id	sid	tid	token	lemma	pos
ejpam-1677	1	1	7_hui.dvi	7_hui.dvi	PROPN
ejpam-1677	1	2	european	european	PROPN
ejpam-1677	1	3	journal	journal	PROPN
ejpam-1677	1	4	of	of	ADP
ejpam-1677	1	5	pure	pure	ADJ
ejpam-1677	1	6	and	and	CCONJ
ejpam-1677	1	7	applied	apply	VERB
ejpam-1677	1	8	mathematics	mathematic	NOUN
ejpam-1677	1	9	vol	vol	NOUN
ejpam-1677	1	10	.	.	PROPN
ejpam-1677	1	11	5	5	NUM
ejpam-1677	1	12	,	,	PUNCT
ejpam-1677	1	13	no	no	INTJ
ejpam-1677	1	14	.	.	NOUN
ejpam-1677	1	15	3	3	NUM
ejpam-1677	1	16	,	,	PUNCT
ejpam-1677	1	17	2012	2012	NUM
ejpam-1677	1	18	,	,	PUNCT
ejpam-1677	1	19	365	365	NUM
ejpam-1677	1	20	-	-	SYM
ejpam-1677	1	21	372	372	NUM
ejpam-1677	1	22	issn	issn	PROPN
ejpam-1677	1	23	1307	1307	NUM
ejpam-1677	1	24	-	-	SYM
ejpam-1677	1	25	5543	5543	NUM
ejpam-1677	1	26	–	–	PUNCT
ejpam-1677	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1677	1	28	a	a	DET
ejpam-1677	1	29	note	note	NOUN
ejpam-1677	1	30	on	on	ADP
ejpam-1677	1	31	nearly	nearly	ADV
ejpam-1677	1	32	quasi	quasi	ADJ
ejpam-1677	1	33	-	-	ADJ
ejpam-1677	1	34	einstein	einstein	ADJ
ejpam-1677	1	35	manifolds	manifolds	PROPN
ejpam-1677	1	36	shyamal	shyamal	PROPN
ejpam-1677	1	37	kumar	kumar	PROPN
ejpam-1677	1	38	hui	hui	PROPN
ejpam-1677	1	39	nikhil	nikhil	PROPN
ejpam-1677	1	40	banga	banga	PROPN
ejpam-1677	1	41	sikshan	sikshan	PROPN
ejpam-1677	1	42	mahavidyalya	mahavidyalya	ADV
ejpam-1677	1	43	,	,	PUNCT
ejpam-1677	1	44	bishnupur	bishnupur	NOUN
ejpam-1677	1	45	,	,	PUNCT
ejpam-1677	1	46	bankura	bankura	NOUN
ejpam-1677	1	47	722	722	NUM
ejpam-1677	1	48	122	122	NUM
ejpam-1677	1	49	,	,	PUNCT
ejpam-1677	1	50	west	west	PROPN
ejpam-1677	1	51	bengal	bengal	PROPN
ejpam-1677	1	52	,	,	PUNCT
ejpam-1677	1	53	india	india	PROPN
ejpam-1677	1	54	abstract	abstract	NOUN
ejpam-1677	1	55	.	.	PUNCT
ejpam-1677	2	1	the	the	DET
ejpam-1677	2	2	object	object	NOUN
ejpam-1677	2	3	of	of	ADP
ejpam-1677	2	4	the	the	DET
ejpam-1677	2	5	present	present	ADJ
ejpam-1677	2	6	paper	paper	NOUN
ejpam-1677	2	7	is	be	AUX
ejpam-1677	2	8	to	to	PART
ejpam-1677	2	9	study	study	VERB
ejpam-1677	2	10	nearly	nearly	ADV
ejpam-1677	2	11	quasi	quasi	ADJ
ejpam-1677	2	12	-	-	ADJ
ejpam-1677	2	13	einstein	einstein	ADJ
ejpam-1677	2	14	manifold	manifold	NOUN
ejpam-1677	2	15	.	.	PUNCT
ejpam-1677	3	1	also	also	ADV
ejpam-1677	3	2	we	we	PRON
ejpam-1677	3	3	have	have	AUX
ejpam-1677	3	4	studied	study	VERB
ejpam-1677	3	5	decomposable	decomposable	ADJ
ejpam-1677	3	6	riemannian	riemannian	NOUN
ejpam-1677	3	7	manifold	manifold	NOUN
ejpam-1677	3	8	and	and	CCONJ
ejpam-1677	3	9	it	it	PRON
ejpam-1677	3	10	is	be	AUX
ejpam-1677	3	11	shown	show	VERB
ejpam-1677	3	12	that	that	SCONJ
ejpam-1677	3	13	a	a	DET
ejpam-1677	3	14	decomposable	decomposable	ADJ
ejpam-1677	3	15	riemannian	riemannian	NOUN
ejpam-1677	3	16	manifold	manifold	NOUN
ejpam-1677	3	17	is	be	AUX
ejpam-1677	3	18	nearly	nearly	ADV
ejpam-1677	3	19	quasi	quasi	ADJ
ejpam-1677	3	20	-	-	NOUN
ejpam-1677	3	21	einstein	einstein	ADJ
ejpam-1677	4	1	if	if	SCONJ
ejpam-1677	4	2	and	and	CCONJ
ejpam-1677	4	3	only	only	ADV
ejpam-1677	4	4	if	if	SCONJ
ejpam-1677	4	5	both	both	CCONJ
ejpam-1677	4	6	the	the	DET
ejpam-1677	4	7	decompositions	decomposition	NOUN
ejpam-1677	4	8	are	be	AUX
ejpam-1677	4	9	einstein	einstein	ADJ
ejpam-1677	4	10	.	.	PUNCT
ejpam-1677	5	1	2010	2010	NUM
ejpam-1677	5	2	mathematics	mathematic	NOUN
ejpam-1677	5	3	subject	subject	NOUN
ejpam-1677	5	4	classifications	classification	NOUN
ejpam-1677	5	5	:	:	PUNCT
ejpam-1677	5	6	53b30	53b30	NUM
ejpam-1677	5	7	,	,	PUNCT
ejpam-1677	5	8	53b50	53b50	NUM
ejpam-1677	5	9	,	,	PUNCT
ejpam-1677	5	10	53c15	53c15	NUM
ejpam-1677	5	11	,	,	PUNCT
ejpam-1677	5	12	53c25	53c25	NUM
ejpam-1677	5	13	key	key	ADJ
ejpam-1677	5	14	words	word	NOUN
ejpam-1677	5	15	and	and	CCONJ
ejpam-1677	5	16	phrases	phrase	NOUN
ejpam-1677	5	17	:	:	PUNCT
ejpam-1677	5	18	quasi	quasi	ADJ
ejpam-1677	5	19	-	-	ADJ
ejpam-1677	5	20	einstein	einstein	ADJ
ejpam-1677	5	21	manifold	manifold	NOUN
ejpam-1677	5	22	,	,	PUNCT
ejpam-1677	5	23	nearly	nearly	ADV
ejpam-1677	5	24	quasi	quasi	ADJ
ejpam-1677	5	25	-	-	ADJ
ejpam-1677	5	26	einstein	einstein	ADJ
ejpam-1677	5	27	manifold	manifold	NOUN
ejpam-1677	5	28	,	,	PUNCT
ejpam-1677	5	29	ricci	ricci	PROPN
ejpam-1677	5	30	-	-	PUNCT
ejpam-1677	5	31	pseudosymmetric	pseudosymmetric	ADJ
ejpam-1677	5	32	,	,	PUNCT
ejpam-1677	5	33	scalar	scalar	ADJ
ejpam-1677	5	34	curvature	curvature	NOUN
ejpam-1677	5	35	,	,	PUNCT
ejpam-1677	5	36	decomposable	decomposable	ADJ
ejpam-1677	5	37	riemannian	riemannian	ADJ
ejpam-1677	5	38	manifold	manifold	NOUN
ejpam-1677	5	39	,	,	PUNCT
ejpam-1677	5	40	killing	kill	VERB
ejpam-1677	5	41	vector	vector	NOUN
ejpam-1677	5	42	field	field	NOUN
ejpam-1677	5	43	,	,	PUNCT
ejpam-1677	5	44	projective	projective	ADJ
ejpam-1677	5	45	killing	kill	VERB
ejpam-1677	5	46	vector	vector	NOUN
ejpam-1677	5	47	field	field	NOUN
ejpam-1677	5	48	1	1	NUM
ejpam-1677	5	49	.	.	PUNCT
ejpam-1677	6	1	introduction	introduction	NOUN
ejpam-1677	6	2	it	it	PRON
ejpam-1677	6	3	is	be	AUX
ejpam-1677	6	4	well	well	ADV
ejpam-1677	6	5	known	know	VERB
ejpam-1677	6	6	that	that	SCONJ
ejpam-1677	6	7	a	a	DET
ejpam-1677	6	8	riemannian	riemannian	ADJ
ejpam-1677	6	9	manifold	manifold	NOUN
ejpam-1677	6	10	(	(	PUNCT
ejpam-1677	6	11	m	m	NOUN
ejpam-1677	6	12	n	n	CCONJ
ejpam-1677	6	13	,	,	PUNCT
ejpam-1677	6	14	g)(n	g)(n	PROPN
ejpam-1677	6	15	>	>	X
ejpam-1677	6	16	2	2	NUM
ejpam-1677	6	17	)	)	PUNCT
ejpam-1677	6	18	is	be	AUX
ejpam-1677	6	19	einstein	einstein	ADJ
ejpam-1677	6	20	if	if	SCONJ
ejpam-1677	6	21	its	its	PRON
ejpam-1677	6	22	ricci	ricci	PROPN
ejpam-1677	6	23	tensor	tensor	NOUN
ejpam-1677	6	24	s	s	PROPN
ejpam-1677	6	25	of	of	ADP
ejpam-1677	6	26	type	type	NOUN
ejpam-1677	6	27	(	(	PUNCT
ejpam-1677	6	28	0,2	0,2	NUM
ejpam-1677	6	29	)	)	PUNCT
ejpam-1677	6	30	is	be	AUX
ejpam-1677	6	31	of	of	ADP
ejpam-1677	6	32	the	the	DET
ejpam-1677	6	33	form	form	NOUN
ejpam-1677	6	34	s	s	PART
