id	sid	tid	token	lemma	pos
ejpam-298	1	1	3_298_nagaraja.dvi	3_298_nagaraja.dvi	NUM
ejpam-298	1	2	european	european	ADJ
ejpam-298	1	3	journal	journal	PROPN
ejpam-298	1	4	of	of	ADP
ejpam-298	1	5	pure	pure	ADJ
ejpam-298	1	6	and	and	CCONJ
ejpam-298	1	7	applied	apply	VERB
ejpam-298	1	8	mathematics	mathematic	NOUN
ejpam-298	1	9	vol	vol	NOUN
ejpam-298	1	10	.	.	PUNCT
ejpam-298	2	1	3	3	NUM
ejpam-298	2	2	,	,	PUNCT
ejpam-298	2	3	no	no	INTJ
ejpam-298	2	4	.	.	NOUN
ejpam-298	2	5	1	1	NUM
ejpam-298	2	6	,	,	PUNCT
ejpam-298	2	7	2010	2010	NUM
ejpam-298	2	8	,	,	PUNCT
ejpam-298	2	9	16	16	NUM
ejpam-298	2	10	-	-	SYM
ejpam-298	2	11	25	25	NUM
ejpam-298	2	12	issn	issn	PROPN
ejpam-298	2	13	1307	1307	NUM
ejpam-298	2	14	-	-	SYM
ejpam-298	2	15	5543	5543	NUM
ejpam-298	2	16	–	–	PUNCT
ejpam-298	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-298	2	18	on	on	ADP
ejpam-298	2	19	n(k)-mixed	n(k)-mixed	PROPN
ejpam-298	2	20	quasi	quasi	PROPN
ejpam-298	2	21	einstein	einstein	PROPN
ejpam-298	2	22	manifolds	manifolds	PROPN
ejpam-298	2	23	h	h	PROPN
ejpam-298	2	24	g	g	PROPN
ejpam-298	2	25	nagaraja	nagaraja	PROPN
ejpam-298	2	26	department	department	PROPN
ejpam-298	2	27	of	of	ADP
ejpam-298	2	28	mathematics	mathematic	NOUN
ejpam-298	2	29	,	,	PUNCT
ejpam-298	2	30	central	central	ADJ
ejpam-298	2	31	college	college	NOUN
ejpam-298	2	32	,	,	PUNCT
ejpam-298	2	33	bangalore	bangalore	PROPN
ejpam-298	2	34	university	university	NOUN
ejpam-298	2	35	,	,	PUNCT
ejpam-298	2	36	bangalore-560	bangalore-560	NOUN
ejpam-298	2	37	001	001	NUM
ejpam-298	2	38	,	,	PUNCT
ejpam-298	2	39	karnataka	karnataka	PROPN
ejpam-298	2	40	,	,	PUNCT
ejpam-298	2	41	india	india	PROPN
ejpam-298	2	42	.	.	PUNCT
ejpam-298	3	1	abstract	abstract	PROPN
ejpam-298	3	2	.	.	PUNCT
ejpam-298	4	1	in	in	ADP
ejpam-298	4	2	this	this	DET
ejpam-298	4	3	paper	paper	NOUN
ejpam-298	4	4	n(k)-mixed	n(k)-mixed	PROPN
ejpam-298	4	5	quasi	quasi	PROPN
ejpam-298	4	6	einstein	einstein	PROPN
ejpam-298	4	7	manifolds	manifolds	PROPN
ejpam-298	4	8	(	(	PUNCT
ejpam-298	4	9	n(k	n(k	PROPN
ejpam-298	4	10	)	)	PUNCT
ejpam-298	4	11	−	−	PROPN
ejpam-298	5	1	(	(	PUNCT
ejpam-298	5	2	mqe)n	mqe)n	NOUN
ejpam-298	5	3	)	)	PUNCT
ejpam-298	5	4	are	be	AUX
ejpam-298	5	5	introduced	introduce	VERB
ejpam-298	5	6	and	and	CCONJ
ejpam-298	5	7	the	the	DET
ejpam-298	5	8	existence	existence	NOUN
ejpam-298	5	9	of	of	ADP
ejpam-298	5	10	these	these	DET
ejpam-298	5	11	manifolds	manifold	NOUN
ejpam-298	5	12	is	be	AUX
ejpam-298	5	13	proved	prove	VERB
ejpam-298	5	14	.	.	PUNCT
ejpam-298	6	1	we	we	PRON
ejpam-298	6	2	give	give	VERB
ejpam-298	6	3	hyper	hyper	ADJ
ejpam-298	6	4	surfaces	surface	NOUN
ejpam-298	6	5	of	of	ADP
ejpam-298	6	6	euclidean	euclidean	ADJ
ejpam-298	6	7	spaces	space	NOUN
ejpam-298	6	8	as	as	ADP
ejpam-298	6	9	examples	example	NOUN
ejpam-298	6	10	of	of	ADP
ejpam-298	6	11	n(k)−	n(k)−	PROPN
ejpam-298	6	12	(	(	PUNCT
ejpam-298	6	13	mqe)n	mqe)n	ADJ
ejpam-298	6	14	and	and	CCONJ
ejpam-298	6	15	semi	semi	ADV
ejpam-298	6	16	symmetric	symmetric	ADJ
ejpam-298	6	17	,	,	PUNCT
ejpam-298	6	18	ricci	ricci	PROPN
ejpam-298	6	19	symmetric	symmetric	NOUN
ejpam-298	6	20	and	and	CCONJ
ejpam-298	6	21	ricci	ricci	PROPN
ejpam-298	6	22	recurrent	recurrent	PROPN
ejpam-298	6	23	n(k)−	n(k)−	PROPN
ejpam-298	6	24	(	(	PUNCT
ejpam-298	6	25	mqe)n	mqe)n	ADJ
ejpam-298	6	26	manifolds	manifold	NOUN
ejpam-298	6	27	are	be	AUX
ejpam-298	6	28	studied	study	VERB
ejpam-298	6	29	.	.	PUNCT
ejpam-298	7	1	2000	2000	NUM
ejpam-298	7	2	mathematics	mathematic	NOUN
ejpam-298	7	3	subject	subject	NOUN
ejpam-298	7	4	classifications	classification	NOUN
ejpam-298	7	5	:	:	PUNCT
ejpam-298	7	6	53c25	53c25	NUM
ejpam-298	7	7	key	key	ADJ
ejpam-298	7	8	words	word	NOUN
ejpam-298	7	9	and	and	CCONJ
ejpam-298	7	10	phrases	phrase	NOUN
ejpam-298	7	11	:	:	PUNCT
ejpam-298	7	12	n(k)-mixed	n(k)-mixed	PROPN
ejpam-298	7	13	quasi	quasi	NOUN
ejpam-298	7	14	einstein	einstein	NOUN
ejpam-298	7	15	,	,	PUNCT
ejpam-298	7	16	mixed	mixed	ADJ
ejpam-298	7	17	quasi	quasi	ADJ
ejpam-298	7	18	constant	constant	ADJ
ejpam-298	7	19	curvature	curvature	NOUN
ejpam-298	7	20	,	,	PUNCT
ejpam-298	7	21	ricci	ricci	PROPN
ejpam-298	7	22	recurrent	recurrent	NOUN
ejpam-298	7	23	,	,	PUNCT
ejpam-298	7	24	semi	semi	ADV
ejpam-298	7	25	symmetric	symmetric	ADJ
ejpam-298	7	26	,	,	PUNCT
ejpam-298	7	27	ricci	ricci	PROPN
ejpam-298	7	28	symmetric	symmetric	ADJ
ejpam-298	7	29	1	1	NUM
ejpam-298	7	30	.	.	PUNCT
ejpam-298	8	1	introduction	introduction	NOUN
ejpam-298	8	2	m.c.chaki	m.c.chaki	PROPN
ejpam-298	8	3	and	and	CCONJ
ejpam-298	8	4	r.k.maity	r.k.maity	NOUN
ejpam-298	9	1	[	[	X
ejpam-298	9	2	1	1	X
ejpam-298	9	3	]	]	PUNCT
ejpam-298	9	4	introduced	introduce	VERB
ejpam-298	9	5	the	the	DET
ejpam-298	9	6	concept	concept	NOUN
ejpam-298	9	7	quasi	quasi	PROPN
ejpam-298	9	8	einstein	einstein	PROPN
ejpam-298	9	9	manifolds	manifolds	PROPN
ejpam-298	9	10	.	.	PUNCT
ejpam-298	10	1	a	a	DET
ejpam-298	10	2	non	non	ADJ
ejpam-298	10	3	-	-	ADJ
ejpam-298	10	4	flat	flat	ADJ
ejpam-298	10	5	riemannian	riemannian	ADJ
ejpam-298	10	6	manifold(m	manifold(m	NOUN
ejpam-298	10	7	n	n	CCONJ
ejpam-298	10	8	,	,	PUNCT
ejpam-298	10	9	g)(n	g)(n	PROPN
ejpam-298	10	10	>	>	X
ejpam-298	10	11	2	2	NUM
ejpam-298	10	12	)	)	PUNCT
ejpam-298	10	13	is	be	AUX
ejpam-298	10	14	said	say	VERB
ejpam-298	10	15	to	to	PART
ejpam-298	10	16	be	be	AUX
ejpam-298	10	17	a	a	DET
ejpam-298	10	18	quasi	quasi	NOUN
ejpam-298	10	19	einstein	einstein	PROPN
ejpam-298	10	20	manifold	manifold	PROPN
ejpam-298	10	21	if	if	SCONJ
ejpam-298	10	22	its	its	PRON
ejpam-298	10	23	ricci	ricci	PROPN
ejpam-298	10	24	tensor	tensor	NOUN
ejpam-298	10	25	s	s	PROPN
ejpam-298	10	26	of	of	ADP
ejpam-298	10	27	type	type	NOUN
ejpam-298	10	28	(	(	PUNCT
ejpam-298	10	29	0,2	0,2	NUM
ejpam-298	10	30	)	)	PUNCT
ejpam-298	10	31	is	be	AUX
ejpam-298	10	32	not	not	PART
ejpam-298	10	33	identically	identically	ADV
ejpam-298	10	34	zero	zero	NUM
ejpam-298	10	35	and	and	CCONJ
ejpam-298	10	36	satisfies	satisfy	VERB
ejpam-298	10	37	the	the	DET
ejpam-298	10	38	condition	condition	NOUN
ejpam-298	10	39	s(x	s(x	NOUN
ejpam-298	10	40	,	,	PUNCT
ejpam-298	10	41	y	y	PROPN
ejpam-298	10	42	)	)	PUNCT
ejpam-298	11	1	=	=	SYM
ejpam-298	11	2	ag(x	ag(x	X
ejpam-298	11	3	,	,	PUNCT
ejpam-298	11	4	y	y	PROPN
ejpam-298	11	5	)	)	PUNCT
ejpam-298	11	6	+	+	CCONJ
ejpam-298	11	7	ba(x	ba(x	X
ejpam-298	11	8	)	)	PUNCT
ejpam-298	11	9	a(y	a(y	PROPN
ejpam-298	11	10	)	)	PUNCT
ejpam-298	11	11	,	,	PUNCT
ejpam-298	11	12	where	where	SCONJ
ejpam-298	11	13	a	a	PRON
ejpam-298	11	14	and	and	CCONJ
ejpam-298	11	15	b	b	NOUN
ejpam-298	11	16	are	be	AUX
ejpam-298	11	17	smooth	smooth	ADJ
ejpam-298	11	18	functions	function	NOUN
ejpam-298	11	19	of	of	ADP
ejpam-298	11	20	which	which	PRON
ejpam-298	11	21	b	b	PROPN
ejpam-298	11	22	6=	6=	NUM
ejpam-298	11	23	0	0	NUM
ejpam-298	11	24	and	and	CCONJ
ejpam-298	11	25	a	a	PRON
ejpam-298	11	26	is	be	AUX
ejpam-298	11	27	a	a	DET
ejpam-298	11	28	non	non	ADJ
ejpam-298	11	29	zero	zero	NUM
ejpam-298	11	30	1	1	NUM
ejpam-298	11	31	-	-	PUNCT
ejpam-298	11	32	form	form	NOUN
ejpam-298	11	33	such	such	ADJ
ejpam-298	11	34	that	that	DET
ejpam-298	11	35	g(x	g(x	PROPN
ejpam-298	11	36	,	,	PUNCT
ejpam-298	11	37	u	u	NOUN
ejpam-298	11	38	)	)	PUNCT
ejpam-298	11	39	=	=	SYM
ejpam-298	11	40	a(x	a(x	NOUN
ejpam-298	11	41	)	)	PUNCT
ejpam-298	11	42	,	,	PUNCT
ejpam-298	11	43	for	for	ADP
ejpam-298	11	44	all	all	DET
ejpam-298	11	45	vector	vector	NOUN
ejpam-298	11	46	fields	field	NOUN
ejpam-298	11	47	x	x	PUNCT
ejpam-298	11	48	and	and	CCONJ
ejpam-298	11	49	u	u	NOUN
ejpam-298	11	50	is	be	AUX
ejpam-298	11	51	a	a	DET
ejpam-298	11	52	unit	unit	NOUN
ejpam-298	11	53	vector	vector	NOUN
ejpam-298	11	54	field	field	NOUN
ejpam-298	11	55	.	.	PUNCT
ejpam-298	12	1	u.c.de	u.c.de	PROPN
ejpam-298	12	2	and	and	CCONJ
ejpam-298	12	3	gopal	gopal	PROPN
ejpam-298	12	4	chandra	chandra	PROPN
ejpam-298	12	5	ghosh	ghosh	PROPN
ejpam-298	13	1	[	[	X
ejpam-298	13	2	4	4	NUM
ejpam-298	13	3	,	,	PUNCT
ejpam-298	13	4	5	5	NUM
ejpam-298	13	5	]	]	PUNCT
ejpam-298	13	6	generalized	generalize	VERB
ejpam-298	13	7	the	the	DET
ejpam-298	13	8	quasi	quasi	PROPN
ejpam-298	13	9	einstein	einstein	PROPN
ejpam-298	13	10	manifolds	manifolds	PROPN
ejpam-298	13	11	.	.	PUNCT
ejpam-298	14	1	a	a	DET
ejpam-298	14	2	non	non	ADJ
ejpam-298	14	3	-	-	ADJ
ejpam-298	14	4	flat	flat	ADJ
ejpam-298	14	5	riemannian	riemannian	ADJ
ejpam-298	14	6	manifold	manifold	NOUN
ejpam-298	14	7	(	(	PUNCT
ejpam-298	14	8	m	m	NOUN
ejpam-298	14	9	n	n	CCONJ
ejpam-298	14	10	,	,	PUNCT
ejpam-298	14	11	g)(n	g)(n	PROPN
ejpam-298	14	12	>	>	X
ejpam-298	14	13	2	2	NUM
ejpam-298	14	14	)	)	PUNCT
ejpam-298	14	15	is	be	AUX
ejpam-298	14	16	said	say	VERB
ejpam-298	14	17	to	to	PART
ejpam-298	14	18	be	be	AUX
ejpam-298	14	19	a	a	DET
ejpam-298	14	20	generalized	generalize	VERB
ejpam-298	14	21	quasi	quasi	NOUN
ejpam-298	14	22	einstein	einstein	PROPN
ejpam-298	14	23	manifold	manifold	PROPN
ejpam-298	14	24	if	if	SCONJ
ejpam-298	14	25	its	its	PRON
ejpam-298	14	26	ricci	ricci	PROPN
ejpam-298	14	27	tensor	tensor	NOUN
ejpam-298	14	28	s	s	PROPN
ejpam-298	14	29	of	of	ADP
ejpam-298	14	30	type	type	NOUN
ejpam-298	14	31	(	(	PUNCT
ejpam-298	14	32	0,2	0,2	NUM
ejpam-298	14	33	)	)	PUNCT
ejpam-298	14	34	is	be	AUX
ejpam-298	14	35	not	not	PART
ejpam-298	14	36	identically	identically	ADV
ejpam-298	14	37	zero	zero	NUM
ejpam-298	14	38	and	and	CCONJ
ejpam-298	14	39	satisfies	satisfy	VERB
ejpam-298	14	40	the	the	DET
ejpam-298	14	41	condition	condition	NOUN
ejpam-298	14	42	s(x	s(x	NOUN
ejpam-298	14	43	,	,	PUNCT
ejpam-298	14	44	y	y	PROPN
ejpam-298	14	45	)	)	PUNCT
ejpam-298	15	1	=	=	SYM
ejpam-298	15	2	ag(x	ag(x	X
ejpam-298	15	3	,	,	PUNCT
ejpam-298	15	4	y	y	PROPN
ejpam-298	15	5	)	)	PUNCT
ejpam-298	15	6	+	+	CCONJ
ejpam-298	15	7	ba(x	ba(x	X
ejpam-298	15	8	)	)	PUNCT
ejpam-298	15	9	a(y	a(y	PROPN
ejpam-298	15	10	)	)	PUNCT
ejpam-298	16	1	+	+	CCONJ
ejpam-298	16	2	cb(x	cb(x	NUM
ejpam-298	16	3	)	)	PUNCT
ejpam-298	16	4	b(y	b(y	PROPN
ejpam-298	16	5	)	)	PUNCT
ejpam-298	16	6	,	,	PUNCT
ejpam-298	16	7	where	where	SCONJ
ejpam-298	16	8	a	a	DET
ejpam-298	16	9	,	,	PUNCT
ejpam-298	16	10	b	b	NOUN
ejpam-298	16	11	and	and	CCONJ
ejpam-298	16	12	c	c	PROPN
ejpam-298	16	13	are	be	AUX
ejpam-298	16	14	certain	certain	ADJ
ejpam-298	16	15	smooth	smooth	ADJ
ejpam-298	16	16	functions	function	NOUN
ejpam-298	16	17	,	,	PUNCT
ejpam-298	16	18	a	a	PRON
ejpam-298	16	19	and	and	CCONJ
ejpam-298	16	20	b	b	NOUN
ejpam-298	16	21	are	be	AUX
ejpam-298	16	22	non	non	X
ejpam-298	16	23	zero	zero	NUM
ejpam-298	16	24	1	1	NUM
ejpam-298	16	25	-	-	NOUN
ejpam-298	16	26	forms	form	NOUN
ejpam-298	16	27	,	,	PUNCT
ejpam-298	16	28	and	and	CCONJ
ejpam-298	16	29	u	u	NOUN
ejpam-298	16	30	and	and	CCONJ
ejpam-298	16	31	v	v	NOUN
ejpam-298	16	32	are	be	AUX
ejpam-298	16	33	unit	unit	NOUN
ejpam-298	16	34	vector	vector	NOUN
ejpam-298	16	35	fields	field	NOUN
ejpam-298	16	36	corresponding	correspond	VERB
ejpam-298	16	37	to	to	ADP
ejpam-298	16	38	1	1	NUM
ejpam-298	16	39	-	-	PUNCT
ejpam-298	16	40	forms	form	NOUN
ejpam-298	16	41	a	a	PRON
ejpam-298	16	42	and	and	CCONJ
ejpam-298	16	43	b	b	NOUN
ejpam-298	16	44	respectively	respectively	ADV
ejpam-298	16	45	such	such	ADJ
ejpam-298	16	46	that	that	SCONJ
ejpam-298	16	47	g(x	g(x	PROPN
ejpam-298	16	48	,	,	PUNCT
ejpam-298	16	49	u	u	NOUN
ejpam-298	16	50	)	)	PUNCT
ejpam-298	16	51	=	=	SYM
ejpam-298	16	52	a(x	a(x	NOUN
ejpam-298	16	53	)	)	PUNCT
ejpam-298	16	54	,	,	PUNCT
ejpam-298	16	55	g(x	g(x	PROPN
ejpam-298	16	56	,	,	PUNCT
ejpam-298	16	57	v	v	NOUN
ejpam-298	16	58	)	)	PUNCT
ejpam-298	16	59	=	=	SYM
ejpam-298	16	60	b(x	b(x	NOUN
ejpam-298	16	61	)	)	PUNCT
ejpam-298	16	62	and	and	CCONJ
ejpam-298	16	63	g(u	g(u	PROPN
ejpam-298	16	64	,	,	PUNCT
ejpam-298	16	65	v	v	NOUN
ejpam-298	16	66	)	)	PUNCT
ejpam-298	17	1	=	=	SYM
ejpam-298	17	2	0	0	X
ejpam-298	17	3	.	.	PUNCT
ejpam-298	18	1	the	the	DET
ejpam-298	18	2	vector	vector	NOUN
ejpam-298	18	3	fields	field	VERB
ejpam-298	18	4	u	u	PROPN
ejpam-298	18	5	and	and	CCONJ
ejpam-298	18	6	v	v	NOUN
ejpam-298	18	7	are	be	AUX
ejpam-298	18	8	called	call	VERB
ejpam-298	18	9	generators	generator	NOUN
ejpam-298	18	10	of	of	ADP
ejpam-298	18	11	email	email	NOUN
ejpam-298	18	12	address	address	NOUN
ejpam-298	18	13	:	:	PUNCT
ejpam-298	18	14	hgnraj	hgnraj	PROPN
ejpam-298	18	15	�	�	PROPN
ejpam-298	18	16	yahoo	yahoo	PROPN
ejpam-298	18	17	.	.	PUNCT
ejpam-298	19	1	om	om	PROPN
ejpam-298	19	2	(	(	PUNCT
ejpam-298	19	3	h.	h.	PROPN
ejpam-298	19	4	nagaraja	nagaraja	PROPN
ejpam-298	19	5	)	)	PUNCT
ejpam-298	19	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-298	20	1	16	16	NUM
ejpam-298	21	1	c	c	X
ejpam-298	21	2	©	©	PROPN
ejpam-298	21	3	2009	2009	NUM
ejpam-298	21	4	ejpam	ejpam	NOUN
ejpam-298	21	5	all	all	DET
ejpam-298	21	6	rights	right	NOUN
ejpam-298	21	7	reserved	reserve	VERB
ejpam-298	21	8	.	.	PUNCT
ejpam-298	22	1	h.	h.	PROPN
ejpam-298	22	2	nagaraja	nagaraja	PROPN
ejpam-298	22	3	/	/	SYM
ejpam-298	22	4	eur	eur	PROPN
ejpam-298	22	5	.	.	PUNCT
ejpam-298	23	1	j.	j.	PROPN
ejpam-298	23	2	pure	pure	PROPN
ejpam-298	23	3	appl	appl	PROPN
ejpam-298	23	4	.	.	PROPN
ejpam-298	23	5	math	math	PROPN
ejpam-298	23	6	,	,	PUNCT
ejpam-298	23	7	3	3	NUM
ejpam-298	23	8	(	(	PUNCT
ejpam-298	23	9	2010	2010	NUM
ejpam-298	23	10	)	)	PUNCT
ejpam-298	23	11	,	,	PUNCT
ejpam-298	23	12	16	16	NUM
ejpam-298	23	13	-	-	SYM
ejpam-298	23	14	25	25	NUM
ejpam-298	23	15	17	17	NUM
ejpam-298	23	16	the	the	DET
ejpam-298	23	17	quasi	quasi	PROPN
ejpam-298	23	18	einstein	einstein	PROPN
ejpam-298	23	19	manifold	manifold	PROPN
ejpam-298	23	20	.	.	PUNCT
ejpam-298	24	1	the	the	DET
ejpam-298	24	2	k	k	ADJ
ejpam-298	24	3	-	-	PUNCT
ejpam-298	24	4	nullity	nullity	NOUN
ejpam-298	24	5	distribution	distribution	NOUN
ejpam-298	24	6	n(k	n(k	PROPN
ejpam-298	24	7	)	)	PUNCT
ejpam-298	25	1	[	[	X
ejpam-298	25	2	8]of	8]of	NUM
ejpam-298	25	3	a	a	DET
ejpam-298	25	4	riemannian	riemannian	ADJ
ejpam-298	25	5	manifold	manifold	NOUN
ejpam-298	25	6	m	m	VERB
ejpam-298	25	7	is	be	AUX
ejpam-298	25	8	defined	define	VERB
ejpam-298	25	9	by	by	ADP
ejpam-298	25	10	n(k	n(k	PROPN
ejpam-298	25	11	)	)	PUNCT
ejpam-298	25	12	:	:	PUNCT
ejpam-298	26	1	p→	p→	NOUN
ejpam-298	26	2	np(k	np(k	NOUN
ejpam-298	26	3	)	)	PUNCT
ejpam-298	26	4	=	=	PRON
ejpam-298	26	5	{	{	PUNCT
ejpam-298	26	6	z	z	NOUN
ejpam-298	26	7	∈	∈	PROPN
ejpam-298	27	1	tpm\r(x	tpm\r(x	PROPN
ejpam-298	27	2	,	,	PUNCT
ejpam-298	27	3	y	y	PROPN
ejpam-298	27	4	)	)	PUNCT
ejpam-298	27	5	z	z	NOUN
ejpam-298	27	6	=	=	SYM
ejpam-298	27	7	k(g(y	k(g(y	PROPN
ejpam-298	27	8	,	,	PUNCT
ejpam-298	27	9	z)x	z)x	PUNCT
ejpam-298	27	10	−	−	PROPN
ejpam-298	27	11	g(x	g(x	PROPN
ejpam-298	27	12	,	,	PUNCT
ejpam-298	27	13	z)y	z)y	NUM
ejpam-298	27	14	)	)	PUNCT
ejpam-298	27	15	}	}	PUNCT
ejpam-298	27	16	for	for	ADP
ejpam-298	27	17	all	all	PRON
ejpam-298	27	18	x	x	SYM
ejpam-298	27	19	,	,	PUNCT
ejpam-298	27	20	y	y	PROPN
ejpam-298	27	21	∈	∈	PROPN
ejpam-298	27	22	t	t	PROPN
ejpam-298	27	23	m	m	PROPN
ejpam-298	27	24	and	and	CCONJ
ejpam-298	27	25	k	k	PROPN
ejpam-298	27	26	is	be	AUX
ejpam-298	27	27	a	a	DET
ejpam-298	27	28	smooth	smooth	ADJ
ejpam-298	27	29	function	function	NOUN
ejpam-298	27	30	.	.	PUNCT
ejpam-298	28	1	m.m.tripathy	m.m.tripathy	ADJ
ejpam-298	28	2	and	and	CCONJ
ejpam-298	28	3	jeong	jeong	PROPN
ejpam-298	28	4	jik	jik	PROPN
ejpam-298	28	5	kim	kim	PROPN
ejpam-298	29	1	[	[	X
ejpam-298	29	2	6	6	NUM
ejpam-298	29	3	]	]	PUNCT
ejpam-298	29	4	introduced	introduce	VERB
ejpam-298	29	5	the	the	DET
ejpam-298	29	6	notion	notion	NOUN
ejpam-298	29	7	of	of	ADP
ejpam-298	29	8	n(k)-quasi	n(k)-quasi	PROPN
ejpam-298	29	9	einstein	einstein	NOUN
ejpam-298	29	10	manifold	manifold	NOUN
ejpam-298	29	11	which	which	PRON
ejpam-298	29	12	is	be	AUX
ejpam-298	29	13	defined	define	VERB
ejpam-298	29	14	as	as	SCONJ
ejpam-298	29	15	follows	follow	VERB
ejpam-298	29	16	:	:	PUNCT
ejpam-298	29	17	if	if	SCONJ
ejpam-298	29	18	the	the	DET
ejpam-298	29	19	generator	generator	NOUN
ejpam-298	29	20	u	u	NOUN
ejpam-298	29	21	belongs	belong	VERB
ejpam-298	29	22	to	to	ADP
ejpam-298	29	23	the	the	DET
ejpam-298	29	24	k	k	ADJ
ejpam-298	29	25	-	-	PUNCT
ejpam-298	29	26	nullity	nullity	NOUN
ejpam-298	29	27	distribution	distribution	NOUN
ejpam-298	29	28	n(k	n(k	PROPN
ejpam-298	29	29	)	)	PUNCT
ejpam-298	29	30	,	,	PUNCT
ejpam-298	29	31	then	then	ADV
ejpam-298	29	32	a	a	DET
ejpam-298	29	33	quasi	quasi	PROPN
ejpam-298	29	34	einstein	einstein	PROPN
ejpam-298	29	35	manifold	manifold	PROPN
ejpam-298	29	36	(	(	PUNCT
