue	issue	NOUN
ejpam-3279	211	6	4(66	4(66	NUM
ejpam-3279	211	7	)	)	PUNCT
ejpam-3279	211	8	,	,	PUNCT
ejpam-3279	211	9	p.219	p.219	NOUN
ejpam-3279	211	10	-	-	SYM
ejpam-3279	211	11	222	222	NUM
ejpam-3279	211	12	,	,	PUNCT
ejpam-3279	211	13	1955	1955	NUM
ejpam-3279	211	14	.	.	PUNCT
ejpam-3279	212	1	[	[	X
ejpam-3279	212	2	19	19	NUM
ejpam-3279	212	3	]	]	SYM
ejpam-3279	212	4	yano	yano	PROPN
ejpam-3279	212	5	k.	k.	PROPN
ejpam-3279	212	6	and	and	CCONJ
ejpam-3279	212	7	bochner	bochner	PROPN
ejpam-3279	212	8	s.	s.	PROPN
ejpam-3279	212	9	,	,	PUNCT
ejpam-3279	212	10	curvature	curvature	NOUN
ejpam-3279	212	11	and	and	CCONJ
ejpam-3279	212	12	betti	betti	NOUN
ejpam-3279	212	13	numbers	number	NOUN
ejpam-3279	212	14	,	,	PUNCT
ejpam-3279	212	15	annals	annal	NOUN
ejpam-3279	212	16	of	of	ADP
ejpam-3279	212	17	mathematics	mathematics	NOUN
ejpam-3279	212	18	studies	study	NOUN
ejpam-3279	212	19	,	,	PUNCT
ejpam-3279	212	20	32	32	NUM
ejpam-3279	212	21	,	,	PUNCT
ejpam-3279	212	22	princeton	princeton	PROPN
ejpam-3279	212	23	university	university	PROPN
ejpam-3279	212	24	press	press	NOUN
ejpam-3279	212	25	world	world	NOUN
ejpam-3279	212	26	,	,	PUNCT
ejpam-3279	212	27	1953	1953	NUM
ejpam-3279	212	28	.	.	PUNCT