ejpam-1677	6	35	=	=	NOUN
ejpam-1677	6	36	αg	αg	NOUN
ejpam-1677	6	37	,	,	PUNCT
ejpam-1677	6	38	where	where	SCONJ
ejpam-1677	6	39	α	α	NOUN
ejpam-1677	6	40	is	be	AUX
ejpam-1677	6	41	a	a	DET
ejpam-1677	6	42	constant	constant	ADJ
ejpam-1677	6	43	,	,	PUNCT
ejpam-1677	6	44	which	which	PRON
ejpam-1677	6	45	reduces	reduce	VERB
ejpam-1677	6	46	to	to	ADP
ejpam-1677	6	47	s	s	PART
ejpam-1677	6	48	=	=	NOUN
ejpam-1677	6	49	r	r	NOUN
ejpam-1677	6	50	n	n	NOUN
ejpam-1677	6	51	g	g	NOUN
ejpam-1677	6	52	,	,	PUNCT
ejpam-1677	6	53	r	r	NOUN
ejpam-1677	6	54	being	be	AUX
ejpam-1677	6	55	the	the	DET
ejpam-1677	6	56	scalar	scalar	ADJ
ejpam-1677	6	57	curvature	curvature	NOUN
ejpam-1677	6	58	(	(	PUNCT
ejpam-1677	6	59	constant	constant	ADJ
ejpam-1677	6	60	)	)	PUNCT
ejpam-1677	6	61	of	of	ADP
ejpam-1677	6	62	the	the	DET
ejpam-1677	6	63	manifold	manifold	NOUN
ejpam-1677	6	64	.	.	PUNCT
ejpam-1677	7	1	the	the	DET
ejpam-1677	7	2	notion	notion	NOUN
ejpam-1677	7	3	of	of	ADP
ejpam-1677	7	4	quasi	quasi	ADJ
ejpam-1677	7	5	-	-	ADJ
ejpam-1677	7	6	einstein	einstein	ADJ
ejpam-1677	7	7	manifolds	manifold	NOUN
ejpam-1677	7	8	arose	arise	VERB
ejpam-1677	7	9	during	during	ADP
ejpam-1677	7	10	the	the	DET
ejpam-1677	7	11	study	study	NOUN
ejpam-1677	7	12	of	of	ADP
ejpam-1677	7	13	exact	exact	ADJ
ejpam-1677	7	14	solutions	solution	NOUN
ejpam-1677	7	15	of	of	ADP
ejpam-1677	7	16	the	the	DET
ejpam-1677	7	17	einstein	einstein	ADJ
ejpam-1677	7	18	field	field	NOUN
ejpam-1677	7	19	equations	equation	NOUN
ejpam-1677	7	20	as	as	ADV
ejpam-1677	7	21	well	well	ADV
ejpam-1677	7	22	as	as	ADP
ejpam-1677	7	23	during	during	ADP
ejpam-1677	7	24	considerations	consideration	NOUN
ejpam-1677	7	25	of	of	ADP
ejpam-1677	7	26	quasi	quasi	ADJ
ejpam-1677	7	27	-	-	ADJ
ejpam-1677	7	28	umbilical	umbilical	ADJ
ejpam-1677	7	29	hypersurfaces	hypersurface	NOUN
ejpam-1677	7	30	.	.	PUNCT
ejpam-1677	8	1	for	for	ADP
ejpam-1677	8	2	instance	instance	NOUN
ejpam-1677	8	3	,	,	PUNCT
ejpam-1677	8	4	the	the	DET
ejpam-1677	8	5	robertson	robertson	PROPN
ejpam-1677	8	6	-	-	PUNCT
ejpam-1677	8	7	walker	walker	PROPN
ejpam-1677	8	8	spacetimes	spacetime	NOUN
ejpam-1677	8	9	are	be	AUX
ejpam-1677	8	10	quasi	quasi	ADJ
ejpam-1677	8	11	-	-	ADJ
ejpam-1677	8	12	einstein	einstein	ADJ
ejpam-1677	8	13	manifolds	manifold	NOUN
ejpam-1677	8	14	.	.	PUNCT
ejpam-1677	9	1	a	a	DET
ejpam-1677	9	2	non	non	ADJ
ejpam-1677	9	3	-	-	ADJ
ejpam-1677	9	4	flat	flat	ADJ
ejpam-1677	9	5	riemannian	riemannian	ADJ
ejpam-1677	9	6	manifold	manifold	NOUN
ejpam-1677	9	7	(	(	PUNCT
ejpam-1677	9	8	m	m	NOUN
ejpam-1677	9	9	n	n	CCONJ
ejpam-1677	9	10	,	,	PUNCT
ejpam-1677	9	11	g)(n	g)(n	PROPN
ejpam-1677	9	12	>	>	X
ejpam-1677	9	13	2	2	NUM
ejpam-1677	9	14	)	)	PUNCT
ejpam-1677	9	15	is	be	AUX
ejpam-1677	9	16	said	say	VERB
ejpam-1677	9	17	to	to	PART
ejpam-1677	9	18	be	be	AUX
ejpam-1677	9	19	quasi	quasi	ADJ
ejpam-1677	9	20	-	-	ADJ
ejpam-1677	9	21	einstein	einstein	ADJ
ejpam-1677	9	22	manifold	manifold	NOUN
ejpam-1677	10	1	[	[	X
ejpam-1677	10	2	1	1	NUM
ejpam-1677	10	3	,	,	PUNCT
ejpam-1677	10	4	3	3	NUM
ejpam-1677	10	5	,	,	PUNCT
ejpam-1677	10	6	5	5	NUM
ejpam-1677	10	7	,	,	PUNCT
ejpam-1677	10	8	6	6	NUM
ejpam-1677	10	9	,	,	PUNCT
ejpam-1677	10	10	7	7	NUM
ejpam-1677	10	11	,	,	PUNCT
ejpam-1677	10	12	8	8	NUM
ejpam-1677	10	13	,	,	PUNCT
ejpam-1677	10	14	9	9	NUM
ejpam-1677	10	15	,	,	PUNCT
ejpam-1677	10	16	10	10	NUM
ejpam-1677	10	17	,	,	PUNCT
ejpam-1677	10	18	11	11	NUM
ejpam-1677	10	19	,	,	PUNCT
ejpam-1677	10	20	12	12	NUM
ejpam-1677	10	21	,	,	PUNCT
ejpam-1677	10	22	15	15	NUM
ejpam-1677	10	23	,	,	PUNCT
ejpam-1677	10	24	16	16	NUM
ejpam-1677	10	25	]	]	PUNCT
ejpam-1677	10	26	if	if	SCONJ
ejpam-1677	10	27	its	its	PRON
ejpam-1677	10	28	ricci	ricci	PROPN
ejpam-1677	10	29	tensor	tensor	NOUN
ejpam-1677	10	30	s	s	PROPN
ejpam-1677	10	31	of	of	ADP
ejpam-1677	10	32	type	type	NOUN
ejpam-1677	10	33	(	(	PUNCT
ejpam-1677	10	34	0,2	0,2	NUM
ejpam-1677	10	35	)	)	PUNCT
ejpam-1677	10	36	is	be	AUX
ejpam-1677	10	37	not	not	PART
ejpam-1677	10	38	identically	identically	ADV
ejpam-1677	10	39	zero	zero	NUM
ejpam-1677	10	40	and	and	CCONJ
ejpam-1677	10	41	satisfies	satisfy	VERB
ejpam-1677	10	42	the	the	DET
ejpam-1677	10	43	following	follow	VERB
ejpam-1677	10	44	:	:	PUNCT
ejpam-1677	10	45	s(x	s(x	NOUN
ejpam-1677	10	46	,	,	PUNCT
ejpam-1677	10	47	y	y	PROPN
ejpam-1677	10	48	)	)	PUNCT
ejpam-1677	11	1	=	=	PRON
ejpam-1677	11	2	αg(x	αg(x	X
ejpam-1677	11	3	,	,	PUNCT
ejpam-1677	11	4	y	y	PROPN
ejpam-1677	11	5	)	)	PUNCT
ejpam-1677	12	1	+	+	CCONJ
ejpam-1677	12	2	βa(x	βa(x	X
ejpam-1677	12	3	)	)	PUNCT
ejpam-1677	12	4	a(y	a(y	PROPN
ejpam-1677	12	5	)	)	PUNCT
ejpam-1677	12	6	,	,	PUNCT
ejpam-1677	12	7	(	(	PUNCT
ejpam-1677	12	8	1	1	X
ejpam-1677	12	9	)	)	PUNCT
ejpam-1677	12	10	where	where	SCONJ
ejpam-1677	12	11	α	α	X
ejpam-1677	12	12	,	,	PUNCT
ejpam-1677	12	13	β	β	X
ejpam-1677	12	14	are	be	AUX
ejpam-1677	12	15	scalars	scalar	NOUN
ejpam-1677	12	16	of	of	ADP
ejpam-1677	12	17	which	which	PRON
ejpam-1677	12	18	β	β	PROPN
ejpam-1677	12	19	6=	6=	ADP
ejpam-1677	12	20	0	0	NUM
ejpam-1677	12	21	and	and	CCONJ
ejpam-1677	12	22	a	a	PRON
ejpam-1677	12	23	is	be	AUX
ejpam-1677	12	24	a	a	DET
ejpam-1677	12	25	nowhere	nowhere	ADV
ejpam-1677	12	26	vanishing	vanish	VERB
ejpam-1677	12	27	1	1	NUM
ejpam-1677	12	28	-	-	PUNCT
ejpam-1677	12	29	form	form	NOUN
ejpam-1677	12	30	defined	define	VERB
ejpam-1677	12	31	by	by	ADP
ejpam-1677	12	32	g(x	g(x	PROPN
ejpam-1677	12	33	,	,	PUNCT
ejpam-1677	12	34	ρ	ρ	NOUN
ejpam-1677	12	35	)	)	PUNCT
ejpam-1677	12	36	=	=	SYM
ejpam-1677	12	37	a(x	a(x	NOUN
ejpam-1677	12	38	)	)	PUNCT
ejpam-1677	12	39	for	for	ADP
ejpam-1677	12	40	all	all	DET
ejpam-1677	12	41	x	x	PROPN
ejpam-1677	12	42	;	;	PUNCT
ejpam-1677	12	43	ρ	ρ	PROPN
ejpam-1677	12	44	being	be	AUX
ejpam-1677	12	45	a	a	DET
ejpam-1677	12	46	unit	unit	NOUN
ejpam-1677	12	47	vector	vector	NOUN
ejpam-1677	12	48	field	field	NOUN
ejpam-1677	12	49	,	,	PUNCT
ejpam-1677	12	50	called	call	VERB