ejpam-298	29	37	m	m	PROPN
ejpam-298	29	38	n	n	CCONJ
ejpam-298	29	39	,	,	PUNCT
ejpam-298	29	40	g	g	NOUN
ejpam-298	29	41	)	)	PUNCT
ejpam-298	29	42	is	be	AUX
ejpam-298	29	43	called	call	VERB
ejpam-298	29	44	n(k)-quasi	n(k)-quasi	PROPN
ejpam-298	29	45	einstein	einstein	NOUN
ejpam-298	29	46	manifold	manifold	NOUN
ejpam-298	29	47	.	.	PUNCT
ejpam-298	30	1	motivated	motivate	VERB
ejpam-298	30	2	by	by	ADP
ejpam-298	30	3	the	the	DET
ejpam-298	30	4	above	above	ADJ
ejpam-298	30	5	definitions	definition	NOUN
ejpam-298	30	6	we	we	PRON
ejpam-298	30	7	give	give	VERB
ejpam-298	30	8	the	the	DET
ejpam-298	30	9	following	follow	VERB
ejpam-298	30	10	definition	definition	NOUN
ejpam-298	30	11	.	.	PUNCT
ejpam-298	31	1	definition	definition	NOUN
ejpam-298	31	2	1	1	NUM
ejpam-298	31	3	.	.	PUNCT
ejpam-298	32	1	let	let	VERB
ejpam-298	32	2	(	(	PUNCT
ejpam-298	32	3	m	m	VERB
ejpam-298	32	4	n	n	CCONJ
ejpam-298	32	5	,	,	PUNCT
ejpam-298	32	6	g	g	NOUN
ejpam-298	32	7	)	)	PUNCT
ejpam-298	32	8	be	be	VERB
ejpam-298	32	9	a	a	DET
ejpam-298	32	10	non	non	ADJ
ejpam-298	32	11	flat	flat	ADJ
ejpam-298	32	12	riemannian	riemannian	ADJ
ejpam-298	32	13	manifold	manifold	NOUN
ejpam-298	32	14	.	.	PUNCT
ejpam-298	33	1	if	if	SCONJ
ejpam-298	33	2	the	the	DET
ejpam-298	33	3	ricci	ricci	PROPN
ejpam-298	33	4	tensor	tensor	NOUN
ejpam-298	33	5	s	s	PROPN
ejpam-298	33	6	of	of	ADP
ejpam-298	33	7	(	(	PUNCT
ejpam-298	33	8	m	m	NOUN
ejpam-298	33	9	n	n	CCONJ
ejpam-298	33	10	,	,	PUNCT
ejpam-298	33	11	g	g	NOUN
ejpam-298	33	12	)	)	PUNCT
ejpam-298	33	13	is	be	AUX
ejpam-298	33	14	non	non	X
ejpam-298	33	15	zero	zero	NUM
ejpam-298	33	16	and	and	CCONJ
ejpam-298	33	17	satisfies	satisfy	VERB
ejpam-298	33	18	s(x	s(x	NOUN
ejpam-298	33	19	,	,	PUNCT
ejpam-298	33	20	y	y	PROPN
ejpam-298	33	21	)	)	PUNCT
ejpam-298	34	1	=	=	SYM
ejpam-298	34	2	ag(x	ag(x	X
ejpam-298	34	3	,	,	PUNCT
ejpam-298	34	4	y	y	PROPN
ejpam-298	34	5	)	)	PUNCT
ejpam-298	34	6	+	+	CCONJ
ejpam-298	34	7	ba(x	ba(x	NOUN
ejpam-298	34	8	)	)	PUNCT
ejpam-298	34	9	b(y	b(y	PROPN
ejpam-298	34	10	)	)	PUNCT
ejpam-298	35	1	+	+	CCONJ
ejpam-298	35	2	cb(x	cb(x	X
ejpam-298	35	3	)	)	PUNCT
ejpam-298	35	4	a(y	a(y	PROPN
ejpam-298	35	5	)	)	PUNCT
ejpam-298	35	6	,	,	PUNCT
ejpam-298	35	7	(	(	PUNCT
ejpam-298	35	8	1	1	X
ejpam-298	35	9	)	)	PUNCT
ejpam-298	35	10	where	where	SCONJ
ejpam-298	35	11	a	a	DET
ejpam-298	35	12	,	,	PUNCT
ejpam-298	35	13	b	b	NOUN
ejpam-298	35	14	and	and	CCONJ
ejpam-298	35	15	c	c	PROPN
ejpam-298	35	16	are	be	AUX
ejpam-298	35	17	smooth	smooth	ADJ
ejpam-298	35	18	functions	function	NOUN
ejpam-298	35	19	and	and	CCONJ
ejpam-298	35	20	a	a	PRON
ejpam-298	35	21	and	and	CCONJ
ejpam-298	35	22	b	b	NOUN
ejpam-298	35	23	are	be	AUX
ejpam-298	35	24	non	non	ADJ
ejpam-298	35	25	zero	zero	NUM
ejpam-298	35	26	1	1	NUM
ejpam-298	35	27	-	-	NOUN
ejpam-298	35	28	forms	form	NOUN
ejpam-298	35	29	such	such	ADJ
ejpam-298	35	30	that	that	SCONJ
ejpam-298	35	31	g(x	g(x	PROPN
ejpam-298	35	32	,	,	PUNCT
ejpam-298	35	33	u	u	NOUN
ejpam-298	35	34	)	)	PUNCT
ejpam-298	35	35	=	=	SYM
ejpam-298	35	36	a(x	a(x	NOUN
ejpam-298	35	37	)	)	PUNCT
ejpam-298	35	38	and	and	CCONJ
ejpam-298	35	39	g(x	g(x	PROPN
ejpam-298	35	40	,	,	PUNCT
ejpam-298	35	41	v	v	NOUN
ejpam-298	35	42	)	)	PUNCT
ejpam-298	35	43	=	=	SYM
ejpam-298	35	44	b(x	b(x	NOUN
ejpam-298	35	45	)	)	PUNCT
ejpam-298	35	46	for	for	ADP
ejpam-298	35	47	all	all	DET
ejpam-298	35	48	vector	vector	NOUN
ejpam-298	35	49	fields	field	NOUN
ejpam-298	35	50	x	x	PUNCT
ejpam-298	35	51	,	,	PUNCT
ejpam-298	35	52	and	and	CCONJ
ejpam-298	35	53	u	u	NOUN
ejpam-298	35	54	and	and	CCONJ
ejpam-298	35	55	v	v	ADP
ejpam-298	35	56	being	be	AUX
ejpam-298	35	57	the	the	DET
ejpam-298	35	58	orthogonal	orthogonal	ADJ
ejpam-298	35	59	unit	unit	NOUN
ejpam-298	35	60	vector	vector	NOUN
ejpam-298	35	61	fields	field	NOUN
ejpam-298	35	62	called	call	VERB
ejpam-298	35	63	generators	generator	NOUN
ejpam-298	35	64	of	of	ADP
ejpam-298	35	65	the	the	DET
ejpam-298	35	66	manifold	manifold	ADJ
ejpam-298	35	67	belong	belong	VERB
ejpam-298	35	68	to	to	ADP
ejpam-298	35	69	n(k	n(k	PROPN
ejpam-298	35	70	)	)	PUNCT
ejpam-298	35	71	,	,	PUNCT
ejpam-298	35	72	then	then	ADV
ejpam-298	35	73	we	we	PRON
ejpam-298	35	74	say	say	VERB
ejpam-298	35	75	that	that	PRON
ejpam-298	35	76	(	(	PUNCT
ejpam-298	35	77	m	m	VERB
ejpam-298	35	78	n	n	CCONJ
ejpam-298	35	79	,	,	PUNCT
ejpam-298	35	80	g	g	NOUN
ejpam-298	35	81	)	)	PUNCT
ejpam-298	35	82	is	be	AUX
ejpam-298	35	83	a	a	DET
ejpam-298	35	84	n(k)-mixed	n(k)-mixed	PROPN
ejpam-298	35	85	quasi	quasi	PROPN
ejpam-298	35	86	einstein	einstein	PROPN
ejpam-298	35	87	manifold	manifold	PROPN
ejpam-298	35	88	and	and	CCONJ
ejpam-298	35	89	is	be	AUX
ejpam-298	35	90	denoted	denote	VERB
ejpam-298	35	91	by	by	ADP
ejpam-298	35	92	n(k)−	n(k)−	PROPN
ejpam-298	35	93	(	(	PUNCT
ejpam-298	35	94	mqe)n	mqe)n	PROPN
ejpam-298	35	95	.	.	PROPN
ejpam-298	35	96	in	in	ADP
ejpam-298	35	97	this	this	DET
ejpam-298	35	98	paper	paper	NOUN
ejpam-298	35	99	we	we	PRON
ejpam-298	35	100	introduce	introduce	VERB
ejpam-298	35	101	another	another	DET
ejpam-298	35	102	notion	notion	NOUN
ejpam-298	35	103	of	of	ADP
ejpam-298	35	104	a	a	DET
ejpam-298	35	105	manifold	manifold	NOUN
ejpam-298	35	106	of	of	ADP
ejpam-298	35	107	mixed	mixed	ADJ
ejpam-298	35	108	quasi	quasi	ADJ
ejpam-298	35	109	constant	constant	ADJ
ejpam-298	35	110	curvature	curvature	NOUN
ejpam-298	35	111	similar	similar	ADJ
ejpam-298	35	112	to	to	ADP
ejpam-298	35	113	manifold	manifold	ADJ
ejpam-298	35	114	of	of	ADP
ejpam-298	35	115	quasi	quasi	ADJ
ejpam-298	35	116	constant	constant	ADJ
ejpam-298	35	117	curvature	curvature	NOUN
ejpam-298	35	118	defined	define	VERB
ejpam-298	35	119	in	in	ADP
ejpam-298	35	120	[	[	X
ejpam-298	35	121	4	4	NUM
ejpam-298	35	122	]	]	PUNCT
ejpam-298	35	123	.	.	PUNCT
ejpam-298	36	1	a	a	DET
ejpam-298	36	2	riemannian	riemannian	ADJ
ejpam-298	36	3	manifold	manifold	NOUN
ejpam-298	36	4	(	(	PUNCT
ejpam-298	36	5	m	m	NOUN
ejpam-298	36	6	n	n	CCONJ
ejpam-298	36	7	,	,	PUNCT
ejpam-298	36	8	g	g	NOUN
ejpam-298	36	9	)	)	PUNCT
ejpam-298	36	10	is	be	AUX
ejpam-298	36	11	called	call	VERB
ejpam-298	36	12	a	a	DET
ejpam-298	36	13	manifold	manifold	NOUN
ejpam-298	36	14	of	of	ADP
ejpam-298	36	15	mixed	mixed	ADJ
ejpam-298	36	16	quasi	quasi	ADJ
ejpam-298	36	17	constant	constant	ADJ
ejpam-298	36	18	curvature	curvature	NOUN
ejpam-298	36	19	if	if	SCONJ
ejpam-298	36	20	it	it	PRON
ejpam-298	36	21	is	be	AUX
ejpam-298	36	22	conformally	conformally	ADV
ejpam-298	36	23	flat	flat	ADJ
ejpam-298	36	24	and	and	CCONJ
ejpam-298	36	25	the	the	DET
ejpam-298	36	26	curvature	curvature	NOUN
ejpam-298	36	27	tensor	tensor	NOUN
ejpam-298	36	28	′r	′r	PROPN
ejpam-298	36	29	of	of	ADP
ejpam-298	36	30	type	type	NOUN
ejpam-298	36	31	(	(	PUNCT
ejpam-298	36	32	0,4	0,4	NOUN
ejpam-298	36	33	)	)	PUNCT
ejpam-298	36	34	satisfies	satisfy	VERB
ejpam-298	36	35	the	the	DET
ejpam-298	36	36	condition	condition	NOUN
ejpam-298	36	37	′r(x	′r(x	PROPN
ejpam-298	36	38	,	,	PUNCT
ejpam-298	36	39	y	y	PROPN
ejpam-298	36	40	,	,	PUNCT
ejpam-298	36	41	z	z	NOUN
ejpam-298	36	42	,	,	PUNCT
ejpam-298	36	43	w	w	PROPN
ejpam-298	36	44	)	)	PUNCT
ejpam-298	36	45	=	=	SYM
ejpam-298	36	46	p[g(y	p[g(y	PROPN
ejpam-298	36	47	,	,	PUNCT
ejpam-298	36	48	z)g(x	z)g(x	NUM
ejpam-298	36	49	,	,	PUNCT
ejpam-298	36	50	w	w	NOUN
ejpam-298	36	51	)	)	PUNCT
ejpam-298	36	52	−	−	PROPN
ejpam-298	37	1	g(x	g(x	PROPN
ejpam-298	37	2	,	,	PUNCT
ejpam-298	37	3	z)g(y	z)g(y	PROPN
ejpam-298	37	4	,	,	PUNCT
ejpam-298	37	5	w	w	NOUN
ejpam-298	37	6	)	)	PUNCT
ejpam-298	37	7	]	]	PUNCT
ejpam-298	38	1	+	+	CCONJ
ejpam-298	38	2	q	q	PROPN
ejpam-298	38	3	�	�	PROPN
ejpam-298	38	4	g(x	g(x	PROPN
ejpam-298	38	5	,	,	PUNCT
ejpam-298	38	6	w	w	NOUN
ejpam-298	38	7	)	)	PUNCT
ejpam-298	38	8	a(y	a(y	PROPN
ejpam-298	38	9	)	)	PUNCT
ejpam-298	38	10	b(z)−	b(z)−	PROPN
ejpam-298	38	11	g(x	g(x	PROPN
ejpam-298	38	12	,	,	PUNCT
ejpam-298	38	13	z)a(y	z)a(y	PROPN
ejpam-298	38	14	)	)	PUNCT
ejpam-298	38	15	b(w	b(w	PROPN
ejpam-298	38	16	)	)	PUNCT
ejpam-298	39	1	+	+	CCONJ
ejpam-298	40	1	g(x	g(x	PROPN
ejpam-298	40	2	,	,	PUNCT
ejpam-298	40	3	w	w	NOUN
ejpam-298	40	4	)	)	PUNCT
ejpam-298	40	5	a(z)b(y	a(z)b(y	ADJ
ejpam-298	40	6	)	)	PUNCT
ejpam-298	40	7	−	−	PROPN
ejpam-298	41	1	g(x	g(x	PROPN
ejpam-298	41	2	,	,	PUNCT
ejpam-298	41	3	z)a(w	z)a(w	NUM
ejpam-298	41	4	)	)	PUNCT
ejpam-298	42	1	b(y	b(y	PROPN
ejpam-298	42	2	)	)	PUNCT
ejpam-298	43	1	�	�	PROPN
ejpam-298	43	2	+	+	CCONJ
ejpam-298	43	3	s[g(y	s[g(y	PROPN
ejpam-298	43	4	,	,	PUNCT
ejpam-298	43	5	z)a(w	z)a(w	NUM
ejpam-298	43	6	)	)	PUNCT
ejpam-298	43	7	b(x	b(x	NOUN
ejpam-298	43	8	)	)	PUNCT
ejpam-298	44	1	−	−	PROPN
ejpam-298	45	1	g(y	g(y	PROPN
ejpam-298	45	2	,	,	PUNCT
ejpam-298	45	3	w	w	NOUN
ejpam-298	45	4	)	)	PUNCT
ejpam-298	45	5	a(z)b(x	a(z)b(x	X
ejpam-298	45	6	)	)	PUNCT
ejpam-298	46	1	+	+	CCONJ
ejpam-298	46	2	g(y	g(y	NOUN
ejpam-298	46	3	,	,	PUNCT
ejpam-298	46	4	z)a(x	z)a(x	NOUN
ejpam-298	46	5	)	)	PUNCT
ejpam-298	46	6	b(w	b(w	PROPN
ejpam-298	46	7	)	)	PUNCT
ejpam-298	46	8	−	−	PROPN
ejpam-298	47	1	g(y	g(y	PROPN
ejpam-298	47	2	,	,	PUNCT
ejpam-298	47	3	w	w	NOUN
ejpam-298	47	4	)	)	PUNCT
ejpam-298	47	5	a(x	a(x	NOUN
ejpam-298	47	6	)	)	PUNCT
ejpam-298	47	7	b(z	b(z	NOUN
ejpam-298	47	8	)	)	PUNCT
ejpam-298	47	9	]	]	PUNCT
ejpam-298	47	10	(	(	PUNCT
ejpam-298	47	11	2	2	X
ejpam-298	47	12	)	)	PUNCT
ejpam-298	47	13	let	let	AUX
ejpam-298	47	14	{	{	PUNCT
ejpam-298	47	15	ei	ei	AUX
ejpam-298	47	16	}	}	PUNCT
ejpam-298	47	17	be	be	AUX
ejpam-298	47	18	an	an	DET
ejpam-298	47	19	orthonormal	orthonormal	ADJ
ejpam-298	47	20	basis	basis	NOUN
ejpam-298	47	21	of	of	ADP
ejpam-298	47	22	the	the	DET
ejpam-298	47	23	tangent	tangent	ADJ
ejpam-298	47	24	space	space	NOUN
ejpam-298	47	25	at	at	ADP
ejpam-298	47	26	each	each	DET
ejpam-298	47	27	point	point	NOUN
ejpam-298	47	28	of	of	ADP
ejpam-298	47	29	the	the	DET
ejpam-298	47	30	manifold	manifold	NOUN
ejpam-298	47	31	.	.	PUNCT
ejpam-298	48	1	taking	take	VERB
ejpam-298	48	2	x	x	PUNCT
ejpam-298	49	1	=	=	NOUN
ejpam-298	49	2	w	w	NOUN
ejpam-298	49	3	=	=	VERB
ejpam-298	49	4	ei	ei	NOUN
ejpam-298	49	5	and	and	CCONJ
ejpam-298	49	6	summing	sum	VERB
ejpam-298	49	7	over	over	ADP
ejpam-298	49	8	i	i	PRON
ejpam-298	49	9	,	,	PUNCT
ejpam-298	49	10	1≤	1≤	INTJ
ejpam-298	49	11	i	i	X
ejpam-298	49	12	≤	≤	PUNCT
ejpam-298	49	13	n	n	CCONJ
ejpam-298	49	14	in	in	ADP
ejpam-298	49	15	(	(	PUNCT
ejpam-298	49	16	2	2	NUM
ejpam-298	49	17	)	)	PUNCT
ejpam-298	49	18	,	,	PUNCT
ejpam-298	49	19	we	we	PRON
ejpam-298	49	20	obtain	obtain	VERB
ejpam-298	49	21	s(y	s(y	PROPN
ejpam-298	49	22	,	,	PUNCT
ejpam-298	49	23	z	z	NOUN
ejpam-298	49	24	)	)	PUNCT
ejpam-298	49	25	=	=	SYM
ejpam-298	50	1	(	(	PUNCT
ejpam-298	50	2	n−	n−	NOUN
ejpam-298	50	3	1)pg(y	1)pg(y	NUM
ejpam-298	50	4	,	,	PUNCT
ejpam-298	50	5	z)+	z)+	NUM
ejpam-298	50	6	(	(	PUNCT
ejpam-298	50	7	n−	n−	PROPN
ejpam-298	50	8	1)q	1)q	NOUN
ejpam-298	50	9	[	[	X
ejpam-298	50	10	a(y	a(y	NOUN
ejpam-298	50	11	)	)	PUNCT
ejpam-298	50	12	b(z	b(z	NOUN
ejpam-298	50	13	)	)	PUNCT
ejpam-298	51	1	+	+	ADP
ejpam-298	51	2	a(z)b(y	a(z)b(y	ADJ
ejpam-298	51	3	)	)	PUNCT
ejpam-298	51	4	]	]	PUNCT
ejpam-298	52	1	+	+	PROPN
ejpam-298	52	2	s	s	X
ejpam-298	52	3	�	�	PROPN
ejpam-298	52	4	2g(y	2g(y	NUM
ejpam-298	52	5	,	,	PUNCT
ejpam-298	52	6	z)−	z)−	PROPN
ejpam-298	52	7	a(z)b(y	a(z)b(y	VERB
ejpam-298	52	8	)	)	PUNCT
ejpam-298	52	9	−	−	PROPN
ejpam-298	52	10	a(y	a(y	PROPN
ejpam-298	52	11	)	)	PUNCT
ejpam-298	52	12	b(z	b(z	NOUN
ejpam-298	52	13	)	)	PUNCT
ejpam-298	52	14	�	�	PROPN
ejpam-298	52	15	which	which	PRON
ejpam-298	52	16	implies	imply	VERB
ejpam-298	52	17	s(y	s(y	PROPN
ejpam-298	52	18	,	,	PUNCT
ejpam-298	52	19	z	z	NOUN
ejpam-298	52	20	)	)	PUNCT
ejpam-298	52	21	=	=	SYM
ejpam-298	52	22	ag(y	ag(y	NUM
ejpam-298	52	23	,	,	PUNCT
ejpam-298	52	24	z	z	NOUN
ejpam-298	52	25	)	)	PUNCT
ejpam-298	52	26	+	+	CCONJ
ejpam-298	52	27	ba(y	ba(y	NOUN
ejpam-298	52	28	)	)	PUNCT
ejpam-298	52	29	b(z	b(z	NOUN
ejpam-298	52	30	)	)	PUNCT
ejpam-298	53	1	+	+	CCONJ
ejpam-298	53	2	ca(z)b(y	ca(z)b(y	NOUN
ejpam-298	53	3	)	)	PUNCT
ejpam-298	53	4	(	(	PUNCT
ejpam-298	53	5	3	3	X
ejpam-298	53	6	)	)	PUNCT
ejpam-298	54	1	where	where	SCONJ
ejpam-298	54	2	b	b	X
ejpam-298	54	3	=	=	SYM
ejpam-298	54	4	c	c	NOUN
ejpam-298	54	5	=	=	PUNCT
ejpam-298	54	6	(	(	PUNCT
ejpam-298	54	7	n−	n−	NOUN
ejpam-298	54	8	1)q−	1)q−	PROPN
ejpam-298	54	9	s	s	PART
ejpam-298	54	10	,	,	PUNCT
ejpam-298	54	11	a	a	PRON
ejpam-298	54	12	=	=	X
ejpam-298	54	13	(	(	PUNCT
ejpam-298	54	14	n−	n−	NOUN
ejpam-298	54	15	1)p+	1)p+	NUM
ejpam-298	54	16	2s	2s	X
ejpam-298	54	17	.	.	PUNCT
ejpam-298	55	1	i.e.	i.e.	X
ejpam-298	55	2	the	the	DET
ejpam-298	55	3	space	space	NOUN
ejpam-298	55	4	(	(	PUNCT
ejpam-298	55	5	m	m	NOUN
ejpam-298	55	6	n	n	CCONJ
ejpam-298	55	7	,	,	PUNCT
ejpam-298	55	8	g)is	g)is	PROPN
ejpam-298	55	9	mixed	mix	VERB
ejpam-298	55	10	quasi	quasi	NOUN
ejpam-298	55	11	einstein	einstein	NOUN
ejpam-298	55	12	.	.	PUNCT
ejpam-298	56	1	thus	thus	ADV
ejpam-298	56	2	we	we	PRON
ejpam-298	56	3	have	have	AUX
ejpam-298	56	4	theorem	theorem	VERB
ejpam-298	56	5	1	1	NUM
ejpam-298	56	6	.	.	PUNCT
ejpam-298	57	1	a	a	DET
ejpam-298	57	2	manifold	manifold	NOUN
ejpam-298	57	3	of	of	ADP
ejpam-298	57	4	mixed	mixed	ADJ
ejpam-298	57	5	quasi	quasi	ADJ
ejpam-298	57	6	constant	constant	ADJ
ejpam-298	57	7	curvature	curvature	NOUN
ejpam-298	57	8	is	be	AUX
ejpam-298	57	9	a	a	DET
ejpam-298	57	10	mixed	mixed	ADJ
ejpam-298	57	11	quasi	quasi	NOUN
ejpam-298	57	12	einstein	einstein	PROPN
ejpam-298	57	13	manifold	manifold	PROPN
ejpam-298	57	14	.	.	PUNCT
ejpam-298	58	1	h.	h.	PROPN
ejpam-298	58	2	nagaraja	nagaraja	PROPN
ejpam-298	58	3	/	/	SYM
ejpam-298	58	4	eur	eur	PROPN
ejpam-298	58	5	.	.	PUNCT
ejpam-298	59	1	j.	j.	PROPN
ejpam-298	59	2	pure	pure	PROPN
ejpam-298	59	3	appl	appl	PROPN
ejpam-298	59	4	.	.	PROPN
ejpam-298	59	5	math	math	PROPN
ejpam-298	59	6	,	,	PUNCT
ejpam-298	59	7	3	3	NUM
ejpam-298	59	8	(	(	PUNCT
ejpam-298	59	9	2010	2010	NUM
ejpam-298	59	10	)	)	PUNCT
ejpam-298	59	11	,	,	PUNCT
ejpam-298	59	12	16	16	NUM
ejpam-298	59	13	-	-	SYM
ejpam-298	59	14	25	25	NUM
ejpam-298	59	15	18	18	NUM
ejpam-298	59	16	conversely	conversely	ADV
ejpam-298	59	17	suppose	suppose	VERB
ejpam-298	59	18	(	(	PUNCT
ejpam-298	59	19	m	m	VERB
ejpam-298	59	20	n	n	CCONJ
ejpam-298	59	21	,	,	PUNCT
ejpam-298	59	22	g	g	NOUN
ejpam-298	59	23	)	)	PUNCT
ejpam-298	59	24	is	be	AUX
ejpam-298	59	25	conformally	conformally	ADV
ejpam-298	59	26	flat	flat	ADJ
ejpam-298	59	27	mixed	mixed	ADJ
ejpam-298	59	28	quasi	quasi	NOUN
ejpam-298	59	29	einstein	einstein	PROPN
ejpam-298	59	30	manifold	manifold	PROPN
ejpam-298	59	31	.	.	PUNCT
ejpam-298	60	1	then	then	ADV
ejpam-298	60	2	r(x	r(x	PROPN
ejpam-298	60	3	,	,	PUNCT
ejpam-298	60	4	y	y	PROPN
ejpam-298	60	5	)	)	PUNCT
ejpam-298	60	6	z	z	NOUN
ejpam-298	60	7	=	=	SYM
ejpam-298	60	8	1	1	NUM
ejpam-298	60	9	n−	n−	NOUN
ejpam-298	60	10	2	2	NUM
ejpam-298	60	11	{	{	PUNCT
ejpam-298	60	12	g(y	g(y	PROPN
ejpam-298	60	13	,	,	PUNCT
ejpam-298	60	14	z)qx	z)qx	PROPN
ejpam-298	60	15	−	−	NOUN
ejpam-298	60	16	g(x	g(x	NOUN
ejpam-298	60	17	,	,	PUNCT
ejpam-298	60	18	z)qy	z)qy	PROPN
ejpam-298	60	19	+	+	CCONJ
ejpam-298	60	20	s(y	s(y	PROPN
ejpam-298	60	21	,	,	PUNCT
ejpam-298	60	22	z)x	z)x	PUNCT
ejpam-298	60	23	−	−	PROPN
ejpam-298	60	24	s(x	s(x	NOUN
ejpam-298	60	25	,	,	PUNCT
ejpam-298	60	26	z)y	z)y	NUM
ejpam-298	60	27	}	}	PUNCT
ejpam-298	60	28	−	−	NOUN
ejpam-298	61	1	r	r	NOUN
ejpam-298	61	2	(	(	PUNCT
ejpam-298	61	3	n−	n−	NOUN
ejpam-298	61	4	1)(n−	1)(n−	PROPN
ejpam-298	61	5	2	2	NUM
ejpam-298	61	6	)	)	PUNCT
ejpam-298	61	7	{	{	PUNCT
ejpam-298	61	8	g(y	g(y	PROPN
ejpam-298	61	9	,	,	PUNCT
ejpam-298	61	10	z)x	z)x	PUNCT
ejpam-298	61	11	−	−	PROPN
ejpam-298	61	12	g(x	g(x	PROPN
ejpam-298	61	13	,	,	PUNCT
ejpam-298	61	14	z)y	z)y	NUM
ejpam-298	61	15	}	}	PUNCT
ejpam-298	61	16	.	.	PUNCT
ejpam-298	62	1	(	(	PUNCT
ejpam-298	62	2	4	4	X
ejpam-298	62	3	)	)	PUNCT
ejpam-298	62	4	here	here	ADV
ejpam-298	62	5	q	q	PROPN
ejpam-298	62	6	is	be	AUX
ejpam-298	62	7	ricci	ricci	NOUN
ejpam-298	62	8	operator	operator	NOUN
ejpam-298	62	9	defined	define	VERB
ejpam-298	62	10	by	by	ADP
ejpam-298	62	11	s(x	s(x	NOUN
ejpam-298	62	12	,	,	PUNCT
ejpam-298	62	13	y	y	PROPN
ejpam-298	62	14	)	)	PUNCT
ejpam-298	63	1	=	=	SYM
ejpam-298	64	1	g(qx	g(qx	PROPN
ejpam-298	64	2	,	,	PUNCT
ejpam-298	64	3	y	y	PROPN
ejpam-298	64	4	)	)	PUNCT
ejpam-298	64	5	.	.	PUNCT
ejpam-298	65	1	from	from	ADP
ejpam-298	65	2	the	the	DET
ejpam-298	65	3	above	above	ADJ
ejpam-298	65	4	equation	equation	NOUN
ejpam-298	65	5	,	,	PUNCT
ejpam-298	65	6	we	we	PRON
ejpam-298	65	7	get	get	VERB
ejpam-298	65	8	′r(x	′r(x	PROPN
ejpam-298	65	9	,	,	PUNCT
ejpam-298	65	10	y	y	PROPN
ejpam-298	65	11	,	,	PUNCT
ejpam-298	65	12	z	z	NOUN
ejpam-298	65	13	,	,	PUNCT
ejpam-298	65	14	w	w	PROPN
ejpam-298	65	15	)	)	PUNCT
ejpam-298	66	1	=	=	PROPN
ejpam-298	66	2	g(r(x	g(r(x	PROPN
ejpam-298	66	3	,	,	PUNCT
ejpam-298	66	4	y	y	PROPN
ejpam-298	66	5	)	)	PUNCT
ejpam-298	66	6	z	z	NOUN
ejpam-298	66	7	,	,	PUNCT
ejpam-298	66	8	w	w	PROPN
ejpam-298	66	9	)	)	PUNCT
ejpam-298	66	10	=	=	SYM
ejpam-298	66	11	1	1	NUM
ejpam-298	66	12	n−	n−	NOUN
ejpam-298	66	13	2	2	NUM
ejpam-298	66	14	�	�	PROPN
ejpam-298	66	15	g(y	g(y	PROPN
ejpam-298	66	16	,	,	PUNCT
ejpam-298	66	17	z)s(x	z)s(x	NOUN
ejpam-298	66	18	,	,	PUNCT
ejpam-298	66	19	w	w	NOUN
ejpam-298	66	20	)	)	PUNCT
ejpam-298	66	21	−	−	PROPN
ejpam-298	67	1	g(x	g(x	PROPN
ejpam-298	67	2	,	,	PUNCT
ejpam-298	67	3	z)s(y	z)s(y	NOUN
ejpam-298	67	4	,	,	PUNCT
ejpam-298	67	5	w	w	NOUN
ejpam-298	67	6	)	)	PUNCT
ejpam-298	68	1	+	+	CCONJ
ejpam-298	68	2	s(y	s(y	PROPN
ejpam-298	68	3	,	,	PUNCT
ejpam-298	68	4	z)g(x	z)g(x	NUM
ejpam-298	68	5	,	,	PUNCT
ejpam-298	68	6	w	w	NOUN
ejpam-298	68	7	)	)	PUNCT
ejpam-298	68	8	−	−	PROPN
ejpam-298	69	1	s(x	s(x	PROPN
ejpam-298	69	2	,	,	PUNCT
ejpam-298	69	3	z)g(y	z)g(y	PROPN
ejpam-298	69	4	,	,	PUNCT
ejpam-298	69	5	w	w	NOUN
ejpam-298	69	6	)	)	PUNCT
ejpam-298	69	7	−	−	NOUN
ejpam-298	70	1	r	r	NOUN
ejpam-298	70	2	(	(	PUNCT
ejpam-298	70	3	n−	n−	NOUN
ejpam-298	70	4	1)(n−	1)(n−	PROPN
ejpam-298	70	5	2	2	NUM
ejpam-298	70	6	)	)	PUNCT
ejpam-298	70	7	�	�	PROPN
ejpam-298	70	8	g(y	g(y	PROPN
ejpam-298	70	9	,	,	PUNCT
ejpam-298	70	10	z)g(x	z)g(x	NUM
ejpam-298	70	11	,	,	PUNCT
ejpam-298	70	12	w	w	NOUN
ejpam-298	70	13	)	)	PUNCT
ejpam-298	70	14	−	−	PROPN
ejpam-298	71	1	g(x	g(x	PROPN
ejpam-298	71	2	,	,	PUNCT
ejpam-298	71	3	z)g(y	z)g(y	PROPN
ejpam-298	71	4	,	,	PUNCT
ejpam-298	71	5	w	w	NOUN
ejpam-298	71	6	)	)	PUNCT
ejpam-298	71	7	(	(	PUNCT
ejpam-298	71	8	5	5	X
ejpam-298	71	9	)	)	PUNCT
ejpam-298	71	10	taking	take	VERB
ejpam-298	71	11	x	x	PUNCT
ejpam-298	71	12	=	=	PUNCT
ejpam-298	71	13	y	y	NOUN
ejpam-298	71	14	=	=	PUNCT
ejpam-298	71	15	ei	ei	PROPN
ejpam-298	71	16	and	and	CCONJ
ejpam-298	71	17	taking	take	VERB
ejpam-298	71	18	summation	summation	NOUN
ejpam-298	71	19	over	over	ADP
ejpam-298	71	20	i	i	PROPN
ejpam-298	71	21	,	,	PUNCT
ejpam-298	71	22	1	1	NUM
ejpam-298	71	23	≤	≤	NUM
ejpam-298	71	24	i	i	PRON
ejpam-298	71	25	≤	≤	NOUN
ejpam-298	71	26	n	n	CCONJ
ejpam-298	71	27	in	in	ADP
ejpam-298	71	28	(	(	PUNCT
ejpam-298	71	29	1	1	NUM
ejpam-298	71	30	)	)	PUNCT
ejpam-298	71	31	,	,	PUNCT
ejpam-298	71	32	we	we	PRON
ejpam-298	71	33	obtain	obtain	VERB
ejpam-298	71	34	r	r	NOUN
ejpam-298	71	35	=	=	PUNCT
ejpam-298	71	36	na	na	NOUN
ejpam-298	71	37	.	.	PUNCT
ejpam-298	71	38	substituting	substitute	VERB
ejpam-298	71	39	this	this	PRON
ejpam-298	71	40	in	in	ADP
ejpam-298	71	41	(	(	PUNCT
ejpam-298	71	42	5	5	NUM
ejpam-298	71	43	)	)	PUNCT
ejpam-298	71	44	and	and	CCONJ
ejpam-298	71	45	using	use	VERB
ejpam-298	71	46	(	(	PUNCT
ejpam-298	71	47	1	1	NUM
ejpam-298	71	48	)	)	PUNCT
ejpam-298	71	49	,	,	PUNCT
ejpam-298	71	50	we	we	PRON
ejpam-298	71	51	get	get	VERB
ejpam-298	71	52	r(x	r(x	PROPN
ejpam-298	71	53	,	,	PUNCT
ejpam-298	71	54	y	y	PROPN
ejpam-298	71	55	,	,	PUNCT
ejpam-298	71	56	z	z	NOUN
ejpam-298	71	57	,	,	PUNCT
ejpam-298	71	58	w	w	PROPN
ejpam-298	71	59	)	)	PUNCT
ejpam-298	71	60	=	=	SYM
ejpam-298	71	61	p[g(y	p[g(y	PROPN
ejpam-298	71	62	,	,	PUNCT
ejpam-298	71	63	z)g(x	z)g(x	NUM
ejpam-298	71	64	,	,	PUNCT
ejpam-298	71	65	w	w	NOUN
ejpam-298	71	66	)	)	PUNCT
ejpam-298	71	67	−	−	PROPN
ejpam-298	72	1	g(x	g(x	PROPN
ejpam-298	72	2	,	,	PUNCT
ejpam-298	72	3	z)g(y	z)g(y	PROPN
ejpam-298	72	4	,	,	PUNCT
ejpam-298	72	5	w	w	NOUN
ejpam-298	72	6	)	)	PUNCT
ejpam-298	72	7	]	]	PUNCT
ejpam-298	73	1	+	+	CCONJ
ejpam-298	73	2	q[g(x	q[g(x	X
ejpam-298	73	3	,	,	PUNCT
ejpam-298	73	4	w	w	X
ejpam-298	73	5	)	)	PUNCT
ejpam-298	73	6	a(y	a(y	PROPN
ejpam-298	73	7	)	)	PUNCT
ejpam-298	73	8	b(z)−	b(z)−	PROPN
ejpam-298	73	9	g(x	g(x	PROPN
ejpam-298	73	10	,	,	PUNCT
ejpam-298	73	11	z)a(y	z)a(y	PROPN
ejpam-298	73	12	)	)	PUNCT
ejpam-298	73	13	b(w	b(w	PROPN
ejpam-298	73	14	)	)	PUNCT
ejpam-298	74	1	+	+	CCONJ
ejpam-298	75	1	g(x	g(x	PROPN
ejpam-298	75	2	,	,	PUNCT
ejpam-298	75	3	w	w	NOUN
ejpam-298	75	4	)	)	PUNCT
ejpam-298	75	5	a(z)b(y	a(z)b(y	ADJ
ejpam-298	75	6	)	)	PUNCT
ejpam-298	75	7	−	−	PROPN
ejpam-298	76	1	g(x	g(x	PROPN
ejpam-298	76	2	,	,	PUNCT
ejpam-298	76	3	z)a(w	z)a(w	NUM
ejpam-298	76	4	)	)	PUNCT
ejpam-298	76	5	b(y	b(y	PROPN
ejpam-298	76	6	)	)	PUNCT
ejpam-298	76	7	]	]	PUNCT
ejpam-298	77	1	+	+	CCONJ
ejpam-298	77	2	s[g(y	s[g(y	PROPN
ejpam-298	77	3	,	,	PUNCT
ejpam-298	77	4	z)a(w)b(x	z)a(w)b(x	NUM
ejpam-298	77	5	)	)	PUNCT
ejpam-298	77	6	−	−	PROPN
ejpam-298	78	1	g(y	g(y	PROPN
ejpam-298	78	2	,	,	PUNCT
ejpam-298	78	3	w	w	NOUN
ejpam-298	78	4	)	)	PUNCT
ejpam-298	78	5	a(z)b(x	a(z)b(x	X
ejpam-298	78	6	)	)	PUNCT
ejpam-298	79	1	+	+	CCONJ
ejpam-298	79	2	g(y	g(y	NOUN
ejpam-298	79	3	,	,	PUNCT
ejpam-298	79	4	z)a(x	z)a(x	NOUN
ejpam-298	79	5	)	)	PUNCT
ejpam-298	79	6	b(w	b(w	PROPN
ejpam-298	79	7	)	)	PUNCT
ejpam-298	79	8	−	−	PROPN
ejpam-298	80	1	g(y	g(y	PROPN
ejpam-298	80	2	,	,	PUNCT
ejpam-298	80	3	w	w	NOUN
ejpam-298	80	4	)	)	PUNCT
ejpam-298	80	5	a(x	a(x	NOUN
ejpam-298	80	6	)	)	PUNCT
ejpam-298	80	7	b(z	b(z	NOUN
ejpam-298	80	8	)	)	PUNCT
ejpam-298	80	9	]	]	PUNCT
ejpam-298	80	10	where	where	SCONJ
ejpam-298	80	11	p	p	NOUN
ejpam-298	80	12	=	=	PUNCT
ejpam-298	80	13	a	a	DET
ejpam-298	80	14	n−	n−	NOUN
ejpam-298	80	15	1	1	NUM
ejpam-298	80	16	,	,	PUNCT
ejpam-298	80	17	q	q	NOUN
ejpam-298	80	18	=	=	SYM
ejpam-298	80	19	b	b	PROPN
ejpam-298	80	20	n−	n−	NOUN
ejpam-298	80	21	2	2	NUM
ejpam-298	80	22	,	,	PUNCT
ejpam-298	80	23	s	s	PART
ejpam-298	80	24	=	=	SYM
ejpam-298	80	25	c	c	X
ejpam-298	80	26	n−	n−	NOUN
ejpam-298	80	27	2	2	NUM
ejpam-298	80	28	.	.	PUNCT
ejpam-298	81	1	i.e.	i.e.	X
ejpam-298	81	2	(	(	PUNCT
ejpam-298	81	3	m	m	VERB
ejpam-298	81	4	n	n	CCONJ
ejpam-298	81	5	,	,	PUNCT
ejpam-298	81	6	g	g	NOUN
ejpam-298	81	7	)	)	PUNCT
ejpam-298	81	8	is	be	AUX
ejpam-298	81	9	a	a	DET
ejpam-298	81	10	manifold	manifold	NOUN
ejpam-298	81	11	of	of	ADP
ejpam-298	81	12	mixed	mixed	ADJ
ejpam-298	81	13	quasi	quasi	ADJ
ejpam-298	81	14	constant	constant	ADJ
ejpam-298	81	15	curvature	curvature	NOUN
ejpam-298	81	16	.	.	PUNCT
ejpam-298	82	1	2	2	X
ejpam-298	82	2	.	.	X
ejpam-298	82	3	existence	existence	NOUN
ejpam-298	82	4	theorem	theorem	NOUN
ejpam-298	82	5	of	of	ADP
ejpam-298	82	6	a	a	DET
ejpam-298	82	7	n(k)-mixed	n(k)-mixed	PROPN
ejpam-298	82	8	quasi	quasi	PROPN
ejpam-298	82	9	einstein	einstein	PROPN
ejpam-298	82	10	manifolds	manifolds	PROPN
ejpam-298	82	11	theorem	theorem	VERB
ejpam-298	82	12	2	2	NUM
ejpam-298	82	13	.	.	PUNCT
ejpam-298	83	1	if	if	SCONJ
ejpam-298	83	2	in	in	ADP
ejpam-298	83	3	a	a	DET
ejpam-298	83	4	conformally	conformally	ADV
ejpam-298	83	5	flat	flat	ADJ
ejpam-298	83	6	riemannian	riemannian	ADJ
ejpam-298	83	7	manifold	manifold	NOUN
ejpam-298	83	8	(	(	PUNCT
ejpam-298	83	9	m	m	NOUN
ejpam-298	83	10	n	n	CCONJ
ejpam-298	83	11	,	,	PUNCT
ejpam-298	83	12	g	g	PROPN
ejpam-298	83	13	)	)	PUNCT
ejpam-298	83	14	,	,	PUNCT
ejpam-298	83	15	the	the	DET
ejpam-298	83	16	ricci	ricci	PROPN
ejpam-298	83	17	tensor	tensor	NOUN
ejpam-298	83	18	s	s	PART
ejpam-298	83	19	satisfies	satisfie	NOUN
ejpam-298	83	20	the	the	DET
ejpam-298	83	21	relation	relation	NOUN
ejpam-298	83	22	s(x	s(x	PROPN
ejpam-298	83	23	,	,	PUNCT
ejpam-298	83	24	z)g(y	z)g(y	PROPN
ejpam-298	83	25	,	,	PUNCT
ejpam-298	83	26	w	w	NOUN
ejpam-298	83	27	)	)	PUNCT
ejpam-298	84	1	−	−	PROPN
ejpam-298	84	2	s(y	s(y	PROPN
ejpam-298	84	3	,	,	PUNCT
ejpam-298	84	4	z)g(x	z)g(x	NUM
ejpam-298	84	5	,	,	PUNCT
ejpam-298	84	6	w	w	NOUN
ejpam-298	84	7	)	)	PUNCT
ejpam-298	85	1	=	=	SYM
ejpam-298	85	2	β(g(y	β(g(y	PROPN
ejpam-298	85	3	,	,	PUNCT
ejpam-298	85	4	z)s(x	z)s(x	NOUN
ejpam-298	85	5	,	,	PUNCT
ejpam-298	85	6	w	w	NOUN
ejpam-298	85	7	)	)	PUNCT
ejpam-298	85	8	−	−	PROPN
ejpam-298	86	1	g(x	g(x	PROPN
ejpam-298	86	2	,	,	PUNCT
ejpam-298	86	3	z)s(y	z)s(y	NOUN
ejpam-298	86	4	,	,	PUNCT
ejpam-298	86	5	w	w	NOUN
ejpam-298	86	6	)	)	PUNCT
ejpam-298	86	7	(	(	PUNCT
ejpam-298	86	8	6	6	NUM
ejpam-298	86	9	)	)	PUNCT
ejpam-298	86	10	where	where	SCONJ
ejpam-298	86	11	β	β	PROPN
ejpam-298	86	12	is	be	AUX
ejpam-298	86	13	a	a	DET
ejpam-298	86	14	non	non	ADJ
ejpam-298	86	15	zero	zero	NUM
ejpam-298	86	16	scalar	scalar	NOUN
ejpam-298	86	17	,	,	PUNCT
ejpam-298	86	18	then	then	ADV
ejpam-298	86	19	(	(	PUNCT
ejpam-298	86	20	m	m	VERB
ejpam-298	86	21	n	n	CCONJ
ejpam-298	86	22	,	,	PUNCT
ejpam-298	86	23	g	g	NOUN
ejpam-298	86	24	)	)	PUNCT
ejpam-298	86	25	is	be	AUX
ejpam-298	86	26	a	a	DET
ejpam-298	86	27	n(k)-mixed	n(k)-mixed	PROPN
ejpam-298	86	28	quasi	quasi	PROPN
ejpam-298	86	29	einstein	einstein	PROPN
ejpam-298	86	30	manifold	manifold	PROPN
ejpam-298	86	31	.	.	PUNCT
ejpam-298	87	1	proof	proof	NOUN
ejpam-298	87	2	.	.	PUNCT
ejpam-298	88	1	let	let	VERB
ejpam-298	88	2	u	u	PRON
ejpam-298	88	3	be	be	AUX
ejpam-298	88	4	a	a	DET
ejpam-298	88	5	vector	vector	NOUN
ejpam-298	88	6	field	field	NOUN
ejpam-298	88	7	defined	define	VERB
ejpam-298	88	8	by	by	ADP
ejpam-298	88	9	g(x	g(x	PROPN
ejpam-298	88	10	,	,	PUNCT
ejpam-298	88	11	u	u	NOUN
ejpam-298	88	12	)	)	PUNCT
ejpam-298	88	13	=	=	SYM
ejpam-298	88	14	a(x	a(x	NOUN
ejpam-298	88	15	)	)	PUNCT
ejpam-298	88	16	,	,	PUNCT
ejpam-298	88	17	∀x	∀x	X
ejpam-298	88	18	∈	∈	PROPN
ejpam-298	88	19	t	t	NOUN
ejpam-298	88	20	m	m	VERB
ejpam-298	88	21	.	.	PUNCT
ejpam-298	89	1	taking	take	VERB
ejpam-298	89	2	x	x	PUNCT
ejpam-298	90	1	=	=	NOUN
ejpam-298	90	2	w	w	NOUN
ejpam-298	90	3	=	=	SYM
ejpam-298	90	4	u	u	NOUN
ejpam-298	90	5	in	in	ADP
ejpam-298	90	6	(	(	PUNCT
ejpam-298	90	7	6	6	NUM
ejpam-298	90	8	)	)	PUNCT
ejpam-298	90	9	,	,	PUNCT
ejpam-298	90	10	we	we	PRON
ejpam-298	90	11	obtain	obtain	VERB
ejpam-298	90	12	s(y	s(y	PROPN
ejpam-298	90	13	,	,	PUNCT
ejpam-298	90	14	z	z	NOUN
ejpam-298	90	15	)	)	PUNCT
ejpam-298	90	16	=	=	SYM
ejpam-298	90	17	ag(y	ag(y	NUM
ejpam-298	90	18	,	,	PUNCT
ejpam-298	90	19	z	z	NOUN
ejpam-298	90	20	)	)	PUNCT
ejpam-298	90	21	+	+	CCONJ
ejpam-298	90	22	ba(y	ba(y	NOUN
ejpam-298	90	23	)	)	PUNCT
ejpam-298	90	24	b(z	b(z	NOUN
ejpam-298	90	25	)	)	PUNCT
ejpam-298	91	1	+	+	CCONJ
ejpam-298	91	2	ca(z)b(y	ca(z)b(y	NOUN
ejpam-298	91	3	)	)	PUNCT
ejpam-298	91	4	(	(	PUNCT
ejpam-298	91	5	7	7	X
ejpam-298	91	6	)	)	PUNCT
ejpam-298	91	7	where	where	SCONJ
ejpam-298	91	8	a	a	DET
ejpam-298	91	9	=	=	SYM
ejpam-298	91	10	−αβ	−αβ	PROPN
ejpam-298	91	11	u	u	NOUN
ejpam-298	91	12	,	,	PUNCT
ejpam-298	91	13	α	α	NOUN
ejpam-298	91	14	=	=	SYM
ejpam-298	91	15	s(u	s(u	PROPN
ejpam-298	91	16	,	,	PUNCT
ejpam-298	91	17	u),u	u),u	PROPN
ejpam-298	91	18	=	=	SYM
ejpam-298	91	19	g(u	g(u	PROPN
ejpam-298	91	20	,	,	PUNCT
ejpam-298	91	21	u	u	NOUN
ejpam-298	91	22	)	)	PUNCT
ejpam-298	91	23	,	,	PUNCT
ejpam-298	91	24	b	b	X
ejpam-298	91	25	=	=	SYM
ejpam-298	91	26	1	1	NUM
ejpam-298	91	27	u	u	NOUN
ejpam-298	91	28	,	,	PUNCT
ejpam-298	91	29	c	c	X
ejpam-298	91	30	=	=	SYM
ejpam-298	91	31	β	β	X
ejpam-298	91	32	u	u	NOUN
ejpam-298	91	33	,	,	PUNCT
ejpam-298	91	34	and	and	CCONJ
ejpam-298	91	35	s(u	s(u	PROPN
ejpam-298	91	36	,	,	PUNCT
ejpam-298	91	37	z	z	NOUN
ejpam-298	91	38	)	)	PUNCT
ejpam-298	92	1	=	=	SYM
ejpam-298	92	2	s(z	s(z	PROPN
ejpam-298	92	3	,	,	PUNCT
ejpam-298	92	4	u	u	NOUN
ejpam-298	92	5	)	)	PUNCT
ejpam-298	92	6	=	=	SYM
ejpam-298	93	1	g(qz	g(qz	PROPN
ejpam-298	93	2	,	,	PUNCT
ejpam-298	93	3	u	u	NOUN
ejpam-298	93	4	)	)	PUNCT
ejpam-298	93	5	=	=	SYM
ejpam-298	93	6	a(qz	a(qz	NUM
ejpam-298	93	7	)	)	PUNCT
ejpam-298	93	8	=	=	SYM
ejpam-298	94	1	b(z	b(z	NOUN
ejpam-298	94	2	)	)	PUNCT
ejpam-298	94	3	.	.	PUNCT
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ejpam-298	95	2	(	(	PUNCT
ejpam-298	95	3	m	m	VERB
ejpam-298	95	4	n	n	CCONJ
ejpam-298	95	5	,	,	PUNCT
ejpam-298	95	6	g	g	NOUN
ejpam-298	95	7	)	)	PUNCT
ejpam-298	95	8	is	be	AUX
ejpam-298	95	9	mixed	mix	VERB
ejpam-298	95	10	quasi	quasi	ADJ
ejpam-298	95	11	einstein	einstein	NOUN
ejpam-298	95	12	.	.	PUNCT
ejpam-298	96	1	h.	h.	PROPN
ejpam-298	96	2	nagaraja	nagaraja	PROPN
ejpam-298	96	3	/	/	SYM
ejpam-298	96	4	eur	eur	PROPN
ejpam-298	96	5	.	.	PUNCT
ejpam-298	97	1	j.	j.	PROPN
ejpam-298	97	2	pure	pure	PROPN
ejpam-298	97	3	appl	appl	PROPN
ejpam-298	97	4	.	.	PROPN
ejpam-298	97	5	math	math	PROPN
ejpam-298	97	6	,	,	PUNCT
ejpam-298	97	7	3	3	NUM
ejpam-298	97	8	(	(	PUNCT
ejpam-298	97	9	2010	2010	NUM
ejpam-298	97	10	)	)	PUNCT
ejpam-298	97	11	,	,	PUNCT
ejpam-298	97	12	16	16	NUM
ejpam-298	97	13	-	-	SYM
ejpam-298	97	14	25	25	NUM
ejpam-298	97	15	19	19	NUM
ejpam-298	97	16	if	if	SCONJ
ejpam-298	97	17	(	(	PUNCT
ejpam-298	97	18	m	m	VERB
ejpam-298	97	19	n	n	CCONJ
ejpam-298	97	20	,	,	PUNCT
ejpam-298	97	21	g	g	NOUN
ejpam-298	97	22	)	)	PUNCT
ejpam-298	97	23	is	be	AUX
ejpam-298	97	24	conformally	conformally	ADV
ejpam-298	97	25	flat	flat	ADJ
ejpam-298	97	26	,	,	PUNCT
ejpam-298	97	27	then	then	ADV
ejpam-298	97	28	taking	take	VERB
ejpam-298	97	29	z	z	NOUN
ejpam-298	97	30	=	=	SYM
ejpam-298	97	31	u	u	NOUN
ejpam-298	97	32	in	in	ADP
ejpam-298	97	33	(	(	PUNCT
ejpam-298	97	34	4	4	NUM
ejpam-298	97	35	)	)	PUNCT
ejpam-298	97	36	,	,	PUNCT
ejpam-298	97	37	we	we	PRON
ejpam-298	97	38	obtain	obtain	VERB
ejpam-298	97	39	r(x	r(x	PROPN
ejpam-298	97	40	,	,	PUNCT
ejpam-298	97	41	y	y	PROPN
ejpam-298	97	42	)	)	PUNCT
ejpam-298	97	43	u	u	NOUN
ejpam-298	97	44	=	=	SYM
ejpam-298	97	45	1	1	NUM
ejpam-298	97	46	n−	n−	NOUN
ejpam-298	97	47	2	2	NUM
ejpam-298	97	48	{	{	PUNCT
ejpam-298	97	49	a(y	a(y	PROPN
ejpam-298	97	50	)	)	PUNCT
ejpam-298	97	51	qx	qx	PROPN
ejpam-298	97	52	−	−	NOUN
ejpam-298	97	53	a(x	a(x	PROPN
ejpam-298	97	54	)	)	PUNCT
ejpam-298	97	55	qy	qy	NOUN
ejpam-298	97	56	+	+	PROPN
ejpam-298	97	57	s(y	s(y	PROPN
ejpam-298	97	58	,	,	PUNCT
ejpam-298	97	59	u)x	u)x	ADJ
ejpam-298	97	60	−	−	PROPN
ejpam-298	97	61	s(x	s(x	NOUN
ejpam-298	97	62	,	,	PUNCT
ejpam-298	97	63	u)y	u)y	ADJ
ejpam-298	97	64	}	}	PUNCT
ejpam-298	97	65	(	(	PUNCT
ejpam-298	97	66	8)	8)	NUM
ejpam-298	97	67	−	−	NOUN
ejpam-298	97	68	r	r	NOUN
ejpam-298	97	69	(	(	PUNCT
ejpam-298	97	70	n−	n−	NOUN
ejpam-298	97	71	1)(n−	1)(n−	PROPN
ejpam-298	97	72	2	2	NUM
ejpam-298	97	73	)	)	PUNCT
ejpam-298	97	74	{	{	PUNCT
ejpam-298	97	75	a(y	a(y	PROPN
ejpam-298	97	76	)	)	PUNCT
ejpam-298	97	77	x	x	SYM
ejpam-298	97	78	−	−	PUNCT
ejpam-298	97	79	a(x	a(x	NOUN
ejpam-298	97	80	)	)	PUNCT
ejpam-298	97	81	y	y	PROPN
ejpam-298	97	82	}	}	PUNCT
ejpam-298	97	83	(	(	PUNCT
ejpam-298	97	84	9	9	X
ejpam-298	97	85	)	)	PUNCT
ejpam-298	97	86	taking	take	VERB
ejpam-298	97	87	β	β	X
ejpam-298	97	88	=	=	SYM
ejpam-298	97	89	1	1	NUM
ejpam-298	97	90	in	in	ADP
ejpam-298	97	91	(	(	PUNCT
ejpam-298	97	92	6	6	NUM
ejpam-298	97	93	)	)	PUNCT
ejpam-298	97	94	,	,	PUNCT
ejpam-298	97	95	we	we	PRON
ejpam-298	97	96	get	get	VERB
ejpam-298	97	97	s(x	s(x	NOUN
ejpam-298	97	98	,	,	PUNCT
ejpam-298	97	99	z)g(y	z)g(y	PROPN
ejpam-298	97	100	,	,	PUNCT
ejpam-298	97	101	w	w	NOUN
ejpam-298	97	102	)	)	PUNCT
ejpam-298	97	103	−	−	PROPN
ejpam-298	98	1	s(y	s(y	PROPN
ejpam-298	98	2	,	,	PUNCT
ejpam-298	98	3	z)g(x	z)g(x	NUM
ejpam-298	98	4	,	,	PUNCT
ejpam-298	98	5	w	w	NOUN
ejpam-298	98	6	)	)	PUNCT
ejpam-298	98	7	−	−	PROPN
ejpam-298	99	1	g(y	g(y	PROPN
ejpam-298	99	2	,	,	PUNCT
ejpam-298	99	3	z)s(x	z)s(x	NOUN
ejpam-298	99	4	,	,	PUNCT
ejpam-298	99	5	w	w	NOUN
ejpam-298	99	6	)	)	PUNCT
ejpam-298	100	1	+	+	CCONJ
ejpam-298	100	2	g(x	g(x	PROPN
ejpam-298	100	3	,	,	PUNCT
ejpam-298	100	4	z)s(y	z)s(y	NOUN
ejpam-298	100	5	,	,	PUNCT
ejpam-298	100	6	w	w	NOUN
ejpam-298	100	7	)	)	PUNCT
ejpam-298	100	8	=	=	SYM
ejpam-298	100	9	0	0	PUNCT
ejpam-298	101	1	taking	take	VERB
ejpam-298	101	2	z	z	NOUN
ejpam-298	101	3	=	=	SYM
ejpam-298	101	4	u	u	NOUN
ejpam-298	101	5	in	in	ADP
ejpam-298	101	6	the	the	DET
ejpam-298	101	7	above	above	ADJ
ejpam-298	101	8	equation	equation	NOUN
ejpam-298	101	9	,	,	PUNCT
ejpam-298	101	10	we	we	PRON
ejpam-298	101	11	obtain	obtain	VERB
ejpam-298	101	12	s(x	s(x	NOUN
ejpam-298	101	13	,	,	PUNCT
ejpam-298	101	14	u)g(y	u)g(y	PROPN
ejpam-298	101	15	,	,	PUNCT
ejpam-298	101	16	w	w	NOUN
ejpam-298	101	17	)	)	PUNCT
ejpam-298	101	18	−	−	PROPN
ejpam-298	102	1	s(y	s(y	PROPN
ejpam-298	102	2	,	,	PUNCT
ejpam-298	102	3	u)g(x	u)g(x	ADJ
ejpam-298	102	4	,	,	PUNCT
ejpam-298	102	5	w	w	NOUN
ejpam-298	102	6	)	)	PUNCT
ejpam-298	102	7	−a(y	−a(y	NOUN
ejpam-298	102	8	)	)	PUNCT