ejpam-1677	12	51	the	the	DET
ejpam-1677	12	52	generator	generator	NOUN
ejpam-1677	12	53	of	of	ADP
ejpam-1677	12	54	the	the	DET
ejpam-1677	12	55	manifold	manifold	NOUN
ejpam-1677	12	56	.	.	PUNCT
ejpam-1677	13	1	such	such	DET
ejpam-1677	13	2	an	an	DET
ejpam-1677	13	3	n	n	ADV
ejpam-1677	13	4	-	-	PUNCT
ejpam-1677	13	5	dimensional	dimensional	ADJ
ejpam-1677	13	6	quasi	quasi	ADJ
ejpam-1677	13	7	-	-	ADJ
ejpam-1677	13	8	einstein	einstein	ADJ
ejpam-1677	13	9	manifold	manifold	NOUN
ejpam-1677	13	10	is	be	AUX
ejpam-1677	13	11	denoted	denote	VERB
ejpam-1677	13	12	by	by	ADP
ejpam-1677	13	13	(	(	PUNCT
ejpam-1677	13	14	qe)n	qe)n	PROPN
ejpam-1677	13	15	.	.	NOUN
ejpam-1677	13	16	the	the	DET
ejpam-1677	13	17	scalars	scalars	PROPN
ejpam-1677	13	18	α	α	PROPN
ejpam-1677	13	19	,	,	PUNCT
ejpam-1677	13	20	β	β	X
ejpam-1677	13	21	are	be	AUX
ejpam-1677	13	22	known	know	VERB
ejpam-1677	13	23	as	as	ADP
ejpam-1677	13	24	the	the	DET
ejpam-1677	13	25	associated	associate	VERB
ejpam-1677	13	26	scalars	scalar	NOUN
ejpam-1677	13	27	of	of	ADP
ejpam-1677	13	28	the	the	DET
ejpam-1677	13	29	manifold	manifold	NOUN
ejpam-1677	13	30	.	.	PUNCT
ejpam-1677	14	1	also	also	ADV
ejpam-1677	14	2	the	the	DET
ejpam-1677	14	3	1	1	NUM
ejpam-1677	14	4	-	-	PUNCT
ejpam-1677	14	5	form	form	NOUN
ejpam-1677	14	6	a	a	NOUN
ejpam-1677	14	7	is	be	AUX
ejpam-1677	14	8	called	call	VERB
ejpam-1677	14	9	the	the	DET
ejpam-1677	14	10	associated	associated	ADJ
ejpam-1677	14	11	1	1	NUM
ejpam-1677	14	12	-	-	PUNCT
ejpam-1677	14	13	form	form	NOUN
ejpam-1677	14	14	of	of	ADP
ejpam-1677	14	15	the	the	DET
ejpam-1677	14	16	manifold	manifold	NOUN
ejpam-1677	14	17	.	.	PUNCT
ejpam-1677	15	1	from	from	ADP
ejpam-1677	15	2	the	the	DET
ejpam-1677	15	3	above	above	ADJ
ejpam-1677	15	4	definition	definition	NOUN
ejpam-1677	15	5	it	it	PRON
ejpam-1677	15	6	follows	follow	VERB
ejpam-1677	15	7	that	that	SCONJ
ejpam-1677	15	8	every	every	DET
ejpam-1677	15	9	einstein	einstein	NOUN
ejpam-1677	15	10	manifold	manifold	NOUN
ejpam-1677	15	11	is	be	AUX
ejpam-1677	15	12	quasi	quasi	ADJ
ejpam-1677	15	13	-	-	NOUN
ejpam-1677	15	14	einstein	einstein	NOUN
ejpam-1677	15	15	.	.	PUNCT
ejpam-1677	16	1	in	in	ADP
ejpam-1677	16	2	particular	particular	ADJ
ejpam-1677	16	3	,	,	PUNCT
ejpam-1677	16	4	every	every	DET
ejpam-1677	16	5	ricci	ricci	NOUN
ejpam-1677	16	6	-	-	PUNCT
ejpam-1677	16	7	flat	flat	ADJ
ejpam-1677	16	8	(	(	PUNCT
ejpam-1677	16	9	e.g.	e.g.	ADV
ejpam-1677	16	10	schwarzschild	schwarzschild	NOUN
ejpam-1677	16	11	spacetime	spacetime	NOUN
ejpam-1677	16	12	)	)	PUNCT
ejpam-1677	16	13	manifold	manifold	NOUN
ejpam-1677	16	14	is	be	AUX
ejpam-1677	16	15	quasi	quasi	NOUN
ejpam-1677	16	16	-	-	NOUN
ejpam-1677	16	17	einstein	einstein	NOUN
ejpam-1677	16	18	.	.	PUNCT
ejpam-1677	17	1	recently	recently	ADV
ejpam-1677	17	2	the	the	DET
ejpam-1677	17	3	notion	notion	NOUN
ejpam-1677	17	4	of	of	ADP
ejpam-1677	17	5	quasi	quasi	ADJ
ejpam-1677	17	6	-	-	ADJ
ejpam-1677	17	7	einstein	einstein	ADJ
ejpam-1677	17	8	manifold	manifold	NOUN
ejpam-1677	17	9	have	have	AUX
ejpam-1677	17	10	been	be	AUX
ejpam-1677	17	11	weakened	weaken	VERB
ejpam-1677	17	12	by	by	ADP
ejpam-1677	17	13	de	de	ADP
ejpam-1677	17	14	and	and	CCONJ
ejpam-1677	17	15	gaji	gaji	NOUN
ejpam-1677	17	16	[	[	X
ejpam-1677	17	17	2	2	NUM
ejpam-1677	17	18	,	,	PUNCT
ejpam-1677	17	19	14	14	NUM
ejpam-1677	17	20	]	]	PUNCT
ejpam-1677	17	21	and	and	CCONJ
ejpam-1677	17	22	they	they	PRON
ejpam-1677	17	23	introduced	introduce	VERB
ejpam-1677	17	24	the	the	DET
ejpam-1677	17	25	notion	notion	NOUN
ejpam-1677	17	26	of	of	ADP
ejpam-1677	17	27	nearly	nearly	ADV
ejpam-1677	17	28	quasi	quasi	ADJ
ejpam-1677	17	29	-	-	ADJ
ejpam-1677	17	30	einstein	einstein	ADJ
ejpam-1677	17	31	manifold	manifold	NOUN
ejpam-1677	17	32	with	with	ADP
ejpam-1677	17	33	the	the	DET
ejpam-1677	17	34	existence	existence	NOUN
ejpam-1677	17	35	of	of	ADP
ejpam-1677	17	36	such	such	ADJ
ejpam-1677	17	37	email	email	NOUN
ejpam-1677	17	38	address	address	NOUN
ejpam-1677	17	39	:	:	PUNCT
ejpam-1677	17	40	shyamal_hui	shyamal_hui	PROPN
ejpam-1677	17	41	�	�	PROPN
ejpam-1677	17	42	yahoo	yahoo	PROPN
ejpam-1677	17	43	.	.	PUNCT
ejpam-1677	18	1	o.in	o.in	AUX
ejpam-1677	18	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1677	18	3	365	365	NUM
ejpam-1677	18	4	c	c	NOUN
ejpam-1677	18	5	©	©	PROPN
ejpam-1677	18	6	2012	2012	NUM
ejpam-1677	18	7	ejpam	ejpam	VERB
ejpam-1677	18	8	all	all	DET
ejpam-1677	18	9	rights	right	NOUN
ejpam-1677	18	10	reserved	reserve	VERB
ejpam-1677	18	11	.	.	PUNCT
ejpam-1677	19	1	s.	s.	PROPN
ejpam-1677	19	2	hui	hui	PROPN
ejpam-1677	19	3	/	/	SYM
ejpam-1677	19	4	eur	eur	PROPN
ejpam-1677	19	5	.	.	PUNCT
ejpam-1677	20	1	j.	j.	PROPN
ejpam-1677	20	2	pure	pure	PROPN
ejpam-1677	20	3	appl	appl	PROPN
ejpam-1677	20	4	.	.	PROPN
ejpam-1677	20	5	math	math	PROPN
ejpam-1677	20	6	,	,	PUNCT
ejpam-1677	20	7	5	5	NUM
ejpam-1677	20	8	(	(	PUNCT
ejpam-1677	20	9	2012	2012	NUM
ejpam-1677	20	10	)	)	PUNCT
ejpam-1677	20	11	,	,	PUNCT
ejpam-1677	20	12	365	365	NUM
ejpam-1677	20	13	-	-	SYM
ejpam-1677	20	14	372	372	NUM
ejpam-1677	20	15	366	366	NUM
ejpam-1677	20	16	notion	notion	NOUN
ejpam-1677	20	17	.	.	PUNCT
ejpam-1677	21	1	a	a	DET
ejpam-1677	21	2	riemannian	riemannian	ADJ
ejpam-1677	21	3	manifold	manifold	NOUN
ejpam-1677	21	4	(	(	PUNCT
ejpam-1677	21	5	m	m	NOUN
ejpam-1677	21	6	n	n	CCONJ
ejpam-1677	21	7	,	,	PUNCT
ejpam-1677	21	8	g)(n	g)(n	PROPN
ejpam-1677	21	9	>	>	X
ejpam-1677	21	10	2	2	NUM
ejpam-1677	21	11	)	)	PUNCT
ejpam-1677	21	12	is	be	AUX
ejpam-1677	21	13	called	call	VERB
ejpam-1677	21	14	nearly	nearly	ADV
ejpam-1677	21	15	quasi	quasi	NOUN
ejpam-1677	21	16	-	-	NOUN
ejpam-1677	21	17	einstein	einstein	ADJ
ejpam-1677	21	18	if	if	SCONJ
ejpam-1677	21	19	its	its	PRON
ejpam-1677	21	20	ricci	ricci	PROPN
ejpam-1677	21	21	tensor	tensor	NOUN
ejpam-1677	21	22	s	s	PART
ejpam-1677	21	23	is	be	AUX
ejpam-1677	21	24	not	not	PART
ejpam-1677	21	25	identically	identically	ADV