ejpam-298	102	9	s(x	s(x	PROPN
ejpam-298	102	10	,	,	PUNCT
ejpam-298	102	11	w	w	NOUN
ejpam-298	102	12	)	)	PUNCT
ejpam-298	103	1	+	+	CCONJ
ejpam-298	103	2	a(x	a(x	NOUN
ejpam-298	103	3	)	)	PUNCT
ejpam-298	103	4	s(y	s(y	PROPN
ejpam-298	103	5	,	,	PUNCT
ejpam-298	103	6	w	w	NOUN
ejpam-298	103	7	)	)	PUNCT
ejpam-298	103	8	=	=	SYM
ejpam-298	103	9	0	0	NUM
ejpam-298	103	10	,	,	PUNCT
ejpam-298	103	11	which	which	PRON
ejpam-298	103	12	can	can	AUX
ejpam-298	103	13	be	be	AUX
ejpam-298	103	14	rewritten	rewrite	VERB
ejpam-298	103	15	as	as	ADP
ejpam-298	103	16	g(s(x	g(s(x	PROPN
ejpam-298	103	17	,	,	PUNCT
ejpam-298	103	18	u)y	u)y	ADJ
ejpam-298	103	19	−	−	PROPN
ejpam-298	103	20	s(y	s(y	PROPN
ejpam-298	103	21	,	,	PUNCT
ejpam-298	103	22	u)x	u)x	NOUN
ejpam-298	103	23	−	−	ADP
ejpam-298	103	24	a(y	a(y	PROPN
ejpam-298	103	25	)	)	PUNCT
ejpam-298	103	26	qx	qx	PROPN
ejpam-298	103	27	+	+	NOUN
ejpam-298	103	28	a(x	a(x	PROPN
ejpam-298	103	29	)	)	PUNCT
ejpam-298	103	30	qy	qy	PROPN
ejpam-298	103	31	,	,	PUNCT
ejpam-298	103	32	w	w	NOUN
ejpam-298	103	33	)	)	PUNCT
ejpam-298	103	34	=	=	SYM
ejpam-298	103	35	0	0	NUM
ejpam-298	103	36	,	,	PUNCT
ejpam-298	103	37	∀w	∀w	PROPN
ejpam-298	103	38	.	.	PUNCT
ejpam-298	104	1	therefore	therefore	ADV
ejpam-298	104	2	we	we	PRON
ejpam-298	104	3	have	have	VERB
ejpam-298	104	4	s(x	s(x	NOUN
ejpam-298	104	5	,	,	PUNCT
ejpam-298	104	6	u)y	u)y	ADJ
ejpam-298	104	7	−	−	PROPN
ejpam-298	105	1	s(y	s(y	PROPN
ejpam-298	105	2	,	,	PUNCT
ejpam-298	105	3	u)x	u)x	NOUN
ejpam-298	105	4	−	−	ADP
ejpam-298	105	5	a(y	a(y	PROPN
ejpam-298	105	6	)	)	PUNCT
ejpam-298	105	7	qx	qx	PROPN
ejpam-298	105	8	+	+	CCONJ
ejpam-298	105	9	a(x	a(x	PROPN
ejpam-298	105	10	)	)	PUNCT
ejpam-298	105	11	qy	qy	NOUN
ejpam-298	105	12	=	=	SYM
ejpam-298	105	13	0	0	PROPN
ejpam-298	105	14	.	.	PUNCT
ejpam-298	106	1	substituting	substitute	VERB
ejpam-298	106	2	this	this	PRON
ejpam-298	106	3	in	in	ADP
ejpam-298	106	4	(	(	PUNCT
ejpam-298	106	5	8)	8)	NUM
ejpam-298	106	6	,	,	PUNCT
ejpam-298	106	7	we	we	PRON
ejpam-298	106	8	get	get	VERB
ejpam-298	106	9	r(x	r(x	PROPN
ejpam-298	106	10	,	,	PUNCT
ejpam-298	106	11	y	y	PROPN
ejpam-298	106	12	)	)	PUNCT
ejpam-298	106	13	u	u	NOUN
ejpam-298	107	1	=	=	NOUN
ejpam-298	107	2	k(a(y	k(a(y	PROPN
ejpam-298	107	3	)	)	PUNCT
ejpam-298	107	4	x	x	X
ejpam-298	107	5	−	−	PUNCT
ejpam-298	107	6	a(x	a(x	NOUN
ejpam-298	107	7	)	)	PUNCT
ejpam-298	107	8	y	y	PROPN
ejpam-298	107	9	)	)	PUNCT
ejpam-298	107	10	,	,	PUNCT
ejpam-298	107	11	where	where	SCONJ
ejpam-298	107	12	k	k	PROPN
ejpam-298	107	13	=	=	SYM
ejpam-298	107	14	−r	−r	PROPN
ejpam-298	107	15	(	(	PUNCT
ejpam-298	107	16	n−1)(n−2	n−1)(n−2	PROPN
ejpam-298	107	17	)	)	PUNCT
ejpam-298	107	18	.	.	PUNCT
ejpam-298	108	1	therefore	therefore	ADV
ejpam-298	108	2	we	we	PRON
ejpam-298	108	3	have	have	VERB
ejpam-298	108	4	u	u	NOUN
ejpam-298	108	5	∈	∈	NOUN
ejpam-298	108	6	np(k	np(k	NOUN
ejpam-298	108	7	)	)	PUNCT
ejpam-298	108	8	,	,	PUNCT
ejpam-298	108	9	where	where	SCONJ
ejpam-298	108	10	k	k	PROPN
ejpam-298	108	11	=	=	SYM
ejpam-298	108	12	−r	−r	PROPN
ejpam-298	108	13	(	(	PUNCT
ejpam-298	108	14	n−1)(n−2	n−1)(n−2	PROPN
ejpam-298	108	15	)	)	PUNCT
ejpam-298	108	16	.	.	PUNCT
ejpam-298	109	1	suppose	suppose	VERB
ejpam-298	109	2	v	v	NOUN
ejpam-298	109	3	is	be	AUX
ejpam-298	109	4	a	a	DET
ejpam-298	109	5	unit	unit	NOUN
ejpam-298	109	6	vector	vector	NOUN
ejpam-298	109	7	field	field	NOUN
ejpam-298	109	8	orthogonal	orthogonal	NOUN
ejpam-298	109	9	to	to	ADP
ejpam-298	109	10	u	u	PRON
ejpam-298	109	11	.	.	PUNCT
ejpam-298	110	1	then	then	ADV
ejpam-298	110	2	,	,	PUNCT
ejpam-298	110	3	we	we	PRON
ejpam-298	110	4	have	have	VERB
ejpam-298	110	5	v	v	NUM
ejpam-298	110	6	∈	∈	NOUN
ejpam-298	110	7	np(k	np(k	NOUN
ejpam-298	110	8	)	)	PUNCT
ejpam-298	110	9	.	.	PUNCT
ejpam-298	111	1	hence	hence	ADV
ejpam-298	111	2	(	(	PUNCT
ejpam-298	111	3	m	m	VERB
ejpam-298	111	4	n	n	CCONJ
ejpam-298	111	5	,	,	PUNCT
ejpam-298	111	6	g	g	NOUN
ejpam-298	111	7	)	)	PUNCT
ejpam-298	111	8	is	be	AUX
ejpam-298	111	9	a	a	DET
ejpam-298	111	10	n(k)-mixed	n(k)-mixed	PROPN
ejpam-298	111	11	quasi	quasi	PROPN
ejpam-298	111	12	einstein	einstein	PROPN
ejpam-298	111	13	manifold	manifold	PROPN
ejpam-298	111	14	.	.	PUNCT
ejpam-298	112	1	as	as	SCONJ
ejpam-298	112	2	it	it	PRON
ejpam-298	112	3	is	be	AUX
ejpam-298	112	4	well	well	ADV
ejpam-298	112	5	known	know	VERB
ejpam-298	112	6	that	that	SCONJ
ejpam-298	112	7	a	a	DET
ejpam-298	112	8	3	3	NUM
ejpam-298	112	9	-	-	PUNCT
ejpam-298	112	10	dimensional	dimensional	ADJ
ejpam-298	112	11	riemannian	riemannian	ADJ
ejpam-298	112	12	manifold	manifold	NOUN
ejpam-298	112	13	is	be	AUX
ejpam-298	112	14	conformally	conformally	ADV
ejpam-298	112	15	flat	flat	ADJ
ejpam-298	112	16	.	.	PUNCT
ejpam-298	113	1	thus	thus	ADV
ejpam-298	113	2	we	we	PRON
ejpam-298	113	3	have	have	VERB
ejpam-298	113	4	corollary	corollary	ADJ
ejpam-298	113	5	1	1	NUM
ejpam-298	113	6	.	.	PUNCT
ejpam-298	114	1	a	a	DET
ejpam-298	114	2	3dimensional	3dimensional	PROPN
ejpam-298	114	3	manifold	manifold	NOUN
ejpam-298	114	4	is	be	AUX
ejpam-298	114	5	n	n	DET
ejpam-298	114	6	�	�	PROPN
ejpam-298	114	7	−r	−r	PROPN
ejpam-298	114	8	(	(	PUNCT
ejpam-298	114	9	n−1)(n−2	n−1)(n−2	ADV
ejpam-298	114	10	)	)	PUNCT
ejpam-298	114	11	�	�	PROPN
ejpam-298	114	12	-mixed	-mixe	VERB
ejpam-298	114	13	quasi	quasi	PROPN
ejpam-298	114	14	einstein	einstein	PROPN
ejpam-298	114	15	manifold	manifold	PROPN
ejpam-298	114	16	provided	provide	VERB
ejpam-298	114	17	(	(	PUNCT
ejpam-298	114	18	6	6	NUM
ejpam-298	114	19	)	)	PUNCT
ejpam-298	114	20	holds	hold	NOUN
ejpam-298	114	21	.	.	PUNCT
ejpam-298	115	1	3	3	X
ejpam-298	115	2	.	.	NOUN
ejpam-298	115	3	example	example	NOUN
ejpam-298	115	4	of	of	ADP
ejpam-298	115	5	a	a	DET
ejpam-298	115	6	n(k)−	n(k)−	PROPN
ejpam-298	115	7	(	(	PUNCT
ejpam-298	115	8	mqe)n	mqe)n	PROPN
ejpam-298	115	9	manifold	manifold	ADJ
ejpam-298	115	10	let	let	NOUN
ejpam-298	115	11	(	(	PUNCT
ejpam-298	115	12	m	m	VERB
ejpam-298	115	13	n	n	CCONJ
ejpam-298	115	14	,	,	PUNCT
ejpam-298	115	15	g̃	g̃	PROPN
ejpam-298	115	16	)	)	PUNCT
ejpam-298	115	17	be	be	VERB
ejpam-298	115	18	a	a	DET
ejpam-298	115	19	hypersurface	hypersurface	NOUN
ejpam-298	115	20	of	of	ADP
ejpam-298	115	21	the	the	DET
ejpam-298	115	22	euclidean	euclidean	ADJ
ejpam-298	115	23	space	space	NOUN
ejpam-298	115	24	en+1	en+1	VERB
ejpam-298	115	25	.	.	PUNCT
ejpam-298	116	1	let	let	VERB
ejpam-298	116	2	a	a	DET
ejpam-298	116	3	be	be	AUX
ejpam-298	116	4	a	a	DET
ejpam-298	116	5	(	(	PUNCT
ejpam-298	116	6	1,1	1,1	NUM
ejpam-298	116	7	)	)	PUNCT
ejpam-298	116	8	tensor	tensor	NOUN
ejpam-298	116	9	corresponding	correspond	VERB
ejpam-298	116	10	to	to	ADP
ejpam-298	116	11	the	the	DET
ejpam-298	116	12	normal	normal	ADJ
ejpam-298	116	13	valued	value	VERB
ejpam-298	116	14	second	second	ADJ
ejpam-298	116	15	fundamental	fundamental	ADJ
ejpam-298	116	16	tensor	tensor	NOUN
ejpam-298	116	17	h.	h.	PROPN
ejpam-298	116	18	g̃(aξ(x	g̃(aξ(x	PROPN
ejpam-298	116	19	)	)	PUNCT
ejpam-298	116	20	,	,	PUNCT
ejpam-298	116	21	y	y	PROPN
ejpam-298	116	22	)	)	PUNCT
ejpam-298	117	1	=	=	SYM
ejpam-298	117	2	g(h(x	g(h(x	PROPN
ejpam-298	117	3	,	,	PUNCT
ejpam-298	117	4	y	y	PROPN
ejpam-298	117	5	)	)	PUNCT
ejpam-298	117	6	,	,	PUNCT
ejpam-298	117	7	ξ	ξ	X
ejpam-298	117	8	)	)	PUNCT
ejpam-298	117	9	(	(	PUNCT
ejpam-298	117	10	10	10	NUM
ejpam-298	117	11	)	)	PUNCT
ejpam-298	117	12	where	where	SCONJ
ejpam-298	117	13	ξ	ξ	PROPN
ejpam-298	117	14	is	be	AUX
ejpam-298	117	15	a	a	DET
ejpam-298	117	16	unit	unit	NOUN
ejpam-298	117	17	normal	normal	ADJ
ejpam-298	117	18	vector	vector	NOUN
ejpam-298	117	19	field	field	NOUN
ejpam-298	117	20	and	and	CCONJ
ejpam-298	117	21	x	x	SYM
ejpam-298	117	22	and	and	CCONJ
ejpam-298	117	23	y	y	PROPN
ejpam-298	117	24	are	be	AUX
ejpam-298	117	25	tangent	tangent	ADJ
ejpam-298	117	26	vector	vector	NOUN
ejpam-298	117	27	fields	field	NOUN
ejpam-298	117	28	.	.	PUNCT
ejpam-298	118	1	further	far	ADV
ejpam-298	118	2	hξ(x	hξ(x	PUNCT
ejpam-298	118	3	,	,	PUNCT
ejpam-298	118	4	y	y	PROPN
ejpam-298	118	5	)	)	PUNCT
ejpam-298	119	1	=	=	PUNCT
ejpam-298	119	2	g̃(aξ(x	g̃(aξ(x	NOUN
ejpam-298	119	3	)	)	PUNCT
ejpam-298	119	4	,	,	PUNCT
ejpam-298	119	5	y	y	PROPN
ejpam-298	119	6	)	)	PUNCT
ejpam-298	119	7	(	(	PUNCT
ejpam-298	119	8	11	11	NUM
ejpam-298	119	9	)	)	PUNCT
ejpam-298	119	10	the	the	DET
ejpam-298	119	11	hypersurface	hypersurface	NOUN
ejpam-298	119	12	(	(	PUNCT
ejpam-298	119	13	m	m	NOUN
ejpam-298	119	14	n	n	CCONJ
ejpam-298	119	15	,	,	PUNCT
ejpam-298	119	16	g̃	g̃	PROPN
ejpam-298	119	17	)	)	PUNCT
ejpam-298	119	18	is	be	AUX
ejpam-298	119	19	quasi	quasi	NOUN
ejpam-298	119	20	umbilical	umbilical	ADJ
ejpam-298	119	21	if	if	SCONJ
ejpam-298	119	22	hξ(x	hξ(x	PRON
ejpam-298	119	23	,	,	PUNCT
ejpam-298	119	24	y	y	PROPN
ejpam-298	119	25	)	)	PUNCT
ejpam-298	120	1	=	=	PUNCT
ejpam-298	121	1	α	α	PRON
ejpam-298	121	2	g̃(x	g̃(x	PROPN
ejpam-298	121	3	,	,	PUNCT
ejpam-298	121	4	y	y	PROPN
ejpam-298	121	5	)	)	PUNCT
ejpam-298	122	1	+	+	CCONJ
ejpam-298	122	2	βc(x	βc(x	X
ejpam-298	122	3	)	)	PUNCT
ejpam-298	122	4	d(y	d(y	NOUN
ejpam-298	122	5	)	)	PUNCT
ejpam-298	122	6	(	(	PUNCT
ejpam-298	122	7	12	12	NUM
ejpam-298	122	8	)	)	PUNCT
ejpam-298	122	9	in	in	ADP
ejpam-298	122	10	view	view	NOUN
ejpam-298	122	11	of	of	ADP
ejpam-298	122	12	(	(	PUNCT
ejpam-298	122	13	10	10	NUM
ejpam-298	122	14	)	)	PUNCT
ejpam-298	122	15	,	,	PUNCT
ejpam-298	122	16	we	we	PRON
ejpam-298	122	17	have	have	VERB
ejpam-298	122	18	h(x	h(x	PROPN
ejpam-298	122	19	,	,	PUNCT
ejpam-298	122	20	y	y	PROPN
ejpam-298	122	21	)	)	PUNCT
ejpam-298	123	1	=	=	PRON
ejpam-298	123	2	αg(x	αg(x	X
ejpam-298	123	3	,	,	PUNCT
ejpam-298	123	4	y	y	PROPN
ejpam-298	123	5	)	)	PUNCT
ejpam-298	123	6	ξ+	ξ+	NUM
ejpam-298	123	7	βc(x	βc(x	PUNCT
ejpam-298	123	8	)	)	PUNCT
ejpam-298	123	9	d(y	d(y	NOUN
ejpam-298	123	10	)	)	PUNCT
ejpam-298	124	1	ξ	ξ	X
ejpam-298	124	2	.	.	PUNCT
ejpam-298	124	3	(	(	PUNCT
ejpam-298	124	4	13	13	NUM
ejpam-298	124	5	)	)	PUNCT
ejpam-298	124	6	h.	h.	PROPN
ejpam-298	124	7	nagaraja	nagaraja	PROPN
ejpam-298	124	8	/	/	SYM
ejpam-298	124	9	eur	eur	PROPN
ejpam-298	124	10	.	.	PUNCT
ejpam-298	125	1	j.	j.	PROPN
ejpam-298	125	2	pure	pure	PROPN
ejpam-298	125	3	appl	appl	PROPN
ejpam-298	125	4	.	.	PROPN
ejpam-298	125	5	math	math	PROPN
ejpam-298	125	6	,	,	PUNCT
ejpam-298	125	7	3	3	NUM
ejpam-298	125	8	(	(	PUNCT
ejpam-298	125	9	2010	2010	NUM
ejpam-298	125	10	)	)	PUNCT
ejpam-298	125	11	,	,	PUNCT
ejpam-298	125	12	16	16	NUM
ejpam-298	125	13	-	-	SYM
ejpam-298	125	14	25	25	NUM
ejpam-298	125	15	20	20	NUM
ejpam-298	125	16	the	the	DET
ejpam-298	125	17	gauss	gauss	ADJ
ejpam-298	125	18	equation	equation	NOUN
ejpam-298	125	19	of	of	ADP
ejpam-298	125	20	m	m	PROPN
ejpam-298	125	21	n	n	ADJ
ejpam-298	125	22	in	in	ADP
ejpam-298	125	23	en+1	en+1	NUM
ejpam-298	125	24	can	can	AUX
ejpam-298	125	25	be	be	AUX
ejpam-298	125	26	written	write	VERB
ejpam-298	125	27	as	as	ADP
ejpam-298	125	28	g̃(r̃(x	g̃(r̃(x	PRON
ejpam-298	125	29	,	,	PUNCT
ejpam-298	125	30	y	y	PROPN
ejpam-298	125	31	)	)	PUNCT
ejpam-298	125	32	z	z	NOUN
ejpam-298	125	33	,	,	PUNCT
ejpam-298	125	34	w	w	PROPN
ejpam-298	125	35	)	)	PUNCT
ejpam-298	126	1	=	=	SYM
ejpam-298	126	2	g̃(h(x	g̃(h(x	PROPN
ejpam-298	126	3	,	,	PUNCT
ejpam-298	126	4	w	w	PROPN
ejpam-298	126	5	)	)	PUNCT
ejpam-298	126	6	,	,	PUNCT
ejpam-298	126	7	h(y	h(y	ADV
ejpam-298	126	8	,	,	PUNCT
ejpam-298	126	9	z))−	z))−	PROPN
ejpam-298	126	10	g̃(h(w	g̃(h(w	PROPN
ejpam-298	126	11	,	,	PUNCT
ejpam-298	126	12	y	y	PROPN
ejpam-298	126	13	)	)	PUNCT
ejpam-298	126	14	,	,	PUNCT
ejpam-298	126	15	h(z	h(z	NOUN
ejpam-298	126	16	,	,	PUNCT
ejpam-298	126	17	x	x	NOUN
ejpam-298	126	18	)	)	PUNCT
ejpam-298	126	19	)	)	PUNCT
ejpam-298	126	20	(	(	PUNCT
ejpam-298	126	21	14	14	NUM
ejpam-298	126	22	)	)	PUNCT
ejpam-298	126	23	from	from	ADP
ejpam-298	126	24	(	(	PUNCT
ejpam-298	126	25	12	12	NUM
ejpam-298	126	26	)	)	PUNCT
ejpam-298	126	27	and	and	CCONJ
ejpam-298	126	28	(	(	PUNCT
ejpam-298	126	29	14	14	NUM
ejpam-298	126	30	)	)	PUNCT
ejpam-298	126	31	,	,	PUNCT
ejpam-298	126	32	we	we	PRON
ejpam-298	126	33	have	have	VERB
ejpam-298	126	34	′r̃(x	′r̃(x	PROPN
ejpam-298	126	35	,	,	PUNCT
ejpam-298	126	36	y	y	PROPN
ejpam-298	126	37	,	,	PUNCT
ejpam-298	126	38	z	z	NOUN
ejpam-298	126	39	,	,	PUNCT
ejpam-298	126	40	w	w	PROPN
ejpam-298	126	41	)	)	PUNCT
ejpam-298	126	42	=	=	PUNCT
ejpam-298	127	1	α2	α2	PROPN
ejpam-298	127	2	g(x	g(x	PROPN
ejpam-298	127	3	,	,	PUNCT
ejpam-298	127	4	w	w	NOUN
ejpam-298	127	5	)	)	PUNCT
ejpam-298	127	6	g(y	g(y	PROPN
ejpam-298	127	7	,	,	PUNCT
ejpam-298	127	8	z	z	NOUN
ejpam-298	127	9	)	)	PUNCT
ejpam-298	128	1	+	+	ADP
ejpam-298	128	2	αβ	αβ	PRON
ejpam-298	128	3	g(x	g(x	ADJ
ejpam-298	128	4	,	,	PUNCT
ejpam-298	128	5	w	w	PROPN
ejpam-298	128	6	)	)	PUNCT
ejpam-298	128	7	c(y	c(y	PROPN
ejpam-298	128	8	)	)	PUNCT
ejpam-298	129	1	d(z	d(z	PROPN
ejpam-298	129	2	)	)	PUNCT
ejpam-298	130	1	+	+	ADP
ejpam-298	130	2	αβ	αβ	PROPN
ejpam-298	130	3	g(y	g(y	NOUN
ejpam-298	130	4	,	,	PUNCT
ejpam-298	130	5	z)c(x	z)c(x	NUM
ejpam-298	130	6	)	)	PUNCT
ejpam-298	130	7	d(w	d(w	PROPN
ejpam-298	130	8	)	)	PUNCT
ejpam-298	130	9	+	+	NOUN
ejpam-298	130	10	β2c(x	β2c(x	NOUN
ejpam-298	130	11	)	)	PUNCT
ejpam-298	130	12	c(y	c(y	PROPN
ejpam-298	130	13	)	)	PUNCT
ejpam-298	130	14	d(w	d(w	PROPN
ejpam-298	130	15	)	)	PUNCT
ejpam-298	130	16	d(z	d(z	PROPN
ejpam-298	130	17	)	)	PUNCT
ejpam-298	131	1	−α2	−α2	PROPN
ejpam-298	132	1	g(w	g(w	PROPN
ejpam-298	132	2	,	,	PUNCT
ejpam-298	132	3	y	y	PROPN
ejpam-298	132	4	)	)	PUNCT
ejpam-298	133	1	g(z	g(z	PROPN
ejpam-298	133	2	,	,	PUNCT
ejpam-298	133	3	x	x	X
ejpam-298	133	4	)	)	PUNCT
ejpam-298	133	5	−αβ	−αβ	PROPN
ejpam-298	133	6	g(w	g(w	PROPN
ejpam-298	133	7	,	,	PUNCT
ejpam-298	133	8	y	y	NOUN
ejpam-298	133	9	)	)	PUNCT
ejpam-298	133	10	c(z)d(x	c(z)d(x	NOUN
ejpam-298	133	11	)	)	PUNCT
ejpam-298	134	1	−αβ	−αβ	PROPN
ejpam-298	134	2	g(z	g(z	PROPN
ejpam-298	134	3	,	,	PUNCT
ejpam-298	134	4	x	x	X
ejpam-298	134	5	)	)	PUNCT
ejpam-298	134	6	c(w	c(w	PROPN
ejpam-298	134	7	)	)	PUNCT
ejpam-298	134	8	d(y	d(y	NOUN
ejpam-298	134	9	)	)	PUNCT
ejpam-298	135	1	−	−	PROPN
ejpam-298	135	2	β2c(w	β2c(w	NUM
ejpam-298	135	3	)	)	PUNCT
ejpam-298	135	4	d(y	d(y	NOUN
ejpam-298	135	5	)	)	PUNCT
ejpam-298	135	6	c(z)d(x	c(z)d(x	NOUN
ejpam-298	135	7	)	)	PUNCT
ejpam-298	135	8	contracting	contract	VERB
ejpam-298	135	9	the	the	DET
ejpam-298	135	10	above	above	ADJ
ejpam-298	135	11	equation	equation	NOUN
ejpam-298	135	12	with	with	ADP
ejpam-298	135	13	x	x	PROPN
ejpam-298	136	1	=	=	X
ejpam-298	136	2	w	w	NOUN
ejpam-298	136	3	=	=	VERB
ejpam-298	136	4	ei	ei	NOUN
ejpam-298	136	5	and	and	CCONJ
ejpam-298	136	6	taking	take	VERB
ejpam-298	136	7	summation	summation	NOUN
ejpam-298	136	8	over	over	ADP
ejpam-298	136	9	i	i	PROPN
ejpam-298	136	10	,	,	PUNCT
ejpam-298	136	11	1	1	NUM
ejpam-298	136	12	≤	≤	NUM
ejpam-298	136	13	i	i	PRON
ejpam-298	136	14	≤	≤	PROPN
ejpam-298	136	15	n	n	CCONJ
ejpam-298	136	16	,	,	PUNCT
ejpam-298	136	17	we	we	PRON
ejpam-298	136	18	obtain	obtain	VERB
ejpam-298	136	19	s̃(y	s̃(y	PROPN
ejpam-298	136	20	,	,	PUNCT
ejpam-298	136	21	z	z	NOUN
ejpam-298	136	22	)	)	PUNCT
ejpam-298	136	23	=	=	SYM
ejpam-298	136	24	ag(y	ag(y	NOUN
ejpam-298	136	25	,	,	PUNCT
ejpam-298	136	26	z)+	z)+	NUM
ejpam-298	136	27	bc(y	bc(y	X
ejpam-298	136	28	)	)	PUNCT
ejpam-298	137	1	d(z)+	d(z)+	ADJ
ejpam-298	137	2	cc(z)d(y	cc(z)d(y	NOUN
ejpam-298	137	3	)	)	PUNCT
ejpam-298	137	4	where	where	SCONJ
ejpam-298	137	5	a	a	DET
ejpam-298	137	6	=	=	X
ejpam-298	137	7	(	(	PUNCT
ejpam-298	137	8	n−	n−	NOUN
ejpam-298	137	9	1)α2	1)α2	NUM
ejpam-298	137	10	,	,	PUNCT
ejpam-298	137	11	b	b	X
ejpam-298	137	12	=	=	SYM
ejpam-298	137	13	(	(	PUNCT
ejpam-298	137	14	n−	n−	PROPN
ejpam-298	137	15	1)αβ	1)αβ	PROPN
ejpam-298	138	1	+	+	CCONJ
ejpam-298	139	1	β2	β2	VERB
ejpam-298	139	2	,	,	PUNCT
ejpam-298	139	3	c	c	NOUN
ejpam-298	139	4	=	=	PUNCT
ejpam-298	140	1	−β(2α+	−β(2α+	PROPN
ejpam-298	140	2	β	β	X
ejpam-298	140	3	)	)	PUNCT
ejpam-298	140	4	.	.	PUNCT
ejpam-298	141	1	hence	hence	ADV
ejpam-298	141	2	(	(	PUNCT
ejpam-298	141	3	m	m	NOUN
ejpam-298	141	4	n	n	CCONJ
ejpam-298	141	5	,	,	PUNCT
ejpam-298	141	6	g̃	g̃	PROPN
ejpam-298	141	7	)	)	PUNCT
ejpam-298	141	8	is	be	AUX
ejpam-298	141	9	a	a	DET
ejpam-298	141	10	mixed	mix	VERB
ejpam-298	141	11	quasi	quasi	NOUN
ejpam-298	141	12	einstein	einstein	PROPN
ejpam-298	141	13	manifold	manifold	PROPN
ejpam-298	141	14	.	.	PUNCT
ejpam-298	142	1	suppose	suppose	VERB
ejpam-298	142	2	u	u	NOUN
ejpam-298	142	3	and	and	CCONJ
ejpam-298	142	4	v	v	NOUN
ejpam-298	142	5	are	be	AUX
ejpam-298	142	6	unit	unit	NOUN
ejpam-298	142	7	orthogonal	orthogonal	ADJ
ejpam-298	142	8	vectorfields	vectorfield	NOUN
ejpam-298	142	9	corresponding	correspond	VERB
ejpam-298	142	10	to	to	ADP
ejpam-298	142	11	the	the	DET
ejpam-298	142	12	1	1	NUM
ejpam-298	142	13	-	-	PUNCT
ejpam-298	142	14	forms	form	NOUN
ejpam-298	142	15	c	c	NOUN
ejpam-298	142	16	and	and	CCONJ
ejpam-298	142	17	d	d	NOUN
ejpam-298	142	18	respectively	respectively	ADV
ejpam-298	142	19	.	.	PUNCT
ejpam-298	143	1	then	then	ADV
ejpam-298	143	2	putting	put	VERB
ejpam-298	143	3	z	z	NOUN
ejpam-298	143	4	=	=	SYM
ejpam-298	143	5	u	u	NOUN
ejpam-298	143	6	in	in	ADP
ejpam-298	143	7	(	(	PUNCT
ejpam-298	143	8	13	13	NUM
ejpam-298	143	9	)	)	PUNCT
ejpam-298	143	10	,	,	PUNCT
ejpam-298	143	11	we	we	PRON
ejpam-298	143	12	get	get	VERB
ejpam-298	143	13	h(x	h(x	PROPN
ejpam-298	143	14	,	,	PUNCT
ejpam-298	143	15	u	u	NOUN
ejpam-298	143	16	)	)	PUNCT
ejpam-298	143	17	=	=	SYM
ejpam-298	143	18	αc(x	αc(x	NUM
ejpam-298	143	19	)	)	PUNCT
ejpam-298	143	20	ξ	ξ	X
ejpam-298	143	21	.	.	PUNCT
ejpam-298	144	1	(	(	PUNCT
ejpam-298	144	2	15	15	X
ejpam-298	144	3	)	)	PUNCT
ejpam-298	144	4	putting	put	VERB
ejpam-298	144	5	z	z	NOUN
ejpam-298	144	6	=	=	SYM
ejpam-298	144	7	u	u	NOUN
ejpam-298	144	8	in	in	ADP
ejpam-298	144	9	(	(	PUNCT
ejpam-298	144	10	14	14	NUM
ejpam-298	144	11	)	)	PUNCT
ejpam-298	144	12	and	and	CCONJ
ejpam-298	144	13	using	use	VERB
ejpam-298	144	14	(	(	PUNCT
ejpam-298	144	15	15	15	NUM
ejpam-298	144	16	)	)	PUNCT
ejpam-298	144	17	,	,	PUNCT
ejpam-298	144	18	we	we	PRON
ejpam-298	144	19	get	get	VERB
ejpam-298	144	20	r̃(x	r̃(x	PROPN
ejpam-298	144	21	,	,	PUNCT
ejpam-298	144	22	y	y	PROPN
ejpam-298	144	23	)	)	PUNCT
ejpam-298	144	24	u	u	NOUN
ejpam-298	144	25	=	=	PROPN
ejpam-298	144	26	k	k	PROPN
ejpam-298	144	27	(	(	PUNCT
ejpam-298	144	28	c(y	c(y	PROPN
ejpam-298	144	29	)	)	PUNCT
ejpam-298	144	30	x	x	SYM
ejpam-298	145	1	−	−	PROPN
ejpam-298	145	2	c(x	c(x	NOUN
ejpam-298	145	3	)	)	PUNCT
ejpam-298	145	4	y	y	PROPN
ejpam-298	145	5	)	)	PUNCT
ejpam-298	145	6	where	where	SCONJ
ejpam-298	145	7	k	k	PROPN
ejpam-298	145	8	=	=	SYM
ejpam-298	145	9	α2	α2	PROPN
ejpam-298	145	10	.	.	PUNCT
ejpam-298	146	1	similarly	similarly	ADV
ejpam-298	146	2	we	we	PRON
ejpam-298	146	3	can	can	AUX
ejpam-298	146	4	show	show	VERB
ejpam-298	146	5	that	that	SCONJ
ejpam-298	146	6	r̃(x	r̃(x	PROPN
ejpam-298	146	7	,	,	PUNCT
ejpam-298	146	8	y	y	PROPN
ejpam-298	146	9	)	)	PUNCT
ejpam-298	146	10	v	v	NOUN
ejpam-298	146	11	=	=	SYM
ejpam-298	146	12	k	k	X
ejpam-298	146	13	(	(	PUNCT
ejpam-298	146	14	d(y	d(y	PROPN
ejpam-298	146	15	)	)	PUNCT
ejpam-298	146	16	x	x	PUNCT
ejpam-298	146	17	−	−	PROPN
ejpam-298	146	18	d(x	d(x	NOUN
ejpam-298	146	19	)	)	PUNCT
ejpam-298	146	20	y	y	PROPN
ejpam-298	146	21	)	)	PUNCT
ejpam-298	146	22	where	where	SCONJ
ejpam-298	146	23	k	k	PROPN
ejpam-298	146	24	=	=	SYM
ejpam-298	146	25	α2	α2	PROPN
ejpam-298	146	26	.	.	PUNCT
ejpam-298	147	1	thus	thus	ADV
ejpam-298	147	2	we	we	PRON
ejpam-298	147	3	have	have	AUX
ejpam-298	147	4	theorem	theorem	VERB
ejpam-298	147	5	3	3	NUM
ejpam-298	147	6	.	.	PUNCT
ejpam-298	148	1	a	a	DET
ejpam-298	148	2	quasi	quasi	ADJ
ejpam-298	148	3	umbilical	umbilical	ADJ
ejpam-298	148	4	hypersurface	hypersurface	NOUN
ejpam-298	148	5	of	of	ADP
ejpam-298	148	6	a	a	DET
ejpam-298	148	7	euclidean	euclidean	ADJ
ejpam-298	148	8	space	space	NOUN
ejpam-298	148	9	en+1is	en+1i	VERB
ejpam-298	148	10	a	a	DET
ejpam-298	148	11	n(k)-mixed	n(k)-mixed	PROPN
ejpam-298	148	12	quasi	quasi	PROPN
ejpam-298	148	13	einstein	einstein	PROPN
ejpam-298	148	14	manifold	manifold	PROPN
ejpam-298	148	15	.	.	PUNCT
ejpam-298	149	1	4	4	X
ejpam-298	149	2	.	.	X
ejpam-298	149	3	ricci	ricci	PROPN
ejpam-298	149	4	curvature	curvature	PROPN
ejpam-298	149	5	,	,	PUNCT
ejpam-298	149	6	eigen	eigen	PROPN
ejpam-298	149	7	vectors	vector	NOUN
ejpam-298	149	8	and	and	CCONJ
ejpam-298	149	9	associated	associate	VERB
ejpam-298	149	10	scalars	scalar	NOUN
ejpam-298	149	11	of	of	ADP
ejpam-298	149	12	a	a	DET
ejpam-298	149	13	n(k)−	n(k)−	NOUN
ejpam-298	149	14	(	(	PUNCT
ejpam-298	149	15	mqe)n	mqe)n	PROPN
ejpam-298	149	16	from	from	ADP
ejpam-298	149	17	(	(	PUNCT
ejpam-298	149	18	1	1	X
ejpam-298	149	19	)	)	PUNCT
ejpam-298	149	20	we	we	PRON
ejpam-298	149	21	have	have	VERB
ejpam-298	149	22	s(u	s(u	PROPN
ejpam-298	149	23	,	,	PUNCT
ejpam-298	149	24	u	u	NOUN
ejpam-298	149	25	)	)	PUNCT
ejpam-298	149	26	=	=	SYM
ejpam-298	150	1	a	a	DET
ejpam-298	150	2	=	=	SYM
ejpam-298	150	3	s(v	s(v	PROPN
ejpam-298	150	4	,	,	PUNCT
ejpam-298	150	5	v	v	NOUN
ejpam-298	150	6	)	)	PUNCT
ejpam-298	150	7	,	,	PUNCT
ejpam-298	150	8	b	b	X
ejpam-298	150	9	=	=	SYM
ejpam-298	150	10	s(u	s(u	PROPN
ejpam-298	150	11	,	,	PUNCT
ejpam-298	150	12	v	v	NOUN
ejpam-298	150	13	)	)	PUNCT
ejpam-298	150	14	=	=	SYM
ejpam-298	150	15	s(v	s(v	PROPN
ejpam-298	150	16	,	,	PUNCT
ejpam-298	150	17	u	u	NOUN
ejpam-298	150	18	)	)	PUNCT
ejpam-298	150	19	=	=	SYM
ejpam-298	150	20	c	c	NOUN
ejpam-298	150	21	,	,	PUNCT
ejpam-298	150	22	since	since	SCONJ
ejpam-298	150	23	g(u	g(u	PROPN
ejpam-298	150	24	,	,	PUNCT
ejpam-298	150	25	v	v	NOUN
ejpam-298	150	26	)	)	PUNCT
ejpam-298	150	27	=	=	SYM
ejpam-298	151	1	0	0	X
ejpam-298	151	2	.	.	PUNCT
ejpam-298	152	1	therefore	therefore	ADV
ejpam-298	152	2	only	only	ADV
ejpam-298	152	3	one	one	NUM
ejpam-298	152	4	of	of	ADP
ejpam-298	152	5	b	b	NOUN
ejpam-298	152	6	or	or	CCONJ
ejpam-298	152	7	c	c	NOUN
ejpam-298	152	8	is	be	AUX
ejpam-298	152	9	sufficient	sufficient	ADJ
ejpam-298	152	10	to	to	PART
ejpam-298	152	11	define	define	VERB
ejpam-298	152	12	a	a	DET
ejpam-298	152	13	mixed	mixed	ADJ
ejpam-298	152	14	quasi	quasi	NOUN
ejpam-298	152	15	einstein	einstein	PROPN
ejpam-298	152	16	space	space	NOUN
ejpam-298	152	17	.	.	PUNCT
ejpam-298	153	1	a	a	DET
ejpam-298	153	2	mixed	mix	VERB
ejpam-298	153	3	quasi	quasi	NOUN
ejpam-298	153	4	einstein	einstein	PROPN
ejpam-298	153	5	space	space	NOUN
ejpam-298	153	6	may	may	AUX
ejpam-298	153	7	be	be	AUX
ejpam-298	153	8	defined	define	VERB
ejpam-298	153	9	as	as	ADP
ejpam-298	153	10	a	a	DET
ejpam-298	153	11	riemannian	riemannian	ADJ
ejpam-298	153	12	manifold	manifold	NOUN
ejpam-298	153	13	in	in	ADP
ejpam-298	153	14	which	which	PRON
ejpam-298	153	15	ricci	ricci	PROPN
ejpam-298	153	16	tensor	tensor	NOUN
ejpam-298	153	17	s	s	PART
ejpam-298	153	18	satisfies	satisfie	NOUN
ejpam-298	153	19	s(x	s(x	NOUN
ejpam-298	153	20	,	,	PUNCT
ejpam-298	153	21	y	y	PROPN
ejpam-298	153	22	)	)	PUNCT
ejpam-298	154	1	=	=	SYM
ejpam-298	154	2	ag(x	ag(x	X
ejpam-298	154	3	,	,	PUNCT
ejpam-298	154	4	y	y	PROPN
ejpam-298	154	5	)	)	PUNCT
ejpam-298	155	1	+	+	CCONJ
ejpam-298	155	2	b(a(x	b(a(x	PROPN
ejpam-298	155	3	)	)	PUNCT
ejpam-298	155	4	b(y	b(y	PROPN
ejpam-298	155	5	)	)	PUNCT
ejpam-298	156	1	+	+	CCONJ
ejpam-298	156	2	b(x	b(x	NOUN
ejpam-298	156	3	)	)	PUNCT
ejpam-298	156	4	a(y	a(y	PROPN
ejpam-298	156	5	)	)	PUNCT
ejpam-298	156	6	)	)	PUNCT
ejpam-298	156	7	,	,	PUNCT
ejpam-298	156	8	it	it	PRON
ejpam-298	156	9	is	be	AUX
ejpam-298	156	10	well	well	ADV
ejpam-298	156	11	known	know	VERB
ejpam-298	156	12	that	that	SCONJ
ejpam-298	156	13	for	for	ADP
ejpam-298	156	14	a	a	DET
ejpam-298	156	15	unit	unit	NOUN
ejpam-298	156	16	vector	vector	NOUN
ejpam-298	156	17	field	field	NOUN
ejpam-298	156	18	x	x	X
ejpam-298	156	19	,	,	PUNCT
ejpam-298	156	20	s(x	s(x	NOUN
ejpam-298	156	21	,	,	PUNCT
ejpam-298	156	22	x	x	X
ejpam-298	156	23	)	)	PUNCT
ejpam-298	156	24	is	be	AUX
ejpam-298	156	25	the	the	DET
ejpam-298	156	26	ricci	ricci	PROPN
ejpam-298	156	27	curvature	curvature	NOUN
ejpam-298	156	28	in	in	ADP
ejpam-298	156	29	the	the	DET
ejpam-298	156	30	direction	direction	NOUN
ejpam-298	156	31	of	of	ADP
ejpam-298	156	32	x	x	X
ejpam-298	156	33	.	.	PUNCT
ejpam-298	157	1	now	now	ADV
ejpam-298	157	2	if	if	SCONJ
ejpam-298	157	3	x	x	PRON
ejpam-298	157	4	is	be	AUX
ejpam-298	157	5	a	a	DET
ejpam-298	157	6	unit	unit	NOUN
ejpam-298	157	7	vector	vector	NOUN
ejpam-298	157	8	field	field	NOUN
ejpam-298	157	9	in	in	ADP
ejpam-298	157	10	the	the	DET
ejpam-298	157	11	section	section	NOUN
ejpam-298	157	12	spanned	span	VERB
ejpam-298	157	13	by	by	ADP
ejpam-298	157	14	u	u	NOUN
ejpam-298	157	15	and	and	CCONJ
ejpam-298	157	16	v	v	NOUN
ejpam-298	157	17	,	,	PUNCT
ejpam-298	157	18	then	then	ADV
ejpam-298	157	19	we	we	PRON
ejpam-298	157	20	have	have	VERB
ejpam-298	157	21	1=	1=	NUM
ejpam-298	157	22	g(x	g(x	X
ejpam-298	157	23	,	,	PUNCT
ejpam-298	157	24	x	x	X
ejpam-298	157	25	)	)	PUNCT
ejpam-298	157	26	=	=	SYM
ejpam-298	157	27	g(αu	g(αu	NOUN
ejpam-298	158	1	+	+	CCONJ
ejpam-298	158	2	βv	βv	PROPN
ejpam-298	158	3	,	,	PUNCT
ejpam-298	158	4	αu	αu	NOUN
ejpam-298	158	5	+	+	NOUN
ejpam-298	158	6	βv	βv	PUNCT
ejpam-298	158	7	)	)	PUNCT
ejpam-298	158	8	=	=	VERB
ejpam-298	158	9	α2	α2	PROPN
ejpam-298	158	10	+	+	CCONJ
ejpam-298	158	11	β2	β2	VERB
ejpam-298	158	12	,	,	PUNCT
ejpam-298	158	13	h.	h.	PROPN
ejpam-298	158	14	nagaraja	nagaraja	PROPN
ejpam-298	158	15	/	/	SYM
ejpam-298	158	16	eur	eur	PROPN
ejpam-298	158	17	.	.	PUNCT
ejpam-298	159	1	j.	j.	PROPN
ejpam-298	159	2	pure	pure	PROPN
ejpam-298	159	3	appl	appl	PROPN
ejpam-298	159	4	.	.	PROPN
ejpam-298	159	5	math	math	PROPN
ejpam-298	159	6	,	,	PUNCT
ejpam-298	159	7	3	3	NUM
ejpam-298	159	8	(	(	PUNCT
ejpam-298	159	9	2010	2010	NUM
ejpam-298	159	10	)	)	PUNCT
ejpam-298	159	11	,	,	PUNCT
ejpam-298	159	12	16	16	NUM
ejpam-298	159	13	-	-	SYM
ejpam-298	159	14	25	25	NUM
ejpam-298	159	15	21	21	NUM
ejpam-298	159	16	since	since	SCONJ
ejpam-298	159	17	g(u	g(u	PROPN
ejpam-298	159	18	,	,	PUNCT
ejpam-298	159	19	v	v	NOUN
ejpam-298	159	20	)	)	PUNCT
ejpam-298	159	21	=	=	SYM
ejpam-298	159	22	0	0	NUM
ejpam-298	159	23	and	and	CCONJ
ejpam-298	159	24	g(u	g(u	PROPN
ejpam-298	159	25	,	,	PUNCT
ejpam-298	159	26	u	u	NOUN
ejpam-298	159	27	)	)	PUNCT
ejpam-298	159	28	=	=	SYM
ejpam-298	160	1	g(v	g(v	X
ejpam-298	160	2	,	,	PUNCT
ejpam-298	160	3	v	v	NOUN
ejpam-298	160	4	)	)	PUNCT
ejpam-298	160	5	=	=	SYM
ejpam-298	161	1	1	1	X
ejpam-298	161	2	.	.	PUNCT
ejpam-298	161	3	now	now	ADV
ejpam-298	161	4	s(x	s(x	NOUN
ejpam-298	161	5	,	,	PUNCT
ejpam-298	161	6	x	x	X
ejpam-298	161	7	)	)	PUNCT
ejpam-298	161	8	=	=	SYM
ejpam-298	162	1	s(αu	s(αu	ADJ
ejpam-298	162	2	+	+	NUM
ejpam-298	162	3	βv	βv	PROPN
ejpam-298	162	4	,	,	PUNCT
ejpam-298	162	5	αu	αu	NOUN
ejpam-298	162	6	+	+	NOUN
ejpam-298	162	7	βv	βv	PUNCT
ejpam-298	162	8	)	)	PUNCT
ejpam-298	162	9	=	=	SYM
ejpam-298	162	10	a+	a+	PUNCT
ejpam-298	162	11	2ba(x	2ba(x	NUM
ejpam-298	162	12	)	)	PUNCT
ejpam-298	162	13	b(x	b(x	NOUN
ejpam-298	162	14	)	)	PUNCT
ejpam-298	162	15	.	.	PUNCT
ejpam-298	163	1	thus	thus	ADV
ejpam-298	163	2	we	we	PRON
ejpam-298	163	3	can	can	AUX
ejpam-298	163	4	state	state	VERB
ejpam-298	163	5	that	that	PRON
ejpam-298	163	6	theorem	theorem	NOUN
ejpam-298	163	7	4	4	NUM
ejpam-298	163	8	.	.	PUNCT
ejpam-298	163	9	in	in	ADP
ejpam-298	163	10	a	a	DET
ejpam-298	163	11	n(k)−	n(k)−	NOUN
ejpam-298	163	12	(	(	PUNCT
ejpam-298	163	13	mqe)n	mqe)n	PROPN
ejpam-298	163	14	manifold	manifold	NOUN
ejpam-298	163	15	,	,	PUNCT
ejpam-298	163	16	the	the	DET
ejpam-298	163	17	ricci	ricci	PROPN
ejpam-298	163	18	curvature	curvature	NOUN
ejpam-298	163	19	in	in	ADP
ejpam-298	163	20	the	the	DET
ejpam-298	163	21	direction	direction	NOUN
ejpam-298	163	22	of	of	ADP
ejpam-298	163	23	both	both	CCONJ
ejpam-298	163	24	u	u	NOUN
ejpam-298	163	25	and	and	CCONJ
ejpam-298	163	26	v	v	NOUN
ejpam-298	163	27	is	be	AUX
ejpam-298	163	28	‘	'	PUNCT
ejpam-298	163	29	a	a	PRON
ejpam-298	163	30	’	'	PUNCT
ejpam-298	163	31	and	and	CCONJ
ejpam-298	163	32	the	the	DET
ejpam-298	163	33	ricci	ricci	PROPN
ejpam-298	163	34	curvature	curvature	NOUN
ejpam-298	163	35	in	in	ADP
ejpam-298	163	36	all	all	DET
ejpam-298	163	37	other	other	ADJ
ejpam-298	163	38	directions	direction	NOUN
ejpam-298	163	39	of	of	ADP
ejpam-298	163	40	the	the	DET
ejpam-298	163	41	section	section	NOUN
ejpam-298	163	42	of	of	ADP
ejpam-298	163	43	u	u	NOUN
ejpam-298	163	44	and	and	CCONJ
ejpam-298	163	45	v	v	NOUN
ejpam-298	163	46	is	be	AUX
ejpam-298	163	47	a+	a+	PRON
ejpam-298	163	48	2ba(x	2ba(x	NUM
ejpam-298	163	49	)	)	PUNCT
ejpam-298	163	50	b(x	b(x	NOUN
ejpam-298	163	51	)	)	PUNCT
ejpam-298	163	52	.	.	PUNCT
ejpam-298	164	1	let	let	VERB
ejpam-298	164	2	(	(	PUNCT
ejpam-298	164	3	m	m	VERB
ejpam-298	164	4	n	n	CCONJ
ejpam-298	164	5	,	,	PUNCT
ejpam-298	164	6	g	g	NOUN
ejpam-298	164	7	)	)	PUNCT
ejpam-298	164	8	be	be	AUX
ejpam-298	164	9	a	a	DET
ejpam-298	164	10	n(k)−	n(k)−	NOUN
ejpam-298	164	11	(	(	PUNCT
ejpam-298	164	12	mqe)n	mqe)n	PROPN
ejpam-298	164	13	manifold	manifold	NOUN
ejpam-298	164	14	.	.	PUNCT
ejpam-298	165	1	then	then	ADV
ejpam-298	165	2	s(u	s(u	PROPN
ejpam-298	165	3	,	,	PUNCT
ejpam-298	165	4	u	u	NOUN
ejpam-298	165	5	)	)	PUNCT
ejpam-298	165	6	=	=	SYM
ejpam-298	165	7	s(v	s(v	PROPN
ejpam-298	165	8	,	,	PUNCT
ejpam-298	165	9	v	v	NOUN
ejpam-298	165	10	)	)	PUNCT
ejpam-298	165	11	=	=	PUNCT
ejpam-298	165	12	a	a	PRON
ejpam-298	165	13	from	from	ADP
ejpam-298	165	14	which	which	PRON
ejpam-298	165	15	we	we	PRON
ejpam-298	165	16	get	get	VERB
ejpam-298	165	17	g(qu	g(qu	NOUN
ejpam-298	165	18	,	,	PUNCT
ejpam-298	165	19	u	u	NOUN
ejpam-298	165	20	)	)	PUNCT
ejpam-298	165	21	=	=	SYM
ejpam-298	165	22	g(qv	g(qv	PROPN
ejpam-298	165	23	,	,	PUNCT
ejpam-298	165	24	v	v	NOUN
ejpam-298	165	25	)	)	PUNCT
ejpam-298	165	26	=	=	PUNCT
ejpam-298	165	27	a.	a.	NOUN
ejpam-298	165	28	since	since	SCONJ
ejpam-298	165	29	u	u	PRON
ejpam-298	165	30	,	,	PUNCT
ejpam-298	165	31	v	v	NOUN
ejpam-298	165	32	∈	∈	NOUN
ejpam-298	165	33	np(k	np(k	NOUN
ejpam-298	165	34	)	)	PUNCT
ejpam-298	165	35	,	,	PUNCT
ejpam-298	165	36	we	we	PRON
ejpam-298	165	37	have	have	VERB
ejpam-298	165	38	,	,	PUNCT
ejpam-298	165	39	g(r(x	g(r(x	PROPN
ejpam-298	165	40	,	,	PUNCT
ejpam-298	165	41	y	y	PROPN
ejpam-298	165	42	)	)	PUNCT
ejpam-298	165	43	u	u	PROPN
ejpam-298	165	44	,	,	PUNCT
ejpam-298	165	45	w	w	PROPN
ejpam-298	165	46	)	)	PUNCT
ejpam-298	166	1	=	=	SYM
ejpam-298	166	2	k	k	PROPN
ejpam-298	166	3	�	�	PROPN
ejpam-298	166	4	a(y	a(y	PROPN
ejpam-298	166	5	)	)	PUNCT
ejpam-298	167	1	g(x	g(x	NOUN
ejpam-298	167	2	,	,	PUNCT
ejpam-298	167	3	w	w	NOUN
ejpam-298	167	4	)	)	PUNCT
ejpam-298	167	5	−	−	PROPN
ejpam-298	167	6	a(x	a(x	PROPN
ejpam-298	167	7	)	)	PUNCT
ejpam-298	167	8	g(y	g(y	PROPN
ejpam-298	167	9	,	,	PUNCT
ejpam-298	167	10	w	w	NOUN
ejpam-298	167	11	)	)	PUNCT
ejpam-298	167	12	.	.	PUNCT
ejpam-298	168	1	putting	put	VERB
ejpam-298	168	2	x	x	PUNCT
ejpam-298	169	1	=	=	NOUN
ejpam-298	169	2	w	w	NOUN
ejpam-298	169	3	=	=	VERB
ejpam-298	169	4	ei	ei	NOUN
ejpam-298	169	5	and	and	CCONJ
ejpam-298	169	6	taking	take	VERB
ejpam-298	169	7	summation	summation	NOUN
ejpam-298	169	8	over	over	ADP
ejpam-298	169	9	i	i	PROPN
ejpam-298	169	10	,	,	PUNCT
ejpam-298	169	11	1≤	1≤	INTJ
ejpam-298	170	1	i	i	ADV
ejpam-298	170	2	≤	≤	PUNCT
ejpam-298	170	3	n	n	CCONJ
ejpam-298	170	4	,	,	PUNCT
ejpam-298	170	5	we	we	PRON
ejpam-298	170	6	obtain	obtain	VERB
ejpam-298	170	7	s(y	s(y	PROPN
ejpam-298	170	8	,	,	PUNCT
ejpam-298	170	9	u	u	NOUN
ejpam-298	170	10	)	)	PUNCT
ejpam-298	170	11	=	=	PUNCT
ejpam-298	171	1	(	(	PUNCT
ejpam-298	171	2	n−	n−	NOUN
ejpam-298	171	3	1)ka(x	1)ka(x	NUM
ejpam-298	171	4	)	)	PUNCT
ejpam-298	171	5	(	(	PUNCT
ejpam-298	171	6	16	16	NUM
ejpam-298	171	7	)	)	PUNCT
ejpam-298	171	8	similarly	similarly	ADV
ejpam-298	171	9	we	we	PRON
ejpam-298	171	10	can	can	AUX
ejpam-298	171	11	get	get	VERB
ejpam-298	171	12	s(y	s(y	NOUN
ejpam-298	171	13	,	,	PUNCT
ejpam-298	171	14	v	v	NOUN
ejpam-298	171	15	)	)	PUNCT
ejpam-298	171	16	=	=	PUNCT
ejpam-298	171	17	(	(	PUNCT
ejpam-298	171	18	n−	n−	NOUN
ejpam-298	171	19	1)kb(x	1)kb(x	NUM
ejpam-298	171	20	)	)	PUNCT
ejpam-298	171	21	(	(	PUNCT
ejpam-298	171	22	17	17	NUM
ejpam-298	171	23	)	)	PUNCT
ejpam-298	171	24	from	from	ADP
ejpam-298	171	25	(	(	PUNCT
ejpam-298	171	26	1	1	NUM
ejpam-298	171	27	)	)	PUNCT
ejpam-298	171	28	,	,	PUNCT
ejpam-298	171	29	we	we	PRON
ejpam-298	171	30	have	have	VERB
ejpam-298	171	31	s(x	s(x	NOUN
ejpam-298	171	32	,	,	PUNCT
ejpam-298	171	33	u	u	NOUN
ejpam-298	171	34	)	)	PUNCT
ejpam-298	171	35	=	=	SYM
ejpam-298	171	36	aa(x	aa(x	NOUN
ejpam-298	171	37	)	)	PUNCT
ejpam-298	171	38	+	+	NUM
ejpam-298	171	39	bb(x	bb(x	PUNCT
ejpam-298	171	40	)	)	PUNCT
ejpam-298	171	41	(	(	PUNCT
ejpam-298	171	42	18	18	NUM
ejpam-298	171	43	)	)	PUNCT
ejpam-298	171	44	s(x	s(x	NOUN
ejpam-298	171	45	,	,	PUNCT
ejpam-298	171	46	v	v	NOUN
ejpam-298	171	47	)	)	PUNCT
ejpam-298	171	48	=	=	NOUN
ejpam-298	171	49	ba(x	ba(x	NOUN
ejpam-298	171	50	)	)	PUNCT