ejpam-1677	21	26	zero	zero	NUM
ejpam-1677	21	27	and	and	CCONJ
ejpam-1677	21	28	satisfies	satisfy	VERB
ejpam-1677	21	29	the	the	DET
ejpam-1677	21	30	condition	condition	NOUN
ejpam-1677	21	31	s(x	s(x	NOUN
ejpam-1677	21	32	,	,	PUNCT
ejpam-1677	21	33	y	y	PROPN
ejpam-1677	21	34	)	)	PUNCT
ejpam-1677	22	1	=	=	PRON
ejpam-1677	22	2	αg(x	αg(x	X
ejpam-1677	22	3	,	,	PUNCT
ejpam-1677	22	4	y	y	PROPN
ejpam-1677	22	5	)	)	PUNCT
ejpam-1677	23	1	+	+	CCONJ
ejpam-1677	23	2	βd(x	βd(x	PUNCT
ejpam-1677	23	3	,	,	PUNCT
ejpam-1677	23	4	y	y	PROPN
ejpam-1677	23	5	)	)	PUNCT
ejpam-1677	23	6	,	,	PUNCT
ejpam-1677	23	7	(	(	PUNCT
ejpam-1677	23	8	2	2	X
ejpam-1677	23	9	)	)	PUNCT
ejpam-1677	23	10	where	where	SCONJ
ejpam-1677	23	11	α	α	X
ejpam-1677	23	12	,	,	PUNCT
ejpam-1677	23	13	β	β	X
ejpam-1677	23	14	are	be	AUX
ejpam-1677	23	15	non	non	ADJ
ejpam-1677	23	16	-	-	ADJ
ejpam-1677	23	17	zero	zero	ADJ
ejpam-1677	23	18	scalars	scalar	NOUN
ejpam-1677	23	19	and	and	CCONJ
ejpam-1677	23	20	d	d	NOUN
ejpam-1677	23	21	is	be	AUX
ejpam-1677	23	22	a	a	DET
ejpam-1677	23	23	symmetric	symmetric	ADJ
ejpam-1677	23	24	non	non	ADJ
ejpam-1677	23	25	-	-	ADJ
ejpam-1677	23	26	zero	zero	NUM
ejpam-1677	23	27	(	(	PUNCT
ejpam-1677	23	28	0	0	NUM
ejpam-1677	23	29	,	,	PUNCT
ejpam-1677	23	30	2	2	NUM
ejpam-1677	23	31	)	)	PUNCT
ejpam-1677	23	32	tensor	tensor	NOUN
ejpam-1677	23	33	.	.	PUNCT
ejpam-1677	24	1	the	the	DET
ejpam-1677	24	2	scalars	scalars	PROPN
ejpam-1677	24	3	α	α	PROPN
ejpam-1677	24	4	,	,	PUNCT
ejpam-1677	24	5	β	β	X
ejpam-1677	24	6	are	be	AUX
ejpam-1677	24	7	known	know	VERB
ejpam-1677	24	8	as	as	ADP
ejpam-1677	24	9	associated	associate	VERB
ejpam-1677	24	10	scalars	scalar	NOUN
ejpam-1677	24	11	and	and	CCONJ
ejpam-1677	24	12	d	d	NOUN
ejpam-1677	24	13	is	be	AUX
ejpam-1677	24	14	called	call	VERB
ejpam-1677	24	15	the	the	DET
ejpam-1677	24	16	associated	associated	ADJ
ejpam-1677	24	17	tensor	tensor	NOUN
ejpam-1677	24	18	of	of	ADP
ejpam-1677	24	19	the	the	DET
ejpam-1677	24	20	manifold	manifold	NOUN
ejpam-1677	24	21	.	.	PUNCT
ejpam-1677	25	1	such	such	DET
ejpam-1677	25	2	an	an	DET
ejpam-1677	25	3	n	n	ADV
ejpam-1677	25	4	-	-	PUNCT
ejpam-1677	25	5	dimensional	dimensional	ADJ
ejpam-1677	25	6	manifold	manifold	NOUN
ejpam-1677	25	7	is	be	AUX
ejpam-1677	25	8	denoted	denote	VERB
ejpam-1677	25	9	by	by	ADP
ejpam-1677	25	10	n(qe)n	n(qe)n	NOUN
ejpam-1677	25	11	.	.	PUNCT
ejpam-1677	26	1	the	the	DET
ejpam-1677	26	2	present	present	ADJ
ejpam-1677	26	3	paper	paper	NOUN
ejpam-1677	26	4	deals	deal	NOUN
ejpam-1677	26	5	with	with	ADP
ejpam-1677	26	6	a	a	DET
ejpam-1677	26	7	study	study	NOUN
ejpam-1677	26	8	of	of	ADP
ejpam-1677	26	9	n(qe)n(n	n(qe)n(n	PROPN
ejpam-1677	26	10	>	>	X
ejpam-1677	26	11	2	2	NUM
ejpam-1677	26	12	)	)	PUNCT
ejpam-1677	26	13	.	.	PUNCT
ejpam-1677	27	1	the	the	DET
ejpam-1677	27	2	paper	paper	NOUN
ejpam-1677	27	3	is	be	AUX
ejpam-1677	27	4	organized	organize	VERB
ejpam-1677	27	5	as	as	SCONJ
ejpam-1677	27	6	follows	follow	VERB
ejpam-1677	27	7	.	.	PUNCT
ejpam-1677	28	1	section	section	NOUN
ejpam-1677	28	2	2	2	NUM
ejpam-1677	28	3	is	be	AUX
ejpam-1677	28	4	concerned	concern	VERB
ejpam-1677	28	5	with	with	ADP
ejpam-1677	28	6	ricci	ricci	PROPN
ejpam-1677	28	7	-	-	PUNCT
ejpam-1677	28	8	pseudosymmetric	pseudosymmetric	NOUN
ejpam-1677	28	9	n(qe)n	n(qe)n	NOUN
ejpam-1677	28	10	and	and	CCONJ
ejpam-1677	28	11	we	we	PRON
ejpam-1677	28	12	obtain	obtain	VERB
ejpam-1677	28	13	a	a	DET
ejpam-1677	28	14	n(qe)n	n(qe)n	NOUN
ejpam-1677	28	15	is	be	AUX
ejpam-1677	28	16	ricci	ricci	NOUN
ejpam-1677	28	17	-	-	PUNCT
ejpam-1677	28	18	pseudosymmetric	pseudosymmetric	ADJ
ejpam-1677	29	1	if	if	SCONJ
ejpam-1677	29	2	and	and	CCONJ
ejpam-1677	29	3	only	only	ADV
ejpam-1677	29	4	if	if	SCONJ
ejpam-1677	29	5	it	it	PRON
ejpam-1677	29	6	is	be	AUX
ejpam-1677	29	7	d	d	NOUN
ejpam-1677	29	8	-	-	ADJ
ejpam-1677	29	9	pseudosymmetric	pseudosymmetric	ADJ
ejpam-1677	29	10	.	.	PUNCT
ejpam-1677	30	1	section	section	NOUN
ejpam-1677	30	2	4	4	NUM
ejpam-1677	30	3	deals	deal	NOUN
ejpam-1677	30	4	with	with	ADP
ejpam-1677	30	5	decomposable	decomposable	ADJ
ejpam-1677	30	6	riemannian	riemannian	ADJ
ejpam-1677	30	7	manifold	manifold	NOUN
ejpam-1677	30	8	.	.	PUNCT
ejpam-1677	31	1	it	it	PRON
ejpam-1677	31	2	is	be	AUX
ejpam-1677	31	3	proved	prove	VERB
ejpam-1677	31	4	that	that	SCONJ
ejpam-1677	31	5	a	a	DET
ejpam-1677	31	6	decomposable	decomposable	ADJ
ejpam-1677	31	7	riemannian	riemannian	NOUN
ejpam-1677	31	8	manifold	manifold	NOUN
ejpam-1677	31	9	is	be	AUX
ejpam-1677	31	10	nearly	nearly	ADV
ejpam-1677	31	11	quasi	quasi	ADJ
ejpam-1677	31	12	-	-	NOUN
ejpam-1677	31	13	einstein	einstein	ADJ
ejpam-1677	32	1	if	if	SCONJ
ejpam-1677	32	2	and	and	CCONJ
ejpam-1677	32	3	only	only	ADV
ejpam-1677	32	4	if	if	SCONJ
ejpam-1677	32	5	both	both	CCONJ
ejpam-1677	32	6	the	the	DET
ejpam-1677	32	7	decompositions	decomposition	NOUN
ejpam-1677	32	8	are	be	AUX
ejpam-1677	32	9	einstein	einstein	ADJ
ejpam-1677	32	10	.	.	PUNCT
ejpam-1677	33	1	section	section	NOUN
ejpam-1677	33	2	5	5	NUM
ejpam-1677	33	3	deals	deal	NOUN
ejpam-1677	33	4	with	with	ADP
ejpam-1677	33	5	some	some	DET
ejpam-1677	33	6	global	global	ADJ
ejpam-1677	33	7	properties	property	NOUN
ejpam-1677	33	8	of	of	ADP
ejpam-1677	33	9	n(qe)n	n(qe)n	NOUN
ejpam-1677	33	10	and	and	CCONJ
ejpam-1677	33	11	it	it	PRON
ejpam-1677	33	12	is	be	AUX
ejpam-1677	33	13	proved	prove	VERB
ejpam-1677	33	14	that	that	SCONJ
ejpam-1677	33	15	under	under	ADP
ejpam-1677	33	16	certain	certain	ADJ
ejpam-1677	33	17	condition	condition	NOUN
ejpam-1677	33	18	such	such	DET
ejpam-1677	33	19	a	a	DET
ejpam-1677	33	20	manifold	manifold	NOUN
ejpam-1677	33	21	does	do	AUX
ejpam-1677	33	22	not	not	PART
ejpam-1677	33	23	admit	admit	VERB
ejpam-1677	33	24	non	non	ADJ
ejpam-1677	33	25	-	-	ADJ
ejpam-1677	33	26	zero	zero	ADJ
ejpam-1677	33	27	killing	kill	VERB
ejpam-1677	33	28	vector	vector	NOUN
ejpam-1677	33	29	field	field	NOUN
ejpam-1677	33	30	,	,	PUNCT
ejpam-1677	33	31	non	non	ADJ
ejpam-1677	33	32	-	-	ADJ
ejpam-1677	33	33	zero	zero	NUM
ejpam-1677	33	34	projective	projective	ADJ
ejpam-1677	33	35	killing	kill	VERB
ejpam-1677	33	36	vector	vector	NOUN
ejpam-1677	33	37	field	field	NOUN
ejpam-1677	33	38	and	and	CCONJ
ejpam-1677	33	39	non	non	ADJ
ejpam-1677	33	40	-	-	ADJ
ejpam-1677	33	41	zero	zero	NUM
ejpam-1677	33	42	conformal	conformal	ADJ
ejpam-1677	33	43	killing	kill	VERB
ejpam-1677	33	44	vector	vector	NOUN
ejpam-1677	33	45	field	field	NOUN
ejpam-1677	33	46	.	.	PUNCT
ejpam-1677	34	1	finally	finally	ADV
ejpam-1677	34	2	the	the	DET
ejpam-1677	34	3	last	last	ADJ
ejpam-1677	34	4	section	section	NOUN
ejpam-1677	34	5	deals	deal	VERB
ejpam-1677	34	6	with	with	ADP
ejpam-1677	34	7	an	an	DET
ejpam-1677	34	8	interesting	interesting	ADJ
ejpam-1677	34	9	example	example	NOUN
ejpam-1677	34	10	of	of	ADP
ejpam-1677	34	11	nearly	nearly	ADV
ejpam-1677	34	12	quasi	quasi	ADJ
ejpam-1677	34	13	-	-	ADJ
ejpam-1677	34	14	einstein	einstein	ADJ
ejpam-1677	34	15	manifold	manifold	NOUN
ejpam-1677	34	16	with	with	ADP
ejpam-1677	34	17	non	non	ADJ
ejpam-1677	34	18	-	-	ADJ
ejpam-1677	34	19	vanishing	vanishing	ADJ
ejpam-1677	34	20	scalar	scalar	ADJ
ejpam-1677	34	21	curvature	curvature	NOUN
ejpam-1677	34	22	which	which	PRON
ejpam-1677	34	23	is	be	AUX
ejpam-1677	34	24	not	not	PART
ejpam-1677	34	25	quasi	quasi	ADJ
ejpam-1677	34	26	-	-	NOUN
ejpam-1677	34	27	einstein	einstein	ADJ
ejpam-1677	34	28	.	.	PUNCT
ejpam-1677	35	1	2	2	X
ejpam-1677	35	2	.	.	X
ejpam-1677	35	3	ricci	ricci	PROPN
ejpam-1677	35	4	-	-	PUNCT
ejpam-1677	35	5	pseudosymmetry	pseudosymmetry	NOUN
ejpam-1677	35	6	n(qe)n	n(qe)n	NOUN
ejpam-1677	35	7	an	an	DET
ejpam-1677	35	8	n	n	ADV
ejpam-1677	35	9	-	-	PUNCT
ejpam-1677	35	10	dimensional	dimensional	ADJ
ejpam-1677	35	11	riemannian	riemannian	ADJ
ejpam-1677	35	12	manifold	manifold	NOUN
ejpam-1677	35	13	(	(	PUNCT
ejpam-1677	35	14	m	m	NOUN
ejpam-1677	35	15	n	n	CCONJ
ejpam-1677	35	16	,	,	PUNCT
ejpam-1677	35	17	g	g	NOUN
ejpam-1677	35	18	)	)	PUNCT
ejpam-1677	35	19	is	be	AUX
ejpam-1677	35	20	called	call	VERB
ejpam-1677	35	21	ricci	ricci	PROPN
ejpam-1677	35	22	-	-	PUNCT
ejpam-1677	35	23	pseudosymmetric	pseudosymmetric	NOUN
ejpam-1677	35	24	[	[	X
ejpam-1677	35	25	4	4	X
ejpam-1677	35	26	]	]	X
ejpam-1677	35	27	if	if	SCONJ
ejpam-1677	35	28	the	the	DET
ejpam-1677	35	29	tensor	tensor	NOUN
ejpam-1677	35	30	r	r	NOUN
ejpam-1677	35	31	·	·	PUNCT
ejpam-1677	35	32	s	s	PART
ejpam-1677	35	33	and	and	CCONJ
ejpam-1677	35	34	q(g	q(g	PROPN
ejpam-1677	35	35	,	,	PUNCT
ejpam-1677	35	36	s	s	PART
ejpam-1677	35	37	)	)	PUNCT
ejpam-1677	35	38	are	be	AUX
ejpam-1677	35	39	linearly	linearly	ADV
ejpam-1677	35	40	dependent	dependent	ADJ
ejpam-1677	35	41	,	,	PUNCT
ejpam-1677	35	42	where	where	SCONJ
ejpam-1677	35	43	(	(	PUNCT
ejpam-1677	35	44	r(x	r(x	NOUN
ejpam-1677	35	45	,	,	PUNCT
ejpam-1677	35	46	y	y	PROPN
ejpam-1677	35	47	)	)	PUNCT
ejpam-1677	35	48	·	·	PUNCT
ejpam-1677	35	49	s)(z	s)(z	NOUN
ejpam-1677	35	50	,	,	PUNCT
ejpam-1677	35	51	u	u	NOUN
ejpam-1677	35	52	)	)	PUNCT
ejpam-1677	35	53	=	=	SYM
ejpam-1677	35	54	−s(r(x	−s(r(x	PROPN
ejpam-1677	35	55	,	,	PUNCT
ejpam-1677	35	56	y	y	PROPN
ejpam-1677	35	57	)	)	PUNCT
ejpam-1677	35	58	z	z	NOUN
ejpam-1677	35	59	,	,	PUNCT
ejpam-1677	35	60	u)−	u)−	PROPN
ejpam-1677	35	61	s(z	s(z	PROPN
ejpam-1677	35	62	,	,	PUNCT
ejpam-1677	35	63	r(x	r(x	PROPN
ejpam-1677	35	64	,	,	PUNCT
ejpam-1677	35	65	y	y	PROPN
ejpam-1677	35	66	)	)	PUNCT
ejpam-1677	35	67	u	u	NOUN
ejpam-1677	35	68	)	)	PUNCT
ejpam-1677	35	69	,	,	PUNCT
ejpam-1677	35	70	(	(	PUNCT
ejpam-1677	35	71	3	3	X
ejpam-1677	35	72	)	)	PUNCT
ejpam-1677	35	73	q(g	q(g	ADJ
ejpam-1677	35	74	,	,	PUNCT
ejpam-1677	35	75	s)(z	s)(z	PROPN
ejpam-1677	35	76	,	,	PUNCT
ejpam-1677	35	77	u	u	NOUN
ejpam-1677	35	78	;	;	PUNCT
ejpam-1677	35	79	x	x	SYM
ejpam-1677	35	80	,	,	PUNCT
ejpam-1677	35	81	y	y	PROPN
ejpam-1677	35	82	)	)	PUNCT
ejpam-1677	36	1	=	=	PUNCT
ejpam-1677	36	2	−s((x	−s((x	NOUN
ejpam-1677	36	3	∧g	∧g	PROPN
ejpam-1677	36	4	y	y	PROPN
ejpam-1677	36	5	)	)	PUNCT
ejpam-1677	36	6	z	z	NOUN
ejpam-1677	36	7	,	,	PUNCT
ejpam-1677	36	8	u)−	u)−	PROPN
ejpam-1677	36	9	s(z	s(z	PROPN
ejpam-1677	36	10	,	,	PUNCT
ejpam-1677	36	11	(	(	PUNCT
ejpam-1677	36	12	x	x	SYM
ejpam-1677	36	13	∧g	∧g	PROPN
ejpam-1677	36	14	y	y	PROPN
ejpam-1677	36	15	)	)	PUNCT
ejpam-1677	36	16	u	u	NOUN
ejpam-1677	36	17	)	)	PUNCT
ejpam-1677	36	18	.	.	PUNCT
ejpam-1677	37	1	(	(	PUNCT
ejpam-1677	37	2	4	4	X
ejpam-1677	37	3	)	)	PUNCT
ejpam-1677	37	4	thus	thus	ADV
ejpam-1677	37	5	the	the	DET
ejpam-1677	37	6	condition	condition	NOUN
ejpam-1677	37	7	of	of	ADP
ejpam-1677	37	8	ricci	ricci	PROPN
ejpam-1677	37	9	-	-	PUNCT
ejpam-1677	37	10	pseudosymmetry	pseudosymmetry	NOUN
ejpam-1677	37	11	is	be	AUX
ejpam-1677	37	12	(	(	PUNCT
ejpam-1677	37	13	r(x	r(x	PROPN
ejpam-1677	37	14	,	,	PUNCT
ejpam-1677	37	15	y	y	PROPN
ejpam-1677	37	16	)	)	PUNCT
ejpam-1677	37	17	·	·	PUNCT
ejpam-1677	38	1	s)(z	s)(z	NOUN
ejpam-1677	38	2	,	,	PUNCT
ejpam-1677	38	3	u	u	NOUN
ejpam-1677	38	4	)	)	PUNCT
ejpam-1677	38	5	=	=	SYM
ejpam-1677	39	1	lsq(g	lsq(g	PROPN
ejpam-1677	39	2	,	,	PUNCT
ejpam-1677	39	3	s)(z	s)(z	NOUN
ejpam-1677	39	4	,	,	PUNCT
ejpam-1677	39	5	u	u	NOUN
ejpam-1677	39	6	;	;	PUNCT
ejpam-1677	39	7	x	x	SYM
ejpam-1677	39	8	,	,	PUNCT
ejpam-1677	39	9	y	y	PROPN
ejpam-1677	39	10	)	)	PUNCT
ejpam-1677	39	11	(	(	PUNCT
ejpam-1677	39	12	5	5	X
ejpam-1677	39	13	)	)	PUNCT
ejpam-1677	39	14	holding	hold	VERB
ejpam-1677	39	15	on	on	ADP
ejpam-1677	39	16	the	the	DET
ejpam-1677	39	17	set	set	NOUN
ejpam-1677	39	18	us	we	PRON
ejpam-1677	39	19	=	=	PUNCT
ejpam-1677	39	20	{	{	PUNCT
ejpam-1677	39	21	x	x	SYM
ejpam-1677	39	22	∈	∈	NOUN
ejpam-1677	39	23	m	m	VERB
ejpam-1677	39	24	:	:	PUNCT
ejpam-1677	39	25	s	s	X
ejpam-1677	39	26	6=	6=	NUM
ejpam-1677	39	27	r	r	NOUN
ejpam-1677	39	28	n	n	PRON
ejpam-1677	39	29	g	g	NOUN
ejpam-1677	39	30	at	at	ADP
ejpam-1677	39	31	x	x	X