ejpam-298	172	1	+	+	CCONJ
ejpam-298	172	2	ab(x	ab(x	NUM
ejpam-298	172	3	)	)	PUNCT
ejpam-298	172	4	(	(	PUNCT
ejpam-298	172	5	19	19	NUM
ejpam-298	172	6	)	)	PUNCT
ejpam-298	172	7	substracting	substracting	NOUN
ejpam-298	172	8	(	(	PUNCT
ejpam-298	172	9	17	17	NUM
ejpam-298	172	10	)	)	PUNCT
ejpam-298	172	11	from	from	ADP
ejpam-298	172	12	(	(	PUNCT
ejpam-298	172	13	16	16	NUM
ejpam-298	172	14	)	)	PUNCT
ejpam-298	172	15	and	and	CCONJ
ejpam-298	172	16	(	(	PUNCT
ejpam-298	172	17	19	19	NUM
ejpam-298	172	18	)	)	PUNCT
ejpam-298	172	19	from	from	ADP
ejpam-298	172	20	(	(	PUNCT
ejpam-298	172	21	18	18	NUM
ejpam-298	172	22	)	)	PUNCT
ejpam-298	172	23	,	,	PUNCT
ejpam-298	172	24	and	and	CCONJ
ejpam-298	172	25	comparing	compare	VERB
ejpam-298	172	26	the	the	DET
ejpam-298	172	27	resulting	result	VERB
ejpam-298	172	28	equations	equation	NOUN
ejpam-298	172	29	,	,	PUNCT
ejpam-298	172	30	we	we	PRON
ejpam-298	172	31	obtain	obtain	VERB
ejpam-298	172	32	k	k	NOUN
ejpam-298	172	33	=	=	PUNCT
ejpam-298	172	34	a−	a−	PROPN
ejpam-298	172	35	b	b	PROPN
ejpam-298	172	36	n−	n−	NOUN
ejpam-298	172	37	1	1	NUM
ejpam-298	172	38	.	.	PUNCT
ejpam-298	173	1	therefore	therefore	ADV
ejpam-298	173	2	s(x	s(x	PROPN
ejpam-298	173	3	,	,	PUNCT
ejpam-298	173	4	u	u	NOUN
ejpam-298	173	5	)	)	PUNCT
ejpam-298	173	6	=	=	SYM
ejpam-298	173	7	(	(	PUNCT
ejpam-298	173	8	a−	a−	PROPN
ejpam-298	173	9	b)g(x	b)g(x	NOUN
ejpam-298	173	10	,	,	PUNCT
ejpam-298	173	11	u	u	NOUN
ejpam-298	173	12	)	)	PUNCT
ejpam-298	173	13	and	and	CCONJ
ejpam-298	173	14	s(x	s(x	NOUN
ejpam-298	173	15	,	,	PUNCT
ejpam-298	173	16	v	v	NOUN
ejpam-298	173	17	)	)	PUNCT
ejpam-298	173	18	=	=	SYM
ejpam-298	173	19	(	(	PUNCT
ejpam-298	173	20	a−	a−	PROPN
ejpam-298	173	21	b)g(x	b)g(x	NOUN
ejpam-298	173	22	,	,	PUNCT
ejpam-298	173	23	v	v	NOUN
ejpam-298	173	24	)	)	PUNCT
ejpam-298	173	25	.	.	PUNCT
ejpam-298	174	1	therefore	therefore	ADV
ejpam-298	174	2	u	u	PROPN
ejpam-298	174	3	and	and	CCONJ
ejpam-298	174	4	v	v	NOUN
ejpam-298	174	5	are	be	AUX
ejpam-298	174	6	eigen	eigen	PROPN
ejpam-298	174	7	vectors	vector	NOUN
ejpam-298	174	8	corresponding	correspond	VERB
ejpam-298	174	9	to	to	ADP
ejpam-298	174	10	the	the	DET
ejpam-298	174	11	eigen	eigen	PROPN
ejpam-298	174	12	value	value	NOUN
ejpam-298	174	13	(	(	PUNCT
ejpam-298	174	14	a−	a−	PROPN
ejpam-298	174	15	b	b	PROPN
ejpam-298	174	16	)	)	PUNCT
ejpam-298	174	17	.	.	PUNCT
ejpam-298	175	1	5	5	X
ejpam-298	175	2	.	.	X
ejpam-298	175	3	semi	semi	ADV
ejpam-298	175	4	symmetric	symmetric	ADJ
ejpam-298	175	5	and	and	CCONJ
ejpam-298	175	6	ricci	ricci	PROPN
ejpam-298	175	7	symmetric	symmetric	PROPN
ejpam-298	175	8	n(k)−	n(k)−	PROPN
ejpam-298	175	9	(	(	PUNCT
ejpam-298	175	10	mqe)n	mqe)n	NOUN
ejpam-298	175	11	manifolds	manifold	VERB
ejpam-298	175	12	a	a	DET
ejpam-298	175	13	riemannian	riemannian	ADJ
ejpam-298	175	14	manifold	manifold	NOUN
ejpam-298	175	15	(	(	PUNCT
ejpam-298	175	16	m	m	NOUN
ejpam-298	175	17	n	n	CCONJ
ejpam-298	175	18	,	,	PUNCT
ejpam-298	175	19	g	g	NOUN
ejpam-298	175	20	)	)	PUNCT
ejpam-298	175	21	is	be	AUX
ejpam-298	175	22	semi	semi	ADV
ejpam-298	175	23	symmetric	symmetric	ADJ
ejpam-298	175	24	if	if	SCONJ
ejpam-298	175	25	r(x	r(x	PROPN
ejpam-298	175	26	,	,	PUNCT
ejpam-298	175	27	y	y	PROPN
ejpam-298	175	28	)	)	PUNCT
ejpam-298	175	29	.r	.r	PROPN
ejpam-298	176	1	=	=	PUNCT
ejpam-298	177	1	0,∀x	0,∀x	NUM
ejpam-298	177	2	,	,	PUNCT
ejpam-298	177	3	y	y	PROPN
ejpam-298	177	4	∈	∈	PROPN
ejpam-298	177	5	t	t	PROPN
ejpam-298	177	6	m	m	VERB
ejpam-298	177	7	since	since	SCONJ
ejpam-298	177	8	u	u	PRON
ejpam-298	177	9	and	and	CCONJ
ejpam-298	177	10	v	v	NOUN
ejpam-298	177	11	are	be	AUX
ejpam-298	177	12	in	in	ADP
ejpam-298	177	13	np(k	np(k	NOUN
ejpam-298	177	14	)	)	PUNCT
ejpam-298	177	15	,	,	PUNCT
ejpam-298	177	16	we	we	PRON
ejpam-298	177	17	have	have	VERB
ejpam-298	177	18	r(x	r(x	PROPN
ejpam-298	177	19	,	,	PUNCT
ejpam-298	177	20	y	y	PROPN
ejpam-298	177	21	)	)	PUNCT
ejpam-298	177	22	u	u	NOUN
ejpam-298	178	1	=	=	PROPN
ejpam-298	178	2	k	k	X
ejpam-298	178	3	(	(	PUNCT
ejpam-298	178	4	a(y	a(y	PROPN
ejpam-298	178	5	)	)	PUNCT
ejpam-298	178	6	x	x	SYM
ejpam-298	178	7	−	−	PUNCT
ejpam-298	178	8	a(x	a(x	NOUN
ejpam-298	178	9	)	)	PUNCT
ejpam-298	178	10	y	y	PROPN
ejpam-298	178	11	)	)	PUNCT
ejpam-298	178	12	(	(	PUNCT
ejpam-298	178	13	20	20	X
ejpam-298	178	14	)	)	PUNCT
ejpam-298	178	15	r(x	r(x	PROPN
ejpam-298	178	16	,	,	PUNCT
ejpam-298	178	17	y	y	PROPN
ejpam-298	178	18	)	)	PUNCT
ejpam-298	178	19	v	v	NOUN
ejpam-298	178	20	=	=	SYM
ejpam-298	178	21	k	k	PROPN
ejpam-298	178	22	(	(	PUNCT
ejpam-298	178	23	b(y	b(y	PROPN
ejpam-298	178	24	)	)	PUNCT
ejpam-298	178	25	x	x	SYM
ejpam-298	179	1	−	−	NOUN
ejpam-298	179	2	b(x	b(x	NOUN
ejpam-298	179	3	)	)	PUNCT
ejpam-298	179	4	y	y	PROPN
ejpam-298	179	5	)	)	PUNCT
ejpam-298	179	6	(	(	PUNCT
ejpam-298	179	7	21	21	NUM
ejpam-298	179	8	)	)	PUNCT
ejpam-298	179	9	h.	h.	PROPN
ejpam-298	179	10	nagaraja	nagaraja	PROPN
ejpam-298	179	11	/	/	SYM
ejpam-298	179	12	eur	eur	PROPN
ejpam-298	179	13	.	.	PUNCT
ejpam-298	180	1	j.	j.	PROPN
ejpam-298	180	2	pure	pure	PROPN
ejpam-298	180	3	appl	appl	PROPN
ejpam-298	180	4	.	.	PROPN
ejpam-298	180	5	math	math	PROPN
ejpam-298	180	6	,	,	PUNCT
ejpam-298	180	7	3	3	NUM
ejpam-298	180	8	(	(	PUNCT
ejpam-298	180	9	2010	2010	NUM
ejpam-298	180	10	)	)	PUNCT
ejpam-298	180	11	,	,	PUNCT
ejpam-298	180	12	16	16	NUM
ejpam-298	180	13	-	-	SYM
ejpam-298	180	14	25	25	NUM
ejpam-298	180	15	22	22	NUM
ejpam-298	180	16	the	the	DET
ejpam-298	180	17	equation	equation	NOUN
ejpam-298	180	18	(	(	PUNCT
ejpam-298	180	19	20	20	NUM
ejpam-298	180	20	)	)	PUNCT
ejpam-298	180	21	is	be	AUX
ejpam-298	180	22	equivalent	equivalent	ADJ
ejpam-298	180	23	to	to	ADP
ejpam-298	180	24	r(u	r(u	PROPN
ejpam-298	180	25	,	,	PUNCT
ejpam-298	180	26	y	y	PROPN
ejpam-298	180	27	)	)	PUNCT
ejpam-298	180	28	z	z	NOUN
ejpam-298	180	29	=	=	SYM
ejpam-298	180	30	k	k	PROPN
ejpam-298	180	31	�	�	PROPN
ejpam-298	180	32	g(y	g(y	PROPN
ejpam-298	180	33	,	,	PUNCT
ejpam-298	180	34	z)u	z)u	NOUN
ejpam-298	180	35	−	−	PUNCT
ejpam-298	180	36	a(z)y	a(z)y	PROPN
ejpam-298	180	37	�	�	PROPN
ejpam-298	180	38	(	(	PUNCT
ejpam-298	180	39	22	22	NUM
ejpam-298	180	40	)	)	PUNCT
ejpam-298	180	41	r(x	r(x	NOUN
ejpam-298	180	42	,	,	PUNCT
ejpam-298	180	43	u)z	u)z	NOUN
ejpam-298	180	44	=	=	SYM
ejpam-298	180	45	k	k	PROPN
ejpam-298	180	46	�	�	PROPN
ejpam-298	180	47	a(z)x	a(z)x	VERB
ejpam-298	180	48	−	−	PROPN
ejpam-298	180	49	g(x	g(x	PROPN
ejpam-298	180	50	,	,	PUNCT
ejpam-298	180	51	z)u	z)u	X
ejpam-298	180	52	�	�	PROPN
ejpam-298	180	53	(	(	PUNCT
ejpam-298	180	54	23	23	NUM
ejpam-298	180	55	)	)	PUNCT
ejpam-298	180	56	the	the	DET
ejpam-298	180	57	equation	equation	NOUN
ejpam-298	180	58	(	(	PUNCT
ejpam-298	180	59	21	21	NUM
ejpam-298	180	60	)	)	PUNCT
ejpam-298	180	61	is	be	AUX
ejpam-298	180	62	equivalent	equivalent	ADJ
ejpam-298	180	63	to	to	ADP
ejpam-298	180	64	r(v	r(v	PROPN
ejpam-298	180	65	,	,	PUNCT
ejpam-298	180	66	y	y	NOUN
ejpam-298	180	67	)	)	PUNCT
ejpam-298	180	68	z	z	NOUN
ejpam-298	180	69	=	=	SYM
ejpam-298	180	70	k	k	PROPN
ejpam-298	180	71	�	�	PROPN
ejpam-298	180	72	g(y	g(y	PROPN
ejpam-298	180	73	,	,	PUNCT
ejpam-298	180	74	z)v	z)v	VERB
ejpam-298	180	75	−	−	NUM
ejpam-298	180	76	b(z)y	b(z)y	PROPN
ejpam-298	180	77	�	�	PROPN
ejpam-298	180	78	(	(	PUNCT
ejpam-298	180	79	24	24	NUM
ejpam-298	180	80	)	)	PUNCT
ejpam-298	180	81	r(x	r(x	PROPN
ejpam-298	180	82	,	,	PUNCT
ejpam-298	180	83	v	v	NOUN
ejpam-298	180	84	)	)	PUNCT
ejpam-298	180	85	z	z	NOUN
ejpam-298	180	86	=	=	SYM
ejpam-298	180	87	k	k	PROPN
ejpam-298	180	88	�	�	PROPN
ejpam-298	180	89	b(z)x	b(z)x	PROPN
ejpam-298	180	90	−	−	PROPN
ejpam-298	180	91	g(x	g(x	PROPN
ejpam-298	180	92	,	,	PUNCT
ejpam-298	180	93	z)v	z)v	X
ejpam-298	180	94	�	�	PROPN
ejpam-298	180	95	(	(	PUNCT
ejpam-298	180	96	25	25	NUM
ejpam-298	180	97	)	)	PUNCT
ejpam-298	180	98	if	if	SCONJ
ejpam-298	180	99	(	(	PUNCT
ejpam-298	180	100	m	m	VERB
ejpam-298	180	101	n	n	CCONJ
ejpam-298	180	102	,	,	PUNCT
ejpam-298	180	103	g	g	NOUN
ejpam-298	180	104	)	)	PUNCT
ejpam-298	180	105	is	be	AUX
ejpam-298	180	106	semi	semi	ADV
ejpam-298	180	107	symmetric	symmetric	ADJ
ejpam-298	180	108	then	then	ADV
ejpam-298	180	109	we	we	PRON
ejpam-298	180	110	have	have	VERB
ejpam-298	180	111	r(x	r(x	PROPN
ejpam-298	180	112	,	,	PUNCT
ejpam-298	180	113	y	y	PROPN
ejpam-298	180	114	)	)	PUNCT
ejpam-298	180	115	r(z	r(z	PROPN
ejpam-298	180	116	,	,	PUNCT
ejpam-298	180	117	w	w	PROPN
ejpam-298	180	118	)	)	PUNCT
ejpam-298	180	119	t	t	NOUN
ejpam-298	180	120	−	−	PROPN
ejpam-298	180	121	r(r(x	r(r(x	PROPN
ejpam-298	180	122	,	,	PUNCT
ejpam-298	180	123	y	y	PROPN
ejpam-298	180	124	)	)	PUNCT
ejpam-298	180	125	z	z	NOUN
ejpam-298	180	126	,	,	PUNCT
ejpam-298	180	127	w	w	PROPN
ejpam-298	180	128	)	)	PUNCT
ejpam-298	180	129	t	t	PROPN
ejpam-298	180	130	−r(z	−r(z	NOUN
ejpam-298	180	131	,	,	PUNCT
ejpam-298	180	132	r(x	r(x	PROPN
ejpam-298	180	133	,	,	PUNCT
ejpam-298	180	134	y	y	PROPN
ejpam-298	180	135	)	)	PUNCT
ejpam-298	180	136	w	w	X
ejpam-298	180	137	)	)	PUNCT
ejpam-298	180	138	t	t	NOUN
ejpam-298	180	139	−	−	PROPN
ejpam-298	180	140	r(z	r(z	PROPN
ejpam-298	180	141	,	,	PUNCT
ejpam-298	180	142	w	w	PROPN
ejpam-298	180	143	)	)	PUNCT
ejpam-298	180	144	r(x	r(x	PROPN
ejpam-298	180	145	,	,	PUNCT
ejpam-298	181	1	y	y	PROPN
ejpam-298	181	2	)	)	PUNCT
ejpam-298	181	3	t	t	PROPN
ejpam-298	182	1	=	=	SYM
ejpam-298	182	2	0	0	NUM
ejpam-298	182	3	(	(	PUNCT
ejpam-298	182	4	26	26	NUM
ejpam-298	182	5	)	)	PUNCT
ejpam-298	182	6	putting	put	VERB
ejpam-298	182	7	x	x	PUNCT
ejpam-298	182	8	=	=	PUNCT
ejpam-298	182	9	u	u	NOUN
ejpam-298	182	10	and	and	CCONJ
ejpam-298	182	11	t	t	NOUN
ejpam-298	182	12	=	=	SYM
ejpam-298	182	13	v	v	NOUN
ejpam-298	182	14	in	in	ADP
ejpam-298	182	15	(	(	PUNCT
ejpam-298	182	16	26	26	NUM
ejpam-298	182	17	)	)	PUNCT
ejpam-298	182	18	,	,	PUNCT
ejpam-298	182	19	then	then	ADV
ejpam-298	182	20	using	use	VERB
ejpam-298	182	21	(	(	PUNCT
ejpam-298	182	22	21	21	NUM
ejpam-298	182	23	)	)	PUNCT
ejpam-298	182	24	and	and	CCONJ
ejpam-298	182	25	(	(	PUNCT
ejpam-298	182	26	22	22	NUM
ejpam-298	182	27	)	)	PUNCT
ejpam-298	182	28	,	,	PUNCT
ejpam-298	182	29	we	we	PRON
ejpam-298	182	30	get	get	VERB
ejpam-298	182	31	k2	k2	PROPN
ejpam-298	182	32	�	�	PROPN
ejpam-298	182	33	2a(z)b(y	2a(z)b(y	PROPN
ejpam-298	182	34	)	)	PUNCT
ejpam-298	183	1	w	w	PROPN
ejpam-298	183	2	+	+	NUM
ejpam-298	183	3	a(w)b(z)y	a(w)b(z)y	PROPN
ejpam-298	183	4	−	−	NOUN
ejpam-298	183	5	2b(z)g(y	2b(z)g(y	NUM
ejpam-298	183	6	,	,	PUNCT
ejpam-298	183	7	w	w	NOUN
ejpam-298	183	8	)	)	PUNCT
ejpam-298	183	9	u	u	NOUN
ejpam-298	183	10	=	=	SYM
ejpam-298	183	11	0	0	NUM
ejpam-298	183	12	(	(	PUNCT
ejpam-298	183	13	27	27	NUM
ejpam-298	183	14	)	)	PUNCT
ejpam-298	183	15	from	from	ADP
ejpam-298	183	16	(	(	PUNCT
ejpam-298	183	17	27),we	27),we	PROPN
ejpam-298	183	18	have	have	AUX
ejpam-298	183	19	if	if	SCONJ
ejpam-298	183	20	k	k	PROPN
ejpam-298	183	21	6=	6=	PROPN
ejpam-298	183	22	0	0	NUM
ejpam-298	183	23	,	,	PUNCT
ejpam-298	183	24	then	then	ADV
ejpam-298	183	25	2a(z)b(y	2a(z)b(y	NUM
ejpam-298	183	26	)	)	PUNCT
ejpam-298	184	1	w	w	X
ejpam-298	184	2	+	+	NUM
ejpam-298	184	3	a(w)b(z)y	a(w)b(z)y	PROPN
ejpam-298	184	4	=	=	SYM
ejpam-298	184	5	2b(z)g(y	2b(z)g(y	NUM
ejpam-298	184	6	,	,	PUNCT
ejpam-298	184	7	w	w	NOUN
ejpam-298	184	8	)	)	PUNCT
ejpam-298	184	9	u	u	NOUN
ejpam-298	184	10	,	,	PUNCT
ejpam-298	184	11	∀y	∀y	NUM
ejpam-298	184	12	,	,	PUNCT
ejpam-298	184	13	z	z	NOUN
ejpam-298	184	14	,	,	PUNCT
ejpam-298	184	15	w	w	PROPN
ejpam-298	184	16	∈	∈	PROPN
ejpam-298	185	1	t	t	NOUN
ejpam-298	185	2	m	m	NOUN
ejpam-298	185	3	holds	hold	NOUN
ejpam-298	185	4	.	.	PUNCT
ejpam-298	186	1	putting	put	VERB
ejpam-298	186	2	z	z	NOUN
ejpam-298	186	3	=	=	SYM
ejpam-298	186	4	v	v	NOUN
ejpam-298	186	5	in	in	ADP
ejpam-298	186	6	the	the	DET
ejpam-298	186	7	above	above	ADJ
ejpam-298	186	8	equation	equation	NOUN
ejpam-298	186	9	,	,	PUNCT
ejpam-298	186	10	we	we	PRON
ejpam-298	186	11	get	get	VERB
ejpam-298	186	12	g(y	g(y	PROPN
ejpam-298	186	13	,	,	PUNCT
ejpam-298	186	14	w	w	NOUN
ejpam-298	186	15	)	)	PUNCT
ejpam-298	186	16	u	u	NOUN
ejpam-298	186	17	=	=	PROPN
ejpam-298	186	18	a(w	a(w	PROPN
ejpam-298	186	19	)	)	PUNCT
ejpam-298	187	1	y	y	PROPN
ejpam-298	187	2	taking	take	VERB
ejpam-298	187	3	covariant	covariant	ADJ
ejpam-298	187	4	derivative	derivative	NOUN
ejpam-298	187	5	on	on	ADP
ejpam-298	187	6	both	both	DET
ejpam-298	187	7	sides	side	NOUN
ejpam-298	187	8	of	of	ADP
ejpam-298	187	9	the	the	DET
ejpam-298	187	10	above	above	ADJ
ejpam-298	187	11	equation	equation	NOUN
ejpam-298	187	12	with	with	ADP
ejpam-298	187	13	respect	respect	NOUN
ejpam-298	187	14	to	to	ADP
ejpam-298	187	15	z	z	NOUN
ejpam-298	187	16	,	,	PUNCT
ejpam-298	187	17	we	we	PRON
ejpam-298	187	18	obtain	obtain	VERB
ejpam-298	187	19	g(x	g(x	PROPN
ejpam-298	187	20	,	,	PUNCT
ejpam-298	187	21	y	y	NOUN
ejpam-298	187	22	)	)	PUNCT
ejpam-298	187	23	∇z	∇z	PROPN
ejpam-298	187	24	u	u	NOUN
ejpam-298	187	25	=	=	SYM
ejpam-298	187	26	(	(	PUNCT
ejpam-298	187	27	za(y	za(y	NOUN
ejpam-298	187	28	)	)	PUNCT
ejpam-298	187	29	x	x	SYM
ejpam-298	188	1	−	−	PROPN
ejpam-298	188	2	a(y	a(y	PROPN
ejpam-298	188	3	)	)	PUNCT
ejpam-298	188	4	)	)	PUNCT
ejpam-298	189	1	∇z	∇z	NOUN
ejpam-298	189	2	x	x	SYM
ejpam-298	189	3	,	,	PUNCT
ejpam-298	189	4	∀x	∀x	X
ejpam-298	189	5	,	,	PUNCT
ejpam-298	189	6	y	y	PROPN
ejpam-298	189	7	putting	put	VERB
ejpam-298	189	8	y	y	PROPN
ejpam-298	189	9	=	=	PUNCT
ejpam-298	189	10	v	v	PROPN
ejpam-298	189	11	,	,	PUNCT
ejpam-298	189	12	we	we	PRON
ejpam-298	189	13	get	get	VERB
ejpam-298	189	14	b(x	b(x	ADJ
ejpam-298	189	15	)	)	PUNCT
ejpam-298	189	16	∇z	∇z	NOUN
ejpam-298	189	17	u	u	NOUN
ejpam-298	189	18	=	=	NOUN
ejpam-298	189	19	0	0	NUM
ejpam-298	189	20	.	.	PUNCT
ejpam-298	190	1	since	since	SCONJ
ejpam-298	190	2	b(x	b(x	PROPN
ejpam-298	190	3	)	)	PUNCT
ejpam-298	190	4	6=	6=	ADP
ejpam-298	190	5	0	0	NUM
ejpam-298	190	6	,	,	PUNCT
ejpam-298	190	7	we	we	PRON
ejpam-298	190	8	obtain	obtain	VERB
ejpam-298	190	9	∇z	∇z	PROPN
ejpam-298	190	10	u	u	NOUN
ejpam-298	190	11	=	=	NOUN
ejpam-298	190	12	0	0	NUM
ejpam-298	190	13	.	.	PUNCT
ejpam-298	191	1	i.e.	i.e.	X
ejpam-298	191	2	u	u	NOUN
ejpam-298	191	3	is	be	AUX
ejpam-298	191	4	a	a	DET
ejpam-298	191	5	parallel	parallel	ADJ
ejpam-298	191	6	vector	vector	NOUN
ejpam-298	191	7	field	field	NOUN
ejpam-298	191	8	.	.	PUNCT
ejpam-298	192	1	similarly	similarly	ADV
ejpam-298	192	2	by	by	ADP
ejpam-298	192	3	taking	take	VERB
ejpam-298	192	4	x	x	PUNCT
ejpam-298	192	5	=	=	SYM
ejpam-298	192	6	v	v	NOUN
ejpam-298	192	7	and	and	CCONJ
ejpam-298	192	8	t	t	NOUN
ejpam-298	192	9	=	=	SYM
ejpam-298	192	10	u	u	PROPN
ejpam-298	192	11	in	in	ADP
ejpam-298	192	12	(	(	PUNCT
ejpam-298	192	13	26	26	NUM
ejpam-298	192	14	)	)	PUNCT
ejpam-298	192	15	,	,	PUNCT
ejpam-298	192	16	we	we	PRON
ejpam-298	192	17	obtain	obtain	VERB
ejpam-298	192	18	∇z	∇z	PROPN
ejpam-298	192	19	v	v	NOUN
ejpam-298	192	20	=	=	SYM
ejpam-298	192	21	0	0	NUM
ejpam-298	192	22	.	.	PUNCT
ejpam-298	193	1	i.e.	i.e.	X
ejpam-298	193	2	v	v	NOUN
ejpam-298	193	3	is	be	AUX
ejpam-298	193	4	a	a	DET
ejpam-298	193	5	parallel	parallel	ADJ
ejpam-298	193	6	vector	vector	NOUN
ejpam-298	193	7	field	field	NOUN
ejpam-298	193	8	.	.	PUNCT
ejpam-298	194	1	conversely	conversely	ADV
ejpam-298	194	2	suppose	suppose	VERB
ejpam-298	194	3	that	that	SCONJ
ejpam-298	194	4	u	u	PROPN
ejpam-298	194	5	and	and	CCONJ
ejpam-298	194	6	v	v	NOUN
ejpam-298	194	7	are	be	AUX
ejpam-298	194	8	parallel	parallel	ADJ
ejpam-298	194	9	vector	vector	NOUN
ejpam-298	194	10	fields	field	NOUN
ejpam-298	194	11	.	.	PUNCT
ejpam-298	195	1	then	then	ADV
ejpam-298	195	2	∇z	∇z	PROPN
ejpam-298	195	3	u	u	NOUN
ejpam-298	195	4	=	=	NOUN
ejpam-298	195	5	0	0	NUM
ejpam-298	195	6	and	and	CCONJ
ejpam-298	195	7	∇z	∇z	PROPN
ejpam-298	195	8	v	v	NOUN
ejpam-298	195	9	=	=	SYM
ejpam-298	195	10	0	0	NUM
ejpam-298	195	11	,	,	PUNCT
ejpam-298	195	12	which	which	PRON
ejpam-298	195	13	then	then	ADV
ejpam-298	195	14	imply	imply	VERB
ejpam-298	195	15	that	that	SCONJ
ejpam-298	195	16	r(x	r(x	PROPN
ejpam-298	195	17	,	,	PUNCT
ejpam-298	195	18	y	y	PROPN
ejpam-298	195	19	)	)	PUNCT
ejpam-298	195	20	u	u	NOUN
ejpam-298	195	21	=	=	NOUN
ejpam-298	195	22	0	0	PROPN
ejpam-298	195	23	and	and	CCONJ
ejpam-298	195	24	r(x	r(x	PROPN
ejpam-298	195	25	,	,	PUNCT
ejpam-298	195	26	y	y	PROPN
ejpam-298	195	27	)	)	PUNCT
ejpam-298	195	28	v	v	NOUN
ejpam-298	195	29	=	=	SYM
ejpam-298	195	30	0	0	NUM
ejpam-298	195	31	.	.	PUNCT
ejpam-298	196	1	substituting	substitute	VERB
ejpam-298	196	2	this	this	PRON
ejpam-298	196	3	in	in	ADP
ejpam-298	196	4	(	(	PUNCT
ejpam-298	196	5	26	26	NUM
ejpam-298	196	6	)	)	PUNCT
ejpam-298	196	7	with	with	ADP
ejpam-298	196	8	x	x	X
ejpam-298	196	9	=	=	SYM
ejpam-298	196	10	u	u	PROPN
ejpam-298	196	11	,	,	PUNCT
ejpam-298	196	12	we	we	PRON
ejpam-298	196	13	obtain	obtain	VERB
ejpam-298	196	14	r(u	r(u	PROPN
ejpam-298	196	15	,	,	PUNCT
ejpam-298	196	16	x	x	X
ejpam-298	196	17	)	)	PUNCT
ejpam-298	196	18	.r=	.r=	NOUN
ejpam-298	197	1	0	0	X
ejpam-298	197	2	.	.	PUNCT
ejpam-298	198	1	similarly	similarly	ADV
ejpam-298	198	2	we	we	PRON
ejpam-298	198	3	get	get	VERB
ejpam-298	198	4	r(v	r(v	PROPN
ejpam-298	198	5	,	,	PUNCT
ejpam-298	198	6	x	x	X
ejpam-298	198	7	)	)	PUNCT
ejpam-298	198	8	.r=	.r=	PROPN
ejpam-298	199	1	0	0	NUM
ejpam-298	199	2	.	.	PUNCT
ejpam-298	200	1	thus	thus	ADV
ejpam-298	200	2	we	we	PRON
ejpam-298	200	3	can	can	AUX
ejpam-298	200	4	state	state	VERB
ejpam-298	200	5	that	that	PRON
ejpam-298	200	6	theorem	theorem	NOUN
ejpam-298	200	7	5	5	NUM
ejpam-298	200	8	.	.	PUNCT
ejpam-298	201	1	a	a	DET
ejpam-298	201	2	n(k)−	n(k)−	NOUN
ejpam-298	201	3	(	(	PUNCT
ejpam-298	201	4	mqe)n	mqe)n	PROPN
ejpam-298	201	5	manifold	manifold	ADJ
ejpam-298	201	6	with	with	ADP
ejpam-298	201	7	k	k	PROPN
ejpam-298	201	8	6=	6=	ADP
ejpam-298	201	9	0	0	NUM
ejpam-298	201	10	satisfies	satisfie	NOUN
ejpam-298	201	11	r(u	r(u	PROPN
ejpam-298	201	12	,	,	PUNCT
ejpam-298	201	13	x	x	X
ejpam-298	201	14	)	)	PUNCT
ejpam-298	201	15	.r	.r	NOUN
ejpam-298	202	1	=	=	PUNCT
ejpam-298	202	2	0	0	PUNCT
ejpam-298	202	3	(	(	PUNCT
ejpam-298	202	4	orr(v	orr(v	PROPN
ejpam-298	202	5	,	,	PUNCT
ejpam-298	202	6	x	x	NOUN
ejpam-298	202	7	)	)	PUNCT
ejpam-298	202	8	.r	.r	NOUN
ejpam-298	203	1	=	=	PUNCT
ejpam-298	203	2	0	0	X
ejpam-298	203	3	)	)	PUNCT
ejpam-298	203	4	if	if	SCONJ
ejpam-298	203	5	and	and	CCONJ
ejpam-298	203	6	only	only	ADV
ejpam-298	203	7	if	if	SCONJ
ejpam-298	203	8	u	u	PROPN
ejpam-298	203	9	(	(	PUNCT
ejpam-298	203	10	orv	orv	PROPN
ejpam-298	203	11	)	)	PUNCT
ejpam-298	203	12	is	be	AUX
ejpam-298	203	13	a	a	DET
ejpam-298	203	14	parallel	parallel	ADJ
ejpam-298	203	15	vector	vector	NOUN
ejpam-298	203	16	field	field	NOUN
ejpam-298	203	17	.	.	PUNCT
ejpam-298	204	1	h.	h.	PROPN
ejpam-298	204	2	nagaraja	nagaraja	PROPN
ejpam-298	204	3	/	/	SYM
ejpam-298	204	4	eur	eur	PROPN
ejpam-298	204	5	.	.	PUNCT
ejpam-298	205	1	j.	j.	PROPN
ejpam-298	205	2	pure	pure	PROPN
ejpam-298	205	3	appl	appl	PROPN
ejpam-298	205	4	.	.	PROPN
ejpam-298	205	5	math	math	PROPN
ejpam-298	205	6	,	,	PUNCT
ejpam-298	205	7	3	3	NUM
ejpam-298	205	8	(	(	PUNCT
ejpam-298	205	9	2010	2010	NUM
ejpam-298	205	10	)	)	PUNCT
ejpam-298	205	11	,	,	PUNCT
ejpam-298	205	12	16	16	NUM
ejpam-298	205	13	-	-	SYM
ejpam-298	205	14	25	25	NUM
ejpam-298	205	15	23	23	NUM
ejpam-298	205	16	let	let	VERB
ejpam-298	205	17	(	(	PUNCT
ejpam-298	205	18	m	m	VERB
ejpam-298	205	19	n	n	CCONJ
ejpam-298	205	20	,	,	PUNCT
ejpam-298	205	21	g	g	NOUN
ejpam-298	205	22	)	)	PUNCT
ejpam-298	205	23	be	be	AUX
ejpam-298	205	24	a	a	DET
ejpam-298	205	25	n(k)−	n(k)−	NOUN
ejpam-298	205	26	(	(	PUNCT
ejpam-298	205	27	mqe)n	mqe)n	PROPN
ejpam-298	205	28	ricci	ricci	NOUN
ejpam-298	205	29	semi	semi	ADV
ejpam-298	205	30	symmetric	symmetric	PROPN
ejpam-298	205	31	manifold	manifold	NOUN
ejpam-298	205	32	.	.	PUNCT
ejpam-298	206	1	then	then	ADV
ejpam-298	206	2	we	we	PRON
ejpam-298	206	3	have	have	VERB
ejpam-298	206	4	s(r(x	s(r(x	PROPN
ejpam-298	206	5	,	,	PUNCT
ejpam-298	206	6	y	y	PROPN
ejpam-298	206	7	)	)	PUNCT
ejpam-298	206	8	z	z	NOUN
ejpam-298	206	9	,	,	PUNCT
ejpam-298	206	10	w	w	PROPN
ejpam-298	206	11	)	)	PUNCT
ejpam-298	207	1	+	+	CCONJ
ejpam-298	207	2	s(z	s(z	PROPN
ejpam-298	207	3	,	,	PUNCT
ejpam-298	207	4	r(x	r(x	PROPN
ejpam-298	207	5	,	,	PUNCT
ejpam-298	207	6	y	y	PROPN
ejpam-298	207	7	)	)	PUNCT
ejpam-298	208	1	w	w	PROPN
ejpam-298	208	2	=	=	SYM
ejpam-298	208	3	0	0	NUM
ejpam-298	208	4	(	(	PUNCT
ejpam-298	208	5	28	28	NUM
ejpam-298	208	6	)	)	PUNCT
ejpam-298	208	7	putting	put	VERB
ejpam-298	208	8	x	x	PUNCT
ejpam-298	208	9	=	=	SYM
ejpam-298	208	10	v	v	NOUN
ejpam-298	208	11	in	in	ADP
ejpam-298	208	12	(	(	PUNCT
ejpam-298	208	13	28	28	NUM
ejpam-298	208	14	)	)	PUNCT
ejpam-298	208	15	we	we	PRON
ejpam-298	208	16	obtain	obtain	VERB
ejpam-298	208	17	k	k	PROPN
ejpam-298	208	18	�	�	PROPN
ejpam-298	208	19	g(y	g(y	PROPN
ejpam-298	208	20	,	,	PUNCT
ejpam-298	208	21	z)s(v	z)s(v	PROPN
ejpam-298	208	22	,	,	PUNCT
ejpam-298	208	23	w	w	NOUN
ejpam-298	208	24	)	)	PUNCT
ejpam-298	208	25	−	−	PROPN
ejpam-298	208	26	b(z)s(y	b(z)s(y	NOUN
ejpam-298	208	27	,	,	PUNCT
ejpam-298	208	28	w	w	NOUN
ejpam-298	208	29	)	)	PUNCT
ejpam-298	209	1	+	+	CCONJ
ejpam-298	209	2	g(y	g(y	NOUN
ejpam-298	209	3	,	,	PUNCT
ejpam-298	209	4	w	w	NOUN
ejpam-298	209	5	)	)	PUNCT
ejpam-298	209	6	s(z	s(z	PROPN
ejpam-298	209	7	,	,	PUNCT
ejpam-298	209	8	v	v	NOUN
ejpam-298	209	9	)	)	PUNCT
ejpam-298	209	10	−	−	PROPN
ejpam-298	209	11	b(w	b(w	NOUN
ejpam-298	209	12	)	)	PUNCT
ejpam-298	210	1	s(z	s(z	PROPN
ejpam-298	210	2	,	,	PUNCT
ejpam-298	210	3	y	y	PROPN
ejpam-298	210	4	)	)	PUNCT
ejpam-298	211	1	=	=	SYM
ejpam-298	211	2	0	0	PUNCT
ejpam-298	212	1	putting	put	VERB
ejpam-298	212	2	w	w	NOUN
ejpam-298	212	3	=	=	ADJ
ejpam-298	212	4	v	v	NOUN
ejpam-298	212	5	in	in	ADP
ejpam-298	212	6	the	the	DET
ejpam-298	212	7	above	above	ADJ
ejpam-298	212	8	equation	equation	NOUN
ejpam-298	212	9	,	,	PUNCT
ejpam-298	212	10	we	we	PRON
ejpam-298	212	11	get	get	VERB
ejpam-298	212	12	k	k	PROPN
ejpam-298	212	13	�	�	PROPN
ejpam-298	212	14	s(z	s(z	PROPN
ejpam-298	212	15	,	,	PUNCT
ejpam-298	212	16	y	y	PROPN
ejpam-298	212	17	)	)	PUNCT
ejpam-298	213	1	−	−	PROPN
ejpam-298	213	2	ag(y	ag(y	NOUN
ejpam-298	213	3	,	,	PUNCT
ejpam-298	213	4	z)+	z)+	NUM
ejpam-298	213	5	ba(y	ba(y	NOUN
ejpam-298	213	6	)	)	PUNCT
ejpam-298	213	7	b(z)−	b(z)−	PROPN
ejpam-298	213	8	ba(z)b(y	ba(z)b(y	ADJ
ejpam-298	213	9	)	)	PUNCT
ejpam-298	213	10	�	�	PROPN
ejpam-298	214	1	=	=	PUNCT
ejpam-298	214	2	0	0	PUNCT
ejpam-298	215	1	if	if	SCONJ
ejpam-298	215	2	k	k	PROPN
ejpam-298	215	3	6=	6=	PROPN
ejpam-298	215	4	0	0	PUNCT
ejpam-298	215	5	then	then	ADV
ejpam-298	215	6	we	we	PRON
ejpam-298	215	7	have	have	VERB
ejpam-298	215	8	s(z	s(z	PROPN
ejpam-298	215	9	,	,	PUNCT
ejpam-298	215	10	y	y	PROPN
ejpam-298	215	11	)	)	PUNCT
ejpam-298	215	12	=	=	PUNCT
ejpam-298	215	13	a	a	DET
ejpam-298	215	14	g(y	g(y	PROPN
ejpam-298	215	15	,	,	PUNCT
ejpam-298	215	16	z	z	NOUN
ejpam-298	215	17	)	)	PUNCT
ejpam-298	215	18	b	b	PROPN
ejpam-298	215	19	a(y	a(y	PROPN
ejpam-298	215	20	)	)	PUNCT
ejpam-298	215	21	b(z	b(z	NOUN
ejpam-298	215	22	)	)	PUNCT
ejpam-298	216	1	+	+	CCONJ
ejpam-298	216	2	b	b	X
ejpam-298	216	3	a(z	a(z	NOUN
ejpam-298	216	4	)	)	PUNCT
ejpam-298	216	5	b(y	b(y	PROPN
ejpam-298	216	6	)	)	PUNCT
ejpam-298	216	7	.	.	PUNCT
ejpam-298	217	1	comparing	compare	VERB
ejpam-298	217	2	this	this	PRON
ejpam-298	217	3	with	with	ADP
ejpam-298	217	4	(	(	PUNCT
ejpam-298	217	5	1	1	NUM
ejpam-298	217	6	)	)	PUNCT
ejpam-298	217	7	,	,	PUNCT
ejpam-298	217	8	we	we	PRON
ejpam-298	217	9	obtain	obtain	VERB
ejpam-298	217	10	b+	b+	X
ejpam-298	217	11	c	c	NOUN
ejpam-298	217	12	=	=	SYM
ejpam-298	217	13	0	0	PROPN
ejpam-298	217	14	.	.	PUNCT
ejpam-298	218	1	but	but	CCONJ
ejpam-298	218	2	we	we	PRON
ejpam-298	218	3	have	have	VERB
ejpam-298	218	4	b−	b−	PROPN
ejpam-298	218	5	c	c	NOUN
ejpam-298	218	6	=	=	SYM
ejpam-298	218	7	0	0	PROPN
ejpam-298	218	8	,	,	PUNCT
ejpam-298	218	9	{	{	PUNCT
ejpam-298	218	10	section	section	NOUN
ejpam-298	218	11	4	4	NUM
ejpam-298	218	12	}	}	PUNCT
ejpam-298	218	13	therefore	therefore	ADV
ejpam-298	218	14	b	b	X
ejpam-298	218	15	=	=	SYM
ejpam-298	218	16	0	0	PROPN
ejpam-298	218	17	and	and	CCONJ
ejpam-298	218	18	c	c	NOUN
ejpam-298	218	19	=	=	SYM
ejpam-298	218	20	0	0	PROPN
ejpam-298	218	21	.	.	PUNCT
ejpam-298	219	1	i.e.	i.e.	X
ejpam-298	219	2	(	(	PUNCT
ejpam-298	219	3	m	m	VERB
ejpam-298	219	4	n	n	CCONJ
ejpam-298	219	5	,	,	PUNCT
ejpam-298	219	6	g	g	NOUN
ejpam-298	219	7	)	)	PUNCT
ejpam-298	219	8	reduces	reduce	VERB
ejpam-298	219	9	to	to	ADP
ejpam-298	219	10	einstein	einstein	ADJ
ejpam-298	219	11	space	space	NOUN
ejpam-298	219	12	which	which	PRON
ejpam-298	219	13	it	it	PRON
ejpam-298	219	14	is	be	AUX
ejpam-298	219	15	not	not	PART
ejpam-298	219	16	.	.	PUNCT
ejpam-298	220	1	therefore	therefore	ADV
ejpam-298	220	2	we	we	PRON
ejpam-298	220	3	must	must	AUX
ejpam-298	220	4	have	have	VERB
ejpam-298	220	5	k	k	NOUN
ejpam-298	220	6	=	=	SYM
ejpam-298	220	7	0	0	X
ejpam-298	220	8	.	.	PUNCT
ejpam-298	221	1	conversely	conversely	ADV
ejpam-298	221	2	suppose	suppose	VERB
ejpam-298	221	3	k	k	PROPN
ejpam-298	221	4	=	=	PUNCT
ejpam-298	221	5	0	0	PROPN
ejpam-298	221	6	.	.	PUNCT
ejpam-298	222	1	then	then	ADV
ejpam-298	222	2	we	we	PRON
ejpam-298	222	3	obtain	obtain	VERB
ejpam-298	222	4	r(v	r(v	PROPN
ejpam-298	222	5	,	,	PUNCT
ejpam-298	222	6	x	x	X
ejpam-298	222	7	)	)	PUNCT
ejpam-298	222	8	y	y	PROPN
ejpam-298	222	9	=	=	PUNCT
ejpam-298	222	10	0	0	NUM
ejpam-298	222	11	which	which	PRON
ejpam-298	222	12	implies	imply	VERB
ejpam-298	222	13	r(v	r(v	PROPN
ejpam-298	222	14	,	,	PUNCT
ejpam-298	222	15	x	x	NOUN
ejpam-298	222	16	)	)	PUNCT
ejpam-298	222	17	.s	.s	NOUN
ejpam-298	223	1	=	=	PUNCT
ejpam-298	223	2	0	0	X
ejpam-298	223	3	.	.	PUNCT
ejpam-298	224	1	similarly	similarly	ADV
ejpam-298	224	2	,	,	PUNCT
ejpam-298	224	3	we	we	PRON
ejpam-298	224	4	have	have	VERB
ejpam-298	224	5	,	,	PUNCT
ejpam-298	224	6	r(u	r(u	PROPN
ejpam-298	224	7	,	,	PUNCT
ejpam-298	224	8	x	x	NOUN
ejpam-298	224	9	)	)	PUNCT
ejpam-298	224	10	.s	.s	NOUN
ejpam-298	225	1	=	=	PUNCT
ejpam-298	225	2	0	0	X
ejpam-298	225	3	.	.	PUNCT
ejpam-298	226	1	if	if	SCONJ
ejpam-298	226	2	and	and	CCONJ
ejpam-298	226	3	only	only	ADV
ejpam-298	226	4	if	if	SCONJ
ejpam-298	226	5	k	k	PROPN
ejpam-298	226	6	=	=	SYM
ejpam-298	226	7	0	0	PROPN
ejpam-298	226	8	.	.	PUNCT
ejpam-298	227	1	thus	thus	ADV
ejpam-298	227	2	we	we	PRON
ejpam-298	227	3	have	have	AUX
ejpam-298	227	4	,	,	PUNCT
ejpam-298	227	5	theorem	theorem	VERB
ejpam-298	227	6	6	6	NUM
ejpam-298	227	7	.	.	PUNCT
ejpam-298	228	1	a	a	DET
ejpam-298	228	2	n(k)−	n(k)−	NOUN
ejpam-298	228	3	(	(	PUNCT
ejpam-298	228	4	mqe)n	mqe)n	ADJ
ejpam-298	228	5	manifold	manifold	ADJ
ejpam-298	228	6	satisfies	satisfie	NOUN
ejpam-298	228	7	r(v	r(v	PROPN
ejpam-298	228	8	,	,	PUNCT
ejpam-298	228	9	x	x	NOUN
ejpam-298	228	10	)	)	PUNCT
ejpam-298	228	11	.s	.s	NOUN
ejpam-298	228	12	=	=	PUNCT
ejpam-298	229	1	0	0	X
ejpam-298	229	2	.	.	PUNCT
ejpam-298	229	3	and	and	CCONJ
ejpam-298	229	4	r(u	r(u	PROPN
ejpam-298	229	5	,	,	PUNCT
ejpam-298	229	6	x	x	NOUN
ejpam-298	229	7	)	)	PUNCT
ejpam-298	229	8	.s	.s	NOUN
ejpam-298	230	1	=	=	PUNCT
ejpam-298	230	2	0	0	PUNCT
ejpam-298	231	1	if	if	SCONJ
ejpam-298	231	2	and	and	CCONJ
ejpam-298	231	3	only	only	ADV
ejpam-298	231	4	if	if	SCONJ
ejpam-298	231	5	k	k	PROPN
ejpam-298	231	6	=	=	SYM
ejpam-298	231	7	0	0	NUM
ejpam-298	231	8	.	.	NOUN
ejpam-298	231	9	6	6	NUM
ejpam-298	231	10	.	.	X
ejpam-298	232	1	ricci	ricci	PROPN
ejpam-298	232	2	recurrent	recurrent	PROPN
ejpam-298	232	3	n(k)−	n(k)−	PROPN
ejpam-298	232	4	(	(	PUNCT
ejpam-298	232	5	mqe)n	mqe)n	ADJ
ejpam-298	232	6	manifolds	manifold	NOUN
ejpam-298	232	7	let	let	VERB
ejpam-298	232	8	(	(	PUNCT
ejpam-298	232	9	m	m	VERB
ejpam-298	232	10	n	n	CCONJ
ejpam-298	232	11	,	,	PUNCT
ejpam-298	232	12	g	g	NOUN
ejpam-298	232	13	)	)	PUNCT
ejpam-298	232	14	be	be	AUX
ejpam-298	232	15	a	a	DET
ejpam-298	232	16	n(k	n(k	NOUN
ejpam-298	232	17	)	)	PUNCT
ejpam-298	232	18	−	−	PROPN
ejpam-298	233	1	(	(	PUNCT
ejpam-298	233	2	mqe)n	mqe)n	NOUN
ejpam-298	233	3	manifold	manifold	NOUN
ejpam-298	233	4	.	.	PUNCT
ejpam-298	234	1	if	if	SCONJ
ejpam-298	234	2	u	u	PROPN
ejpam-298	234	3	and	and	CCONJ
ejpam-298	234	4	v	v	NOUN
ejpam-298	234	5	are	be	AUX
ejpam-298	234	6	parallel	parallel	ADJ
ejpam-298	234	7	vector	vector	NOUN
ejpam-298	234	8	fields	field	NOUN
ejpam-298	234	9	,	,	PUNCT
ejpam-298	234	10	then	then	ADV
ejpam-298	234	11	∇x	∇x	VERB
ejpam-298	234	12	u	u	NOUN
ejpam-298	234	13	=	=	NOUN
ejpam-298	234	14	0	0	NUM
ejpam-298	234	15	and	and	CCONJ
ejpam-298	234	16	∇x	∇x	NOUN
ejpam-298	234	17	v	v	ADP
ejpam-298	234	18	=	=	NOUN
ejpam-298	234	19	0	0	NUM
ejpam-298	234	20	.	.	PUNCT
ejpam-298	235	1	from	from	ADP
ejpam-298	235	2	which	which	PRON
ejpam-298	235	3	we	we	PRON
ejpam-298	235	4	get	get	VERB
ejpam-298	235	5	that	that	DET
ejpam-298	235	6	r(x	r(x	PROPN
ejpam-298	235	7	,	,	PUNCT
ejpam-298	235	8	y	y	PROPN
ejpam-298	235	9	)	)	PUNCT
ejpam-298	235	10	u	u	NOUN
ejpam-298	235	11	=	=	NOUN
ejpam-298	235	12	0	0	PROPN
ejpam-298	235	13	and	and	CCONJ
ejpam-298	235	14	r(x	r(x	PROPN
ejpam-298	235	15	,	,	PUNCT
ejpam-298	235	16	y	y	PROPN
ejpam-298	235	17	)	)	PUNCT
ejpam-298	235	18	u	u	NOUN
ejpam-298	235	19	=	=	NOUN
ejpam-298	235	20	0	0	PROPN
ejpam-298	235	21	.	.	PUNCT
ejpam-298	236	1	therefore	therefore	ADV
ejpam-298	236	2	s(x	s(x	PROPN
ejpam-298	236	3	,	,	PUNCT
ejpam-298	236	4	u	u	NOUN
ejpam-298	236	5	)	)	PUNCT
ejpam-298	236	6	=	=	PUNCT
ejpam-298	237	1	0,s(x	0,s(x	NUM
ejpam-298	237	2	,	,	PUNCT
ejpam-298	237	3	v	v	NOUN
ejpam-298	237	4	)	)	PUNCT
ejpam-298	237	5	=	=	SYM
ejpam-298	237	6	0	0	NUM
ejpam-298	238	1	(	(	PUNCT
ejpam-298	238	2	29	29	NUM
ejpam-298	238	3	)	)	PUNCT
ejpam-298	238	4	from	from	ADP
ejpam-298	238	5	(	(	PUNCT
ejpam-298	238	6	1	1	NUM
ejpam-298	238	7	)	)	PUNCT
ejpam-298	238	8	,	,	PUNCT
ejpam-298	238	9	we	we	PRON
ejpam-298	238	10	have	have	VERB
ejpam-298	238	11	s(x	s(x	NOUN
ejpam-298	238	12	,	,	PUNCT
ejpam-298	238	13	u	u	NOUN
ejpam-298	238	14	)	)	PUNCT
ejpam-298	238	15	=	=	SYM
ejpam-298	238	16	aa(x	aa(x	NOUN
ejpam-298	238	17	)	)	PUNCT
ejpam-298	238	18	+	+	NUM
ejpam-298	238	19	bb(x	bb(x	PUNCT
ejpam-298	238	20	)	)	PUNCT
ejpam-298	238	21	and	and	CCONJ
ejpam-298	238	22	(	(	PUNCT
ejpam-298	238	23	30	30	NUM
ejpam-298	238	24	)	)	PUNCT
ejpam-298	238	25	s(x	s(x	NOUN
ejpam-298	238	26	,	,	PUNCT
ejpam-298	238	27	v	v	NOUN
ejpam-298	238	28	)	)	PUNCT
ejpam-298	238	29	=	=	NOUN
ejpam-298	238	30	ab(x	ab(x	X
ejpam-298	238	31	)	)	PUNCT
ejpam-298	239	1	+	+	CCONJ
ejpam-298	239	2	ba(x	ba(x	NOUN
ejpam-298	239	3	)	)	PUNCT
ejpam-298	239	4	(	(	PUNCT
ejpam-298	239	5	31	31	NUM
ejpam-298	239	6	)	)	PUNCT
ejpam-298	239	7	from	from	ADP
ejpam-298	239	8	(	(	PUNCT
ejpam-298	239	9	29	29	NUM
ejpam-298	239	10	)	)	PUNCT
ejpam-298	239	11	,	,	PUNCT
ejpam-298	239	12	(	(	PUNCT
ejpam-298	239	13	30	30	NUM
ejpam-298	239	14	)	)	PUNCT
ejpam-298	239	15	and	and	CCONJ
ejpam-298	239	16	(	(	PUNCT
ejpam-298	239	17	31	31	NUM
ejpam-298	239	18	)	)	PUNCT
ejpam-298	239	19	,	,	PUNCT
ejpam-298	239	20	we	we	PRON
ejpam-298	239	21	have	have	VERB
ejpam-298	239	22	a	a	DET
ejpam-298	239	23	=	=	X
ejpam-298	239	24	b.	b.	NOUN
ejpam-298	239	25	therefore	therefore	ADV
ejpam-298	239	26	we	we	PRON
ejpam-298	239	27	can	can	AUX
ejpam-298	239	28	rewrite	rewrite	VERB
ejpam-298	239	29	the	the	DET
ejpam-298	239	30	equation	equation	NOUN
ejpam-298	239	31	(	(	PUNCT
ejpam-298	239	32	1	1	X
ejpam-298	239	33	)	)	PUNCT
ejpam-298	239	34	in	in	ADP
ejpam-298	239	35	the	the	DET
ejpam-298	239	36	following	follow	VERB
ejpam-298	239	37	form	form	NOUN
ejpam-298	239	38	:	:	PUNCT
ejpam-298	239	39	s(x	s(x	NOUN
ejpam-298	239	40	,	,	PUNCT
ejpam-298	239	41	y	y	PROPN
ejpam-298	239	42	)	)	PUNCT
ejpam-298	239	43	=	=	PUNCT
ejpam-298	240	1	a	a	DET
ejpam-298	240	2	�	�	PROPN
ejpam-298	240	3	g(x	g(x	PROPN
ejpam-298	240	4	,	,	PUNCT
ejpam-298	240	5	y	y	PROPN
ejpam-298	240	6	)	)	PUNCT
ejpam-298	240	7	+	+	CCONJ
ejpam-298	240	8	a(x	a(x	X
ejpam-298	240	9	)	)	PUNCT
ejpam-298	240	10	b(y	b(y	PROPN
ejpam-298	240	11	)	)	PUNCT
ejpam-298	241	1	+	+	CCONJ
ejpam-298	241	2	b(x	b(x	NOUN
ejpam-298	241	3	)	)	PUNCT
ejpam-298	241	4	a(y	a(y	PROPN
ejpam-298	241	5	)	)	PUNCT
ejpam-298	241	6	.	.	PUNCT
ejpam-298	242	1	taking	take	VERB
ejpam-298	242	2	the	the	DET
ejpam-298	242	3	covariant	covariant	ADJ
ejpam-298	242	4	derivative	derivative	NOUN
ejpam-298	242	5	of	of	ADP
ejpam-298	242	6	the	the	DET
ejpam-298	242	7	above	above	ADJ
ejpam-298	242	8	equation	equation	NOUN
ejpam-298	242	9	with	with	ADP
ejpam-298	242	10	respect	respect	NOUN
ejpam-298	242	11	to	to	ADP
ejpam-298	242	12	z	z	NOUN
ejpam-298	242	13	,	,	PUNCT
ejpam-298	242	14	we	we	PRON
ejpam-298	242	15	obtain	obtain	VERB
ejpam-298	242	16	∇zs(x	∇zs(x	PRON
ejpam-298	242	17	,	,	PUNCT
ejpam-298	242	18	y	y	PROPN
ejpam-298	242	19	)	)	PUNCT
ejpam-298	242	20	=	=	SYM
ejpam-298	242	21	da(z	da(z	X
ejpam-298	242	22	)	)	PUNCT
ejpam-298	242	23	�	�	PROPN
ejpam-298	242	24	g(x	g(x	PROPN