ejpam-1677	39	32	}	}	PUNCT
ejpam-1677	39	33	,	,	PUNCT
ejpam-1677	39	34	where	where	SCONJ
ejpam-1677	39	35	ls	ls	ADJ
ejpam-1677	39	36	is	be	AUX
ejpam-1677	39	37	some	some	DET
ejpam-1677	39	38	function	function	NOUN
ejpam-1677	39	39	on	on	ADP
ejpam-1677	39	40	us	we	PRON
ejpam-1677	39	41	.	.	PUNCT
ejpam-1677	40	1	if	if	SCONJ
ejpam-1677	40	2	r	r	NOUN
ejpam-1677	40	3	·	·	PUNCT
ejpam-1677	40	4	s	s	PART
ejpam-1677	40	5	=	=	NOUN
ejpam-1677	40	6	0	0	NUM
ejpam-1677	40	7	then	then	ADV
ejpam-1677	40	8	m	m	VERB
ejpam-1677	40	9	is	be	AUX
ejpam-1677	40	10	called	call	VERB
ejpam-1677	40	11	ricci	ricci	PROPN
ejpam-1677	40	12	-	-	PUNCT
ejpam-1677	40	13	semisymmetric	semisymmetric	NOUN
ejpam-1677	40	14	.	.	PUNCT
ejpam-1677	41	1	every	every	DET
ejpam-1677	41	2	ricci	ricci	PROPN
ejpam-1677	41	3	-	-	PUNCT
ejpam-1677	41	4	semisymmetric	semisymmetric	PROPN
ejpam-1677	41	5	manifold	manifold	NOUN
ejpam-1677	41	6	is	be	AUX
ejpam-1677	41	7	ricci	ricci	NOUN
ejpam-1677	41	8	-	-	PUNCT
ejpam-1677	41	9	pseudosymmetric	pseudosymmetric	NOUN
ejpam-1677	41	10	but	but	CCONJ
ejpam-1677	41	11	the	the	DET
ejpam-1677	41	12	converse	converse	NOUN
ejpam-1677	41	13	is	be	AUX
ejpam-1677	41	14	not	not	PART
ejpam-1677	41	15	true	true	ADJ
ejpam-1677	41	16	[	[	X
ejpam-1677	41	17	4	4	NUM
ejpam-1677	41	18	]	]	PUNCT
ejpam-1677	41	19	.	.	PUNCT
ejpam-1677	42	1	in	in	ADP
ejpam-1677	42	2	[	[	X
ejpam-1677	42	3	2	2	NUM
ejpam-1677	42	4	]	]	X
ejpam-1677	42	5	de	de	X
ejpam-1677	42	6	and	and	CCONJ
ejpam-1677	42	7	gaji	gaji	NOUN
ejpam-1677	42	8	studied	study	VERB
ejpam-1677	42	9	riccisemisymmetric	riccisemisymmetric	NOUN
ejpam-1677	42	10	n(qe)n	n(qe)n	NOUN
ejpam-1677	42	11	.	.	PUNCT
ejpam-1677	43	1	now	now	ADV
ejpam-1677	43	2	we	we	PRON
ejpam-1677	43	3	prove	prove	VERB
ejpam-1677	43	4	the	the	DET
ejpam-1677	43	5	following	following	NOUN
ejpam-1677	43	6	:	:	PUNCT
ejpam-1677	43	7	theorem	theorem	NOUN
ejpam-1677	43	8	1	1	NUM
ejpam-1677	43	9	.	.	PUNCT
ejpam-1677	44	1	a	a	DET
ejpam-1677	44	2	nearly	nearly	ADV
ejpam-1677	44	3	quasi	quasi	ADJ
ejpam-1677	44	4	-	-	ADJ
ejpam-1677	44	5	einstein	einstein	ADJ
ejpam-1677	44	6	manifold	manifold	NOUN
ejpam-1677	44	7	is	be	AUX
ejpam-1677	44	8	ricci	ricci	NOUN
ejpam-1677	44	9	-	-	PUNCT
ejpam-1677	44	10	pseudosymmetric	pseudosymmetric	ADJ
ejpam-1677	44	11	if	if	SCONJ
ejpam-1677	45	1	and	and	CCONJ
ejpam-1677	45	2	only	only	ADV
ejpam-1677	45	3	if	if	SCONJ
ejpam-1677	45	4	it	it	PRON
ejpam-1677	45	5	is	be	AUX
ejpam-1677	45	6	dpseudosymmetric	dpseudosymmetric	ADJ
ejpam-1677	45	7	.	.	PUNCT
ejpam-1677	46	1	proof	proof	NOUN
ejpam-1677	46	2	.	.	PUNCT
ejpam-1677	47	1	we	we	PRON
ejpam-1677	47	2	now	now	ADV
ejpam-1677	47	3	consider	consider	VERB
ejpam-1677	47	4	a	a	DET
ejpam-1677	47	5	ricci	ricci	NOUN
ejpam-1677	47	6	-	-	PUNCT
ejpam-1677	47	7	pseudosymmetric	pseudosymmetric	ADJ
ejpam-1677	47	8	n(qe)n	n(qe)n	NOUN
ejpam-1677	47	9	.	.	PUNCT
ejpam-1677	48	1	then	then	ADV
ejpam-1677	48	2	from	from	ADP
ejpam-1677	48	3	(	(	PUNCT
ejpam-1677	48	4	3)–(5	3)–(5	NOUN
ejpam-1677	48	5	)	)	PUNCT
ejpam-1677	48	6	,	,	PUNCT
ejpam-1677	48	7	we	we	PRON
ejpam-1677	48	8	can	can	AUX
ejpam-1677	48	9	write	write	VERB
ejpam-1677	48	10	s(r(x	s(r(x	PROPN
ejpam-1677	48	11	,	,	PUNCT
ejpam-1677	48	12	y	y	PROPN
ejpam-1677	48	13	)	)	PUNCT
ejpam-1677	48	14	z	z	NOUN
ejpam-1677	48	15	,	,	PUNCT
ejpam-1677	48	16	u	u	NOUN
ejpam-1677	48	17	)	)	PUNCT
ejpam-1677	49	1	+	+	CCONJ
ejpam-1677	49	2	s(z	s(z	PROPN
ejpam-1677	49	3	,	,	PUNCT
ejpam-1677	49	4	r(x	r(x	PROPN
ejpam-1677	49	5	,	,	PUNCT
ejpam-1677	49	6	y	y	PROPN
ejpam-1677	49	7	)	)	PUNCT
ejpam-1677	49	8	u	u	NOUN
ejpam-1677	49	9	)	)	PUNCT
ejpam-1677	50	1	=	=	SYM
ejpam-1677	50	2	ls{s(x	ls{s(x	ADJ
ejpam-1677	50	3	,	,	PUNCT
ejpam-1677	50	4	u)g(y	u)g(y	PROPN
ejpam-1677	50	5	,	,	PUNCT
ejpam-1677	50	6	z	z	NOUN
ejpam-1677	50	7	)	)	PUNCT
ejpam-1677	50	8	(	(	PUNCT
ejpam-1677	50	9	6	6	NUM
ejpam-1677	50	10	)	)	PUNCT
ejpam-1677	50	11	−s(y	−s(y	ADJ
ejpam-1677	50	12	,	,	PUNCT
ejpam-1677	50	13	u)g(x	u)g(x	ADJ
ejpam-1677	50	14	,	,	PUNCT
ejpam-1677	50	15	z)+	z)+	NUM
ejpam-1677	50	16	s(x	s(x	NOUN
ejpam-1677	50	17	,	,	PUNCT
ejpam-1677	50	18	z)g(y	z)g(y	PROPN
ejpam-1677	50	19	,	,	PUNCT
ejpam-1677	50	20	u)−	u)−	PROPN
ejpam-1677	50	21	s(y	s(y	PROPN
ejpam-1677	50	22	,	,	PUNCT
ejpam-1677	50	23	z)g(x	z)g(x	NUM
ejpam-1677	50	24	,	,	PUNCT
ejpam-1677	50	25	u	u	NOUN
ejpam-1677	50	26	)	)	PUNCT
ejpam-1677	50	27	}	}	PUNCT
ejpam-1677	50	28	.	.	PUNCT
ejpam-1677	51	1	s.	s.	PROPN
ejpam-1677	51	2	hui	hui	PROPN
ejpam-1677	51	3	/	/	SYM
ejpam-1677	51	4	eur	eur	PROPN
ejpam-1677	51	5	.	.	PUNCT
ejpam-1677	52	1	j.	j.	PROPN
ejpam-1677	52	2	pure	pure	PROPN
ejpam-1677	52	3	appl	appl	PROPN
ejpam-1677	52	4	.	.	PROPN
ejpam-1677	52	5	math	math	PROPN
ejpam-1677	52	6	,	,	PUNCT
ejpam-1677	52	7	5	5	NUM
ejpam-1677	52	8	(	(	PUNCT
ejpam-1677	52	9	2012	2012	NUM
ejpam-1677	52	10	)	)	PUNCT
ejpam-1677	52	11	,	,	PUNCT
ejpam-1677	52	12	365	365	NUM
ejpam-1677	52	13	-	-	SYM
ejpam-1677	52	14	372	372	NUM
ejpam-1677	52	15	367	367	NUM
ejpam-1677	52	16	using	use	VERB
ejpam-1677	52	17	(	(	PUNCT
ejpam-1677	52	18	2	2	NUM
ejpam-1677	52	19	)	)	PUNCT
ejpam-1677	52	20	in	in	ADP
ejpam-1677	52	21	(	(	PUNCT
ejpam-1677	52	22	6	6	NUM
ejpam-1677	52	23	)	)	PUNCT
ejpam-1677	52	24	,	,	PUNCT
ejpam-1677	52	25	we	we	PRON
ejpam-1677	52	26	get	get	VERB
ejpam-1677	52	27	d(r(x	d(r(x	PROPN
ejpam-1677	52	28	,	,	PUNCT
ejpam-1677	52	29	y	y	PROPN
ejpam-1677	52	30	)	)	PUNCT
ejpam-1677	52	31	z	z	NOUN
ejpam-1677	52	32	,	,	PUNCT
ejpam-1677	52	33	u	u	NOUN
ejpam-1677	52	34	)	)	PUNCT
ejpam-1677	52	35	+	+	CCONJ
ejpam-1677	52	36	d(z	d(z	NOUN
ejpam-1677	52	37	,	,	PUNCT
ejpam-1677	52	38	r(x	r(x	PROPN
ejpam-1677	52	39	,	,	PUNCT
ejpam-1677	52	40	y	y	PROPN
ejpam-1677	52	41	)	)	PUNCT
ejpam-1677	52	42	u	u	NOUN
ejpam-1677	52	43	)	)	PUNCT
ejpam-1677	52	44	=	=	SYM
ejpam-1677	53	1	ls{d(x	ls{d(x	NOUN
ejpam-1677	53	2	,	,	PUNCT
ejpam-1677	53	3	u)g(y	u)g(y	PROPN