ejpam-298	242	25	,	,	PUNCT
ejpam-298	242	26	y	y	PROPN
ejpam-298	242	27	)	)	PUNCT
ejpam-298	243	1	+	+	ADJ
ejpam-298	243	2	a(x	a(x	NOUN
ejpam-298	243	3	)	)	PUNCT
ejpam-298	243	4	b(y	b(y	PROPN
ejpam-298	243	5	)	)	PUNCT
ejpam-298	244	1	+	+	CCONJ
ejpam-298	244	2	b(x	b(x	NOUN
ejpam-298	244	3	)	)	PUNCT
ejpam-298	244	4	a(y	a(y	PROPN
ejpam-298	244	5	)	)	PUNCT
ejpam-298	244	6	references	reference	NOUN
ejpam-298	244	7	24	24	NUM
ejpam-298	244	8	since	since	SCONJ
ejpam-298	244	9	∇x	∇x	NOUN
ejpam-298	244	10	u	u	NOUN
ejpam-298	244	11	=	=	NOUN
ejpam-298	244	12	0	0	NUM
ejpam-298	244	13	and	and	CCONJ
ejpam-298	244	14	∇x	∇x	NOUN
ejpam-298	244	15	v	v	ADP
ejpam-298	244	16	=	=	SYM
ejpam-298	244	17	0	0	NUM
ejpam-298	244	18	imply	imply	VERB
ejpam-298	244	19	that	that	SCONJ
ejpam-298	244	20	∇za(x	∇za(x	VERB
ejpam-298	244	21	)	)	PUNCT
ejpam-298	244	22	=	=	SYM
ejpam-298	244	23	0	0	NUM
ejpam-298	244	24	and	and	CCONJ
ejpam-298	244	25	∇z	∇z	ADJ
ejpam-298	244	26	b(x	b(x	ADJ
ejpam-298	244	27	)	)	PUNCT
ejpam-298	245	1	=	=	SYM
ejpam-298	245	2	0	0	X
ejpam-298	245	3	.	.	PUNCT
ejpam-298	246	1	therefore	therefore	ADV
ejpam-298	246	2	(	(	PUNCT
ejpam-298	246	3	∇zs)(x	∇zs)(x	NOUN
ejpam-298	246	4	,	,	PUNCT
ejpam-298	246	5	y	y	PROPN
ejpam-298	246	6	)	)	PUNCT
ejpam-298	246	7	=	=	SYM
ejpam-298	246	8	da(z	da(z	X
ejpam-298	246	9	)	)	PUNCT
ejpam-298	246	10	a	a	DET
ejpam-298	246	11	s(x	s(x	PROPN
ejpam-298	246	12	,	,	PUNCT
ejpam-298	246	13	y	y	PROPN
ejpam-298	246	14	)	)	PUNCT
ejpam-298	246	15	,	,	PUNCT
ejpam-298	246	16	i.e.	i.e.	X
ejpam-298	246	17	the	the	DET
ejpam-298	246	18	manifold	manifold	ADJ
ejpam-298	246	19	(	(	PUNCT
ejpam-298	246	20	m	m	NOUN
ejpam-298	246	21	n	n	CCONJ
ejpam-298	246	22	,	,	PUNCT
ejpam-298	246	23	g	g	NOUN
ejpam-298	246	24	)	)	PUNCT
ejpam-298	246	25	is	be	AUX
ejpam-298	246	26	ricci	ricci	PROPN
ejpam-298	246	27	recurrent	recurrent	NOUN
ejpam-298	246	28	.	.	PUNCT
ejpam-298	247	1	conversely	conversely	ADV
ejpam-298	247	2	,	,	PUNCT
ejpam-298	247	3	suppose	suppose	VERB
ejpam-298	247	4	that	that	SCONJ
ejpam-298	247	5	n(k)−	n(k)−	PROPN
ejpam-298	247	6	(	(	PUNCT
ejpam-298	247	7	mqe)n	mqe)n	PROPN
ejpam-298	247	8	manifold	manifold	NOUN
ejpam-298	247	9	is	be	AUX
ejpam-298	247	10	ricci	ricci	PROPN
ejpam-298	247	11	recurrent	recurrent	NOUN
ejpam-298	247	12	.	.	PUNCT
ejpam-298	248	1	then	then	ADV
ejpam-298	248	2	�	�	PROPN
ejpam-298	248	3	∇x	∇x	PROPN
ejpam-298	248	4	s	s	PART
ejpam-298	248	5	�	�	PROPN
ejpam-298	248	6	(	(	PUNCT
ejpam-298	248	7	y	y	PROPN
ejpam-298	248	8	,	,	PUNCT
ejpam-298	248	9	z	z	NOUN
ejpam-298	248	10	)	)	PUNCT
ejpam-298	248	11	=	=	SYM
ejpam-298	248	12	d(x	d(x	NOUN
ejpam-298	248	13	)	)	PUNCT
ejpam-298	248	14	s(y	s(y	PROPN
ejpam-298	248	15	,	,	PUNCT
ejpam-298	248	16	z	z	NOUN
ejpam-298	248	17	)	)	PUNCT
ejpam-298	248	18	,	,	PUNCT
ejpam-298	248	19	d(x	d(x	PROPN
ejpam-298	248	20	)	)	PUNCT
ejpam-298	249	1	6=	6=	ADP
ejpam-298	249	2	0	0	X
ejpam-298	249	3	.	.	PUNCT
ejpam-298	250	1	but	but	CCONJ
ejpam-298	250	2	�	�	PROPN
ejpam-298	250	3	∇x	∇x	PROPN
ejpam-298	250	4	s	s	PART
ejpam-298	250	5	�	�	PROPN
ejpam-298	250	6	(	(	PUNCT
ejpam-298	250	7	y	y	PROPN
ejpam-298	250	8	,	,	PUNCT
ejpam-298	250	9	z	z	NOUN
ejpam-298	250	10	)	)	PUNCT
ejpam-298	250	11	=	=	SYM
ejpam-298	250	12	x	x	PUNCT
ejpam-298	250	13	s(y	s(y	PROPN
ejpam-298	250	14	,	,	PUNCT
ejpam-298	250	15	z)−	z)−	PROPN
ejpam-298	250	16	s	s	PART
ejpam-298	250	17	�	�	PROPN
ejpam-298	250	18	∇x	∇x	PROPN
ejpam-298	250	19	y	y	PROPN
ejpam-298	250	20	,	,	PUNCT
ejpam-298	250	21	z	z	PROPN
ejpam-298	250	22	�	�	PROPN
ejpam-298	251	1	−	−	NOUN
ejpam-298	251	2	s	s	PART
ejpam-298	251	3	�	�	PROPN
ejpam-298	251	4	y,∇x	y,∇x	PROPN
ejpam-298	251	5	z	z	PROPN
ejpam-298	251	6	�	�	PROPN
ejpam-298	251	7	therefore	therefore	ADV
ejpam-298	251	8	d(x	d(x	PROPN
ejpam-298	251	9	)	)	PUNCT
ejpam-298	252	1	s(y	s(y	PROPN
ejpam-298	252	2	,	,	PUNCT
ejpam-298	252	3	z	z	NOUN
ejpam-298	252	4	)	)	PUNCT
ejpam-298	252	5	=	=	SYM
ejpam-298	253	1	x	x	PUNCT
ejpam-298	253	2	s(y	s(y	PROPN
ejpam-298	253	3	,	,	PUNCT
ejpam-298	253	4	z)−	z)−	PROPN
ejpam-298	253	5	s	s	PART
ejpam-298	253	6	�	�	PROPN
ejpam-298	253	7	∇x	∇x	PROPN
ejpam-298	253	8	y	y	PROPN
ejpam-298	253	9	,	,	PUNCT
ejpam-298	253	10	z	z	PROPN
ejpam-298	253	11	�	�	PROPN
ejpam-298	254	1	−	−	NOUN
ejpam-298	254	2	s	s	PART
ejpam-298	254	3	�	�	PROPN
ejpam-298	254	4	y,∇x	y,∇x	PROPN
ejpam-298	254	5	z	z	PROPN
ejpam-298	254	6	�	�	PROPN
ejpam-298	254	7	putting	put	VERB
ejpam-298	254	8	y	y	NOUN
ejpam-298	254	9	=	=	PUNCT
ejpam-298	254	10	z	z	NOUN
ejpam-298	254	11	=	=	SYM
ejpam-298	254	12	u	u	PROPN
ejpam-298	254	13	,	,	PUNCT
ejpam-298	254	14	we	we	PRON
ejpam-298	254	15	obtain	obtain	VERB
ejpam-298	254	16	x	x	SYM
ejpam-298	254	17	a−	a−	X
ejpam-298	254	18	ad(x	ad(x	PUNCT
ejpam-298	254	19	)	)	PUNCT
ejpam-298	255	1	=	=	SYM
ejpam-298	255	2	2a	2a	NUM
ejpam-298	255	3	�	�	PROPN
ejpam-298	255	4	g	g	PROPN
ejpam-298	255	5	�	�	PROPN
ejpam-298	255	6	∇x	∇x	PROPN
ejpam-298	255	7	u	u	NOUN
ejpam-298	255	8	,	,	PUNCT
ejpam-298	255	9	u	u	PROPN
ejpam-298	255	10	�	�	PROPN
ejpam-298	255	11	+	+	CCONJ
ejpam-298	255	12	b(∇x	b(∇x	NUM
ejpam-298	255	13	u	u	NOUN
ejpam-298	255	14	)	)	PUNCT
ejpam-298	255	15	�	�	PROPN
ejpam-298	255	16	i.e.	i.e.	X
ejpam-298	255	17	(	(	PUNCT
ejpam-298	255	18	da−	da−	NOUN
ejpam-298	255	19	ad)x	ad)x	PROPN
ejpam-298	255	20	=	=	SYM
ejpam-298	255	21	2ab(∇x	2ab(∇x	NUM
ejpam-298	255	22	u	u	NOUN
ejpam-298	255	23	)	)	PUNCT
ejpam-298	255	24	.	.	PUNCT
ejpam-298	256	1	since	since	SCONJ
ejpam-298	256	2	g(u	g(u	PROPN
ejpam-298	256	3	,	,	PUNCT
ejpam-298	256	4	u	u	NOUN
ejpam-298	256	5	)	)	PUNCT
ejpam-298	256	6	=	=	SYM
ejpam-298	256	7	1	1	NUM
ejpam-298	256	8	implies	imply	VERB
ejpam-298	256	9	g(∇x	g(∇x	NUM
ejpam-298	256	10	u	u	NOUN
ejpam-298	256	11	,	,	PUNCT
ejpam-298	256	12	u	u	NOUN
ejpam-298	256	13	)	)	PUNCT
ejpam-298	256	14	=	=	SYM
ejpam-298	256	15	0	0	NUM
ejpam-298	256	16	therefore	therefore	ADV
ejpam-298	256	17	b(∇x	b(∇x	NUM
ejpam-298	256	18	u	u	NOUN
ejpam-298	256	19	)	)	PUNCT
ejpam-298	256	20	=	=	SYM
ejpam-298	256	21	0	0	PUNCT
ejpam-298	257	1	if	if	SCONJ
ejpam-298	257	2	and	and	CCONJ
ejpam-298	257	3	only	only	ADV
ejpam-298	257	4	if	if	SCONJ
ejpam-298	257	5	(	(	PUNCT
ejpam-298	257	6	da)(x	da)(x	PROPN
ejpam-298	257	7	)	)	PUNCT
ejpam-298	257	8	=	=	NOUN
ejpam-298	257	9	ad(x	ad(x	X
ejpam-298	257	10	)	)	PUNCT
ejpam-298	257	11	(	(	PUNCT
ejpam-298	257	12	32	32	NUM
ejpam-298	257	13	)	)	PUNCT
ejpam-298	257	14	but	but	CCONJ
ejpam-298	257	15	b(∇x	b(∇x	NUM
ejpam-298	257	16	u	u	NOUN
ejpam-298	257	17	)	)	PUNCT
ejpam-298	257	18	=	=	SYM
ejpam-298	257	19	0	0	NUM
ejpam-298	257	20	implies	imply	VERB
ejpam-298	257	21	that	that	SCONJ
ejpam-298	257	22	either	either	CCONJ
ejpam-298	257	23	u	u	NOUN
ejpam-298	257	24	is	be	AUX
ejpam-298	257	25	a	a	DET
ejpam-298	257	26	parallel	parallel	ADJ
ejpam-298	257	27	vector	vector	NOUN
ejpam-298	257	28	field	field	NOUN
ejpam-298	257	29	or	or	CCONJ
ejpam-298	257	30	∇x	∇x	NOUN
ejpam-298	257	31	u	u	NOUN
ejpam-298	257	32	⊥	⊥	PROPN
ejpam-298	257	33	v.	v.	ADP
ejpam-298	257	34	similarly	similarly	ADV
ejpam-298	257	35	we	we	PRON
ejpam-298	257	36	have	have	VERB
ejpam-298	257	37	,	,	PUNCT
ejpam-298	257	38	if	if	SCONJ
ejpam-298	257	39	(	(	PUNCT
ejpam-298	257	40	32	32	NUM
ejpam-298	257	41	)	)	PUNCT
ejpam-298	257	42	holds	hold	VERB
ejpam-298	257	43	then	then	ADV
ejpam-298	257	44	either	either	CCONJ
ejpam-298	257	45	v	v	NOUN
ejpam-298	257	46	is	be	AUX
ejpam-298	257	47	a	a	DET
ejpam-298	257	48	parallel	parallel	ADJ
ejpam-298	257	49	vector	vector	NOUN
ejpam-298	257	50	field	field	NOUN
ejpam-298	257	51	or	or	CCONJ
ejpam-298	257	52	∇x	∇x	NOUN
ejpam-298	257	53	v	v	ADP
ejpam-298	257	54	⊥	⊥	NUM
ejpam-298	257	55	u	u	NOUN
ejpam-298	257	56	.	.	PUNCT
ejpam-298	258	1	thus	thus	ADV
ejpam-298	258	2	we	we	PRON
ejpam-298	258	3	can	can	AUX
ejpam-298	258	4	state	state	VERB
ejpam-298	258	5	that	that	PRON
ejpam-298	258	6	theorem	theorem	NOUN
ejpam-298	258	7	7	7	NUM
ejpam-298	258	8	.	.	PUNCT
ejpam-298	259	1	a	a	DET
ejpam-298	259	2	n(k)(mqe)n	n(k)(mqe)n	PROPN
ejpam-298	259	3	manifold	manifold	NOUN
ejpam-298	259	4	,	,	PUNCT
ejpam-298	259	5	where	where	SCONJ
ejpam-298	259	6	the	the	DET
ejpam-298	259	7	generators	generator	NOUN
ejpam-298	259	8	u	u	NOUN
ejpam-298	259	9	and	and	CCONJ
ejpam-298	259	10	v	v	NOUN
ejpam-298	259	11	are	be	AUX
ejpam-298	259	12	parallel	parallel	ADJ
ejpam-298	259	13	is	be	AUX
ejpam-298	259	14	a	a	DET
ejpam-298	259	15	ricci	ricci	NOUN
ejpam-298	259	16	recurrent	recurrent	NOUN
ejpam-298	259	17	manifold.conversely	manifold.conversely	ADV
ejpam-298	259	18	suppose	suppose	VERB
ejpam-298	259	19	that	that	SCONJ
ejpam-298	259	20	n(k	n(k	PROPN
ejpam-298	259	21	)	)	PUNCT
ejpam-298	259	22	−	−	PROPN
ejpam-298	260	1	(	(	PUNCT
ejpam-298	260	2	mqe)n	mqe)n	ADJ
ejpam-298	260	3	manifold	manifold	NOUN
ejpam-298	260	4	is	be	AUX
ejpam-298	260	5	ricci	ricci	PROPN
ejpam-298	260	6	recurrent	recurrent	NOUN
ejpam-298	260	7	,	,	PUNCT
ejpam-298	260	8	then	then	ADV
ejpam-298	260	9	either	either	CCONJ
ejpam-298	260	10	the	the	DET
ejpam-298	260	11	vector	vector	NOUN
ejpam-298	260	12	field	field	NOUN
ejpam-298	260	13	u	u	NOUN
ejpam-298	260	14	(	(	PUNCT
ejpam-298	260	15	or	or	CCONJ
ejpam-298	260	16	v	v	NOUN
ejpam-298	260	17	)	)	PUNCT
ejpam-298	260	18	is	be	AUX
ejpam-298	260	19	parallel	parallel	ADJ
ejpam-298	260	20	or	or	CCONJ
ejpam-298	260	21	∇x	∇x	NOUN
ejpam-298	260	22	u	u	NOUN
ejpam-298	260	23	⊥	⊥	PROPN
ejpam-298	260	24	v	v	NOUN
ejpam-298	260	25	(	(	PUNCT
ejpam-298	260	26	or	or	CCONJ
ejpam-298	260	27	∇x	∇x	PROPN
ejpam-298	260	28	v	v	NUM
ejpam-298	260	29	⊥	⊥	NUM
ejpam-298	260	30	u	u	NOUN
ejpam-298	260	31	)	)	PUNCT
ejpam-298	260	32	.	.	PUNCT
ejpam-298	261	1	references	reference	NOUN
ejpam-298	261	2	[	[	X
ejpam-298	261	3	1	1	NUM
ejpam-298	261	4	]	]	PUNCT
ejpam-298	261	5	m.c.chaki	m.c.chaki	NOUN
ejpam-298	261	6	and	and	CCONJ
ejpam-298	261	7	r.k.maity	r.k.maity	NOUN
ejpam-298	261	8	,	,	PUNCT
ejpam-298	261	9	on	on	ADP
ejpam-298	261	10	quasi	quasi	PROPN
ejpam-298	261	11	einstein	einstein	PROPN
ejpam-298	261	12	manifolds	manifolds	PROPN
ejpam-298	261	13	,	,	PUNCT
ejpam-298	261	14	publ	publ	NOUN
ejpam-298	261	15	.	.	PUNCT
ejpam-298	262	1	math	math	NOUN
ejpam-298	262	2	.	.	PUNCT
ejpam-298	263	1	debrecen	debrecen	PROPN
ejpam-298	263	2	,	,	PUNCT
ejpam-298	263	3	57(2000	57(2000	NUM
ejpam-298	263	4	)	)	PUNCT
ejpam-298	263	5	297	297	NUM
ejpam-298	263	6	-	-	SYM
ejpam-298	263	7	306	306	NUM
ejpam-298	263	8	.	.	PUNCT
ejpam-298	264	1	[	[	X
ejpam-298	264	2	2	2	NUM
ejpam-298	264	3	]	]	PUNCT
ejpam-298	264	4	b.y.chen	b.y.chen	NOUN
ejpam-298	264	5	,	,	PUNCT
ejpam-298	264	6	geometry	geometry	NOUN
ejpam-298	264	7	of	of	ADP
ejpam-298	264	8	submanifolds	submanifolds	PROPN
ejpam-298	264	9	,	,	PUNCT
ejpam-298	264	10	marcel	marcel	PROPN
ejpam-298	264	11	dekker	dekker	PROPN
ejpam-298	264	12	,	,	PUNCT
ejpam-298	264	13	inc	inc	PROPN
ejpam-298	264	14	.	.	PROPN
ejpam-298	264	15	,	,	PUNCT
ejpam-298	264	16	new	new	PROPN
ejpam-298	264	17	york	york	PROPN
ejpam-298	264	18	,	,	PUNCT
ejpam-298	264	19	1973	1973	NUM
ejpam-298	264	20	.	.	PUNCT
ejpam-298	265	1	[	[	X
ejpam-298	265	2	3	3	X
ejpam-298	265	3	]	]	X
ejpam-298	265	4	b.y.chen	b.y.chen	NOUN
ejpam-298	265	5	and	and	CCONJ
ejpam-298	265	6	k.	k.	PROPN
ejpam-298	265	7	yano	yano	PROPN
ejpam-298	265	8	,	,	PUNCT
ejpam-298	265	9	hypersurfaces	hypersurface	NOUN
ejpam-298	265	10	of	of	ADP
ejpam-298	265	11	a	a	DET
ejpam-298	265	12	conformally	conformally	ADV
ejpam-298	265	13	flat	flat	ADJ
ejpam-298	265	14	space	space	NOUN
ejpam-298	265	15	,	,	PUNCT
ejpam-298	265	16	tensor	tensor	NOUN
ejpam-298	265	17	,	,	PUNCT
ejpam-298	265	18	n.s	n.s	PROPN
ejpam-298	265	19	.	.	PROPN
ejpam-298	265	20	,	,	PUNCT
ejpam-298	265	21	26	26	NUM
ejpam-298	265	22	(	(	PUNCT
ejpam-298	265	23	1972	1972	NUM
ejpam-298	265	24	)	)	PUNCT
ejpam-298	265	25	318	318	NUM
ejpam-298	265	26	-	-	SYM
ejpam-298	265	27	322	322	NUM
ejpam-298	265	28	.	.	PUNCT
ejpam-298	266	1	[	[	X
ejpam-298	266	2	4	4	NUM
ejpam-298	266	3	]	]	PUNCT
ejpam-298	266	4	u.c.de	u.c.de	PROPN
ejpam-298	266	5	and	and	CCONJ
ejpam-298	266	6	gopal	gopal	PROPN
ejpam-298	266	7	chandra	chandra	PROPN
ejpam-298	266	8	ghosh	ghosh	PROPN
ejpam-298	266	9	,	,	PUNCT
ejpam-298	266	10	on	on	ADP
ejpam-298	266	11	quasi	quasi	PROPN
ejpam-298	266	12	einstein	einstein	PROPN
ejpam-298	266	13	manifolds	manifolds	PROPN
ejpam-298	266	14	,	,	PUNCT
ejpam-298	266	15	periodica	periodica	PROPN
ejpam-298	266	16	mathematica	mathematica	PROPN
ejpam-298	266	17	hungarica	hungarica	PROPN
ejpam-298	266	18	,	,	PUNCT
ejpam-298	266	19	48(1	48(1	NOUN
ejpam-298	266	20	-	-	PUNCT
ejpam-298	266	21	2)(2004	2)(2004	ADJ
ejpam-298	266	22	)	)	PUNCT
ejpam-298	266	23	223	223	NUM
ejpam-298	266	24	-	-	SYM
ejpam-298	266	25	231	231	NUM
ejpam-298	266	26	.	.	PUNCT
ejpam-298	267	1	[	[	X
ejpam-298	267	2	5	5	NUM
ejpam-298	267	3	]	]	PUNCT
ejpam-298	267	4	u.c.de	u.c.de	PROPN
ejpam-298	267	5	and	and	CCONJ
ejpam-298	267	6	gopal	gopal	PROPN
ejpam-298	267	7	chandra	chandra	PROPN
ejpam-298	267	8	ghosh	ghosh	PROPN
ejpam-298	267	9	,	,	PUNCT
ejpam-298	267	10	on	on	ADP
ejpam-298	267	11	generalized	generalize	VERB
ejpam-298	267	12	quasi	quasi	PROPN
ejpam-298	267	13	einstein	einstein	PROPN
ejpam-298	267	14	manifolds	manifolds	PROPN
ejpam-298	267	15	,	,	PUNCT
ejpam-298	267	16	kyungpook	kyungpook	PROPN
ejpam-298	267	17	math	math	NOUN
ejpam-298	267	18	.	.	PUNCT
ejpam-298	268	1	j.	j.	PROPN
ejpam-298	268	2	,	,	PUNCT
ejpam-298	268	3	44(2004	44(2004	PROPN
ejpam-298	268	4	)	)	PUNCT
ejpam-298	268	5	607	607	NUM
ejpam-298	268	6	-	-	SYM
ejpam-298	268	7	615	615	NUM
ejpam-298	268	8	.	.	PUNCT
ejpam-298	269	1	[	[	X
ejpam-298	269	2	6	6	NUM
ejpam-298	269	3	]	]	X
ejpam-298	269	4	mukut	mukut	PROPN
ejpam-298	269	5	mani	mani	PROPN
ejpam-298	269	6	tripathi	tripathi	PROPN
ejpam-298	269	7	and	and	CCONJ
ejpam-298	269	8	jeong	jeong	PROPN
ejpam-298	269	9	-	-	PUNCT
ejpam-298	269	10	sik	sik	PROPN
ejpam-298	269	11	kim	kim	PROPN
ejpam-298	269	12	,	,	PUNCT
ejpam-298	269	13	on	on	ADP
ejpam-298	269	14	n(k)-quasi	n(k)-quasi	PROPN
ejpam-298	269	15	einstein	einstein	NOUN
ejpam-298	269	16	manifolds	manifolds	PROPN
ejpam-298	269	17	,	,	PUNCT
ejpam-298	269	18	commun	commun	PROPN
ejpam-298	269	19	.	.	PUNCT
ejpam-298	270	1	korean	korean	ADJ
ejpam-298	270	2	math	math	PROPN
ejpam-298	270	3	.	.	PUNCT
ejpam-298	271	1	soc	soc	PROPN
ejpam-298	271	2	.	.	PUNCT
ejpam-298	272	1	22(3	22(3	NUM
ejpam-298	272	2	)	)	PUNCT
ejpam-298	272	3	(	(	PUNCT
ejpam-298	272	4	2007),411	2007),411	NUM
ejpam-298	272	5	-	-	SYM
ejpam-298	272	6	417	417	NUM
ejpam-298	272	7	.	.	PUNCT
ejpam-298	273	1	references	reference	NOUN
ejpam-298	273	2	25	25	NUM
ejpam-298	273	3	[	[	X
ejpam-298	273	4	7	7	NUM
ejpam-298	273	5	]	]	ADJ
ejpam-298	273	6	özgür	özgür	NOUN
ejpam-298	273	7	cihan	cihan	VERB
ejpam-298	273	8	and	and	CCONJ
ejpam-298	273	9	sular	sular	ADJ
ejpam-298	273	10	sibel	sibel	NOUN
ejpam-298	273	11	,	,	PUNCT
ejpam-298	273	12	on	on	ADP
ejpam-298	273	13	n(k)-quasi	n(k)-quasi	DET
ejpam-298	273	14	einstein	einstein	NOUN
ejpam-298	273	15	manifolds	manifold	NOUN
ejpam-298	273	16	satisfying	satisfy	VERB
ejpam-298	273	17	certain	certain	ADJ
ejpam-298	273	18	conditions	condition	NOUN
ejpam-298	273	19	,	,	PUNCT
ejpam-298	273	20	balkan	balkan	PROPN
ejpam-298	273	21	j.	j.	PROPN
ejpam-298	273	22	geom	geom	PROPN
ejpam-298	273	23	.	.	PUNCT
ejpam-298	274	1	appl	appl	PROPN
ejpam-298	274	2	.	.	PUNCT
ejpam-298	275	1	13(2008	13(2008	NUM
ejpam-298	275	2	)	)	PUNCT
ejpam-298	275	3	,	,	PUNCT
ejpam-298	275	4	no	no	INTJ
ejpam-298	275	5	:	:	SYM
ejpam-298	275	6	2	2	NUM
ejpam-298	275	7	,	,	PUNCT
ejpam-298	275	8	74	74	NUM
ejpam-298	275	9	-	-	SYM
ejpam-298	275	10	79	79	NUM
ejpam-298	275	11	.	.	PUNCT
ejpam-298	276	1	[	[	X
ejpam-298	276	2	8	8	NUM
ejpam-298	276	3	]	]	PUNCT
ejpam-298	276	4	s.tanno	s.tanno	NOUN
ejpam-298	276	5	,	,	PUNCT
ejpam-298	276	6	ricci	ricci	NOUN
ejpam-298	276	7	curvatures	curvature	NOUN
ejpam-298	276	8	of	of	ADP
ejpam-298	276	9	contact	contact	NOUN
ejpam-298	276	10	riemannian	riemannian	NOUN
ejpam-298	276	11	manifolds	manifold	NOUN
ejpam-298	276	12	,	,	PUNCT
ejpam-298	276	13	tohoku	tohoku	PROPN
ejpam-298	276	14	math	math	NOUN
ejpam-298	276	15	.	.	PUNCT
ejpam-298	277	1	j.	j.	PROPN
ejpam-298	277	2	40	40	NUM
ejpam-298	277	3	(	(	PUNCT
ejpam-298	277	4	1988	1988	NUM
ejpam-298	277	5	)	)	PUNCT
ejpam-298	277	6	441	441	NUM
ejpam-298	277	7	-	-	SYM
ejpam-298	277	8	448	448	NUM
ejpam-298	277	9	.	.	PUNCT