ejpam-1677	53	4	,	,	PUNCT
ejpam-1677	53	5	z	z	NOUN
ejpam-1677	53	6	)	)	PUNCT
ejpam-1677	53	7	(	(	PUNCT
ejpam-1677	53	8	7	7	X
ejpam-1677	53	9	)	)	PUNCT
ejpam-1677	53	10	−d(y	−d(y	NOUN
ejpam-1677	53	11	,	,	PUNCT
ejpam-1677	53	12	u)g(x	u)g(x	ADJ
ejpam-1677	53	13	,	,	PUNCT
ejpam-1677	53	14	z)+	z)+	NUM
ejpam-1677	53	15	d(x	d(x	NOUN
ejpam-1677	53	16	,	,	PUNCT
ejpam-1677	53	17	z)g(y	z)g(y	PROPN
ejpam-1677	53	18	,	,	PUNCT
ejpam-1677	53	19	u)−	u)−	PROPN
ejpam-1677	53	20	d(y	d(y	PROPN
ejpam-1677	53	21	,	,	PUNCT
ejpam-1677	53	22	z)g(x	z)g(x	NUM
ejpam-1677	53	23	,	,	PUNCT
ejpam-1677	53	24	u	u	NOUN
ejpam-1677	53	25	)	)	PUNCT
ejpam-1677	53	26	}	}	PUNCT
ejpam-1677	53	27	,	,	PUNCT
ejpam-1677	53	28	which	which	PRON
ejpam-1677	53	29	implies	imply	VERB
ejpam-1677	53	30	that	that	SCONJ
ejpam-1677	53	31	the	the	DET
ejpam-1677	53	32	manifold	manifold	NOUN
ejpam-1677	53	33	is	be	AUX
ejpam-1677	53	34	d	d	NOUN
ejpam-1677	53	35	-	-	NOUN
ejpam-1677	53	36	pseudosymmetric	pseudosymmetric	ADJ
ejpam-1677	53	37	.	.	PUNCT
ejpam-1677	54	1	conversely	conversely	ADV
ejpam-1677	54	2	,	,	PUNCT
ejpam-1677	54	3	if	if	SCONJ
ejpam-1677	54	4	the	the	DET
ejpam-1677	54	5	manifold	manifold	NOUN
ejpam-1677	54	6	is	be	AUX
ejpam-1677	54	7	d	d	NOUN
ejpam-1677	54	8	-	-	NOUN
ejpam-1677	54	9	pseudosymmetric	pseudosymmetric	ADJ
ejpam-1677	54	10	,	,	PUNCT
ejpam-1677	54	11	then	then	ADV
ejpam-1677	54	12	(	(	PUNCT
ejpam-1677	54	13	7	7	X
ejpam-1677	54	14	)	)	PUNCT
ejpam-1677	54	15	holds	hold	NOUN
ejpam-1677	54	16	.	.	PUNCT
ejpam-1677	55	1	by	by	ADP
ejpam-1677	55	2	virue	virue	NOUN
ejpam-1677	55	3	of	of	ADP
ejpam-1677	55	4	(	(	PUNCT
ejpam-1677	55	5	2	2	NUM
ejpam-1677	55	6	)	)	PUNCT
ejpam-1677	55	7	,	,	PUNCT
ejpam-1677	55	8	it	it	PRON
ejpam-1677	55	9	follows	follow	VERB
ejpam-1677	55	10	from	from	ADP
ejpam-1677	55	11	(	(	PUNCT
ejpam-1677	55	12	7	7	NUM
ejpam-1677	55	13	)	)	PUNCT
ejpam-1677	55	14	,	,	PUNCT
ejpam-1677	55	15	we	we	PRON
ejpam-1677	55	16	get	get	VERB
ejpam-1677	55	17	the	the	DET
ejpam-1677	55	18	relation(6	relation(6	PROPN
ejpam-1677	55	19	)	)	PUNCT
ejpam-1677	55	20	and	and	CCONJ
ejpam-1677	55	21	consequently	consequently	ADV
ejpam-1677	55	22	,	,	PUNCT
ejpam-1677	55	23	the	the	DET
ejpam-1677	55	24	manifold	manifold	NOUN
ejpam-1677	55	25	is	be	AUX
ejpam-1677	55	26	ricci	ricci	NOUN
ejpam-1677	55	27	-	-	PUNCT
ejpam-1677	55	28	pseudosymmetric	pseudosymmetric	NOUN
ejpam-1677	55	29	.	.	PUNCT
ejpam-1677	56	1	corollary	corollary	ADJ
ejpam-1677	56	2	1	1	NUM
ejpam-1677	56	3	.	.	PUNCT
ejpam-1677	57	1	a	a	DET
ejpam-1677	57	2	nearly	nearly	ADV
ejpam-1677	57	3	quasi	quasi	ADJ
ejpam-1677	57	4	-	-	ADJ
ejpam-1677	57	5	einstein	einstein	ADJ
ejpam-1677	57	6	manifold	manifold	NOUN
ejpam-1677	57	7	is	be	AUX
ejpam-1677	57	8	ricci	ricci	PROPN
ejpam-1677	57	9	-	-	PUNCT
ejpam-1677	57	10	semisymmetric	semisymmetric	PROPN
ejpam-1677	57	11	if	if	SCONJ
ejpam-1677	58	1	and	and	CCONJ
ejpam-1677	58	2	only	only	ADV
ejpam-1677	58	3	if	if	SCONJ
ejpam-1677	58	4	it	it	PRON
ejpam-1677	58	5	is	be	AUX
ejpam-1677	58	6	dsemisymmetric	dsemisymmetric	ADJ
ejpam-1677	58	7	[	[	X
ejpam-1677	58	8	2	2	NUM
ejpam-1677	58	9	]	]	PUNCT
ejpam-1677	58	10	.	.	PUNCT
ejpam-1677	59	1	3	3	X
ejpam-1677	59	2	.	.	X
ejpam-1677	59	3	decomposable	decomposable	ADJ
ejpam-1677	59	4	riemannian	riemannian	NOUN
ejpam-1677	59	5	manifold	manifold	VERB
ejpam-1677	59	6	a	a	DET
ejpam-1677	59	7	non	non	ADJ
ejpam-1677	59	8	-	-	ADJ
ejpam-1677	59	9	flat	flat	ADJ
ejpam-1677	59	10	riemannian	riemannian	ADJ
ejpam-1677	59	11	manifold	manifold	NOUN
ejpam-1677	59	12	(	(	PUNCT
ejpam-1677	59	13	m	m	NOUN
ejpam-1677	59	14	n	n	CCONJ
ejpam-1677	59	15	,	,	PUNCT
ejpam-1677	59	16	g	g	NOUN
ejpam-1677	59	17	)	)	PUNCT
ejpam-1677	59	18	is	be	AUX
ejpam-1677	59	19	said	say	VERB
ejpam-1677	59	20	to	to	PART
ejpam-1677	59	21	be	be	AUX
ejpam-1677	59	22	decomposable	decomposable	ADJ
ejpam-1677	59	23	[	[	X
ejpam-1677	59	24	19	19	NUM
ejpam-1677	59	25	]	]	X
ejpam-1677	59	26	if	if	SCONJ
ejpam-1677	59	27	it	it	PRON
ejpam-1677	59	28	can	can	AUX
ejpam-1677	59	29	be	be	AUX
ejpam-1677	59	30	expressed	express	VERB
ejpam-1677	59	31	as	as	ADP
ejpam-1677	59	32	m	m	PROPN
ejpam-1677	59	33	p	p	NOUN
ejpam-1677	59	34	1	1	NUM
ejpam-1677	59	35	×m	×m	NOUN
ejpam-1677	59	36	n−p	n−p	NOUN
ejpam-1677	59	37	2	2	NUM
ejpam-1677	59	38	for	for	ADP
ejpam-1677	59	39	2≤	2≤	NUM
ejpam-1677	59	40	p	p	NOUN
ejpam-1677	59	41	≤	≤	NUM
ejpam-1677	59	42	n−	n−	NOUN
ejpam-1677	59	43	2	2	NUM
ejpam-1677	59	44	,	,	PUNCT
ejpam-1677	59	45	that	that	ADV
ejpam-1677	59	46	is	is	ADV
ejpam-1677	59	47	,	,	PUNCT
ejpam-1677	59	48	in	in	ADP
ejpam-1677	59	49	some	some	DET
ejpam-1677	59	50	coordinate	coordinate	NOUN
ejpam-1677	59	51	neighbourhood	neighbourhood	NOUN
ejpam-1677	59	52	of	of	ADP
ejpam-1677	59	53	the	the	DET
ejpam-1677	59	54	riemannian	riemannian	ADJ
ejpam-1677	59	55	manifold	manifold	NOUN
ejpam-1677	59	56	(	(	PUNCT
ejpam-1677	59	57	m	m	NOUN
ejpam-1677	59	58	n	n	CCONJ
ejpam-1677	59	59	,	,	PUNCT
ejpam-1677	59	60	g	g	PROPN
ejpam-1677	59	61	)	)	PUNCT
ejpam-1677	59	62	,	,	PUNCT
ejpam-1677	59	63	the	the	DET
ejpam-1677	59	64	metric	metric	NOUN
ejpam-1677	59	65	can	can	AUX
ejpam-1677	59	66	be	be	AUX
ejpam-1677	59	67	expressed	express	VERB
ejpam-1677	59	68	as	as	ADP
ejpam-1677	59	69	ds2	ds2	PROPN
ejpam-1677	59	70	=	=	PUNCT
ejpam-1677	59	71	gi	gi	PROPN
ejpam-1677	59	72	jd	jd	NOUN
ejpam-1677	59	73	x	x	PUNCT
ejpam-1677	60	1	i	i	NOUN
ejpam-1677	60	2	d	d	NOUN
ejpam-1677	60	3	x	x	X
ejpam-1677	60	4	j	j	PROPN
ejpam-1677	60	5	=	=	PUNCT
ejpam-1677	60	6	g̃abd	g̃abd	NOUN
ejpam-1677	60	7	x	x	SYM
ejpam-1677	60	8	ad	ad	NOUN
ejpam-1677	60	9	x	x	X
ejpam-1677	60	10	b+	b+	X
ejpam-1677	60	11	∗	∗	NOUN
ejpam-1677	60	12	g	g	PROPN
ejpam-1677	61	1	αβ	αβ	INTJ
ejpam-1677	61	2	d	d	NOUN
ejpam-1677	61	3	xαd	xαd	VERB
ejpam-1677	61	4	xβ	xβ	PROPN
ejpam-1677	61	5	,	,	PUNCT
ejpam-1677	61	6	(	(	PUNCT
ejpam-1677	61	7	8)	8)	NUM
ejpam-1677	61	8	where	where	SCONJ
ejpam-1677	61	9	g̃ab	g̃ab	NOUN
ejpam-1677	61	10	are	be	AUX
ejpam-1677	61	11	functions	function	NOUN
ejpam-1677	61	12	of	of	ADP
ejpam-1677	61	13	x1	x1	PROPN
ejpam-1677	61	14	,	,	PUNCT
ejpam-1677	61	15	x2	x2	PROPN
ejpam-1677	61	16	,	,	PUNCT
ejpam-1677	61	17	·	·	PUNCT
ejpam-1677	61	18	·	·	PUNCT
ejpam-1677	61	19	·	·	PUNCT
ejpam-1677	61	20	,	,	PUNCT
ejpam-1677	61	21	x	x	PUNCT
ejpam-1677	61	22	p(p	p(p	ADV
ejpam-1677	61	23	<	<	X
ejpam-1677	61	24	n	n	CCONJ
ejpam-1677	61	25	)	)	PUNCT
ejpam-1677	61	26	denoted	denote	VERB
ejpam-1677	61	27	by	by	ADP
ejpam-1677	61	28	x̃	x̃	PROPN
ejpam-1677	61	29	and	and	CCONJ
ejpam-1677	61	30	∗	∗	NOUN
ejpam-1677	61	31	g	g	NOUN
ejpam-1677	61	32	αβ	αβ	NOUN
ejpam-1677	61	33	are	be	AUX
ejpam-1677	61	34	functions	function	NOUN
ejpam-1677	61	35	of	of	ADP
ejpam-1677	61	36	x	x	SYM
ejpam-1677	61	37	p+1	p+1	NOUN
ejpam-1677	61	38	,	,	PUNCT
ejpam-1677	61	39	x	x	PROPN
ejpam-1677	61	40	p+2	p+2	PROPN
ejpam-1677	61	41	,	,	PUNCT
ejpam-1677	61	42	·	·	PUNCT
ejpam-1677	61	43	·	·	PUNCT
ejpam-1677	61	44	·	·	PUNCT
ejpam-1677	61	45	,	,	PUNCT
ejpam-1677	61	46	xn	xn	PROPN
ejpam-1677	61	47	denoted	denote	VERB
ejpam-1677	61	48	by	by	ADP
ejpam-1677	61	49	∗	∗	NOUN
ejpam-1677	61	50	x	x	SYM
ejpam-1677	61	51	;	;	PUNCT
ejpam-1677	61	52	a	a	DET
ejpam-1677	61	53	,	,	PUNCT
ejpam-1677	61	54	b	b	NOUN
ejpam-1677	61	55	,	,	PUNCT
ejpam-1677	61	56	c	c	NOUN
ejpam-1677	61	57	,	,	PUNCT
ejpam-1677	61	58	·	·	PUNCT
ejpam-1677	61	59	·	·	PUNCT
ejpam-1677	61	60	·	·	PUNCT
ejpam-1677	61	61	run	run	VERB
ejpam-1677	61	62	from	from	ADP
ejpam-1677	61	63	1	1	NUM
ejpam-1677	61	64	to	to	ADP
ejpam-1677	61	65	p	p	NOUN
ejpam-1677	61	66	and	and	CCONJ
ejpam-1677	61	67	α	α	NOUN
ejpam-1677	61	68	,	,	PUNCT
ejpam-1677	61	69	β	β	X
ejpam-1677	61	70	,	,	PUNCT
ejpam-1677	61	71	γ	γ	X
ejpam-1677	61	72	,	,	PUNCT
ejpam-1677	61	73	·	·	PUNCT
ejpam-1677	61	74	·	·	PUNCT
ejpam-1677	61	75	·	·	PUNCT
ejpam-1677	61	76	run	run	VERB
ejpam-1677	61	77	from	from	ADP
ejpam-1677	61	78	p+	p+	NOUN
ejpam-1677	61	79	1	1	NUM
ejpam-1677	61	80	to	to	PART
ejpam-1677	61	81	n.	n.	VERB
ejpam-1677	61	82	the	the	DET
ejpam-1677	61	83	two	two	NUM
ejpam-1677	61	84	parts	part	NOUN
ejpam-1677	61	85	of	of	ADP
ejpam-1677	61	86	(	(	PUNCT
ejpam-1677	61	87	8)	8)	NUM
ejpam-1677	61	88	are	be	AUX
ejpam-1677	61	89	the	the	DET
ejpam-1677	61	90	metrics	metric	NOUN
ejpam-1677	61	91	of	of	ADP
ejpam-1677	61	92	m	m	PROPN
ejpam-1677	61	93	p	p	NOUN
ejpam-1677	61	94	1	1	NUM
ejpam-1677	61	95	(	(	PUNCT
ejpam-1677	61	96	p	p	NOUN
ejpam-1677	61	97	≥	≥	NOUN
ejpam-1677	61	98	2	2	NUM
ejpam-1677	61	99	)	)	PUNCT
ejpam-1677	61	100	and	and	CCONJ
ejpam-1677	61	101	m	m	PROPN
ejpam-1677	61	102	n−p	n−p	PROPN
ejpam-1677	61	103	2	2	NUM
ejpam-1677	61	104	(	(	PUNCT
ejpam-1677	61	105	n−	n−	NOUN
ejpam-1677	61	106	p	p	NOUN
ejpam-1677	61	107	≥	≥	NUM
ejpam-1677	61	108	2	2	NUM
ejpam-1677	61	109	)	)	PUNCT
ejpam-1677	61	110	which	which	PRON
ejpam-1677	61	111	are	be	AUX
ejpam-1677	61	112	called	call	VERB
ejpam-1677	61	113	the	the	DET
ejpam-1677	61	114	decomposition	decomposition	NOUN
ejpam-1677	61	115	of	of	ADP
ejpam-1677	61	116	the	the	DET
ejpam-1677	61	117	manifold	manifold	ADJ
ejpam-1677	61	118	m	m	PROPN
ejpam-1677	61	119	n	n	NOUN
ejpam-1677	61	120	=	=	NOUN
ejpam-1677	61	121	m	m	VERB
ejpam-1677	61	122	p	p	NOUN
ejpam-1677	61	123	1	1	NUM
ejpam-1677	61	124	×m	×m	NOUN
ejpam-1677	61	125	n−p	n−p	NOUN
ejpam-1677	61	126	2	2	NUM
ejpam-1677	61	127	(	(	PUNCT
ejpam-1677	61	128	2≤	2≤	NUM
ejpam-1677	61	129	p	p	NOUN
ejpam-1677	61	130	≤	≤	NUM
ejpam-1677	61	131	n−	n−	NOUN
ejpam-1677	61	132	2	2	NUM
ejpam-1677	61	133	)	)	PUNCT
ejpam-1677	61	134	.	.	PUNCT
ejpam-1677	62	1	let	let	VERB
ejpam-1677	62	2	(	(	PUNCT
ejpam-1677	62	3	m	m	VERB
ejpam-1677	62	4	n	n	CCONJ
ejpam-1677	62	5	,	,	PUNCT
ejpam-1677	62	6	g	g	NOUN
ejpam-1677	62	7	)	)	PUNCT
ejpam-1677	62	8	be	be	AUX
ejpam-1677	62	9	a	a	DET
ejpam-1677	62	10	riemannian	riemannian	ADJ
ejpam-1677	62	11	manifold	manifold	NOUN
ejpam-1677	63	1	such	such	ADJ
ejpam-1677	63	2	that	that	SCONJ
ejpam-1677	63	3	m	m	VERB
ejpam-1677	63	4	p	p	NOUN
ejpam-1677	63	5	1	1	NUM
ejpam-1677	63	6	×	×	NOUN
ejpam-1677	63	7	m	m	NOUN
ejpam-1677	63	8	n−p	n−p	NOUN
ejpam-1677	63	9	2	2	NUM
ejpam-1677	63	10	for	for	ADP
ejpam-1677	63	11	2	2	NUM
ejpam-1677	63	12	≤	≤	NOUN
ejpam-1677	63	13	p	p	NOUN
ejpam-1677	63	14	≤	≤	NOUN
ejpam-1677	63	15	n	n	CCONJ
ejpam-1677	63	16	−	−	PROPN
ejpam-1677	63	17	2	2	NUM
ejpam-1677	63	18	.	.	PUNCT
ejpam-1677	63	19	here	here	ADV
ejpam-1677	63	20	throughout	throughout	ADP
ejpam-1677	63	21	this	this	DET
ejpam-1677	63	22	section	section	NOUN
ejpam-1677	63	23	each	each	DET
ejpam-1677	63	24	object	object	NOUN
ejpam-1677	63	25	denoted	denote	VERB
ejpam-1677	63	26	by	by	ADP
ejpam-1677	63	27	a	a	DET
ejpam-1677	63	28	“	"	PUNCT
ejpam-1677	63	29	tilde	tilde	NOUN
ejpam-1677	63	30	”	"	PUNCT
ejpam-1677	63	31	is	be	AUX
ejpam-1677	63	32	assumed	assume	VERB
ejpam-1677	63	33	to	to	PART
ejpam-1677	63	34	be	be	AUX
ejpam-1677	63	35	from	from	ADP
ejpam-1677	63	36	m1	m1	PROPN
ejpam-1677	63	37	and	and	CCONJ
ejpam-1677	63	38	each	each	DET
ejpam-1677	63	39	object	object	NOUN
ejpam-1677	63	40	denoted	denote	VERB
ejpam-1677	63	41	by	by	ADP
ejpam-1677	63	42	a	a	DET
ejpam-1677	63	43	“	"	PUNCT
ejpam-1677	63	44	star	star	NOUN
ejpam-1677	63	45	”	"	PUNCT
ejpam-1677	63	46	is	be	AUX
ejpam-1677	63	47	assumed	assume	VERB
ejpam-1677	63	48	to	to	PART
ejpam-1677	63	49	be	be	AUX
ejpam-1677	63	50	from	from	ADP
ejpam-1677	63	51	m2	m2	PROPN
ejpam-1677	63	52	.	.	PUNCT
ejpam-1677	64	1	let	let	VERB
ejpam-1677	64	2	x̃	x̃	PROPN
ejpam-1677	64	3	,	,	PUNCT
ejpam-1677	64	4	ỹ	ỹ	PROPN
ejpam-1677	64	5	,	,	PUNCT
ejpam-1677	64	6	z̃	z̃	PROPN
ejpam-1677	64	7	,	,	PUNCT
ejpam-1677	64	8	ũ	ũ	PROPN
ejpam-1677	64	9	,	,	PUNCT
ejpam-1677	64	10	ṽ	ṽ	PROPN
ejpam-1677	64	11	∈	∈	PROPN
ejpam-1677	64	12	χ(m1	χ(m1	NOUN
ejpam-1677	64	13	)	)	PUNCT
ejpam-1677	64	14	and	and	CCONJ
ejpam-1677	64	15	∗	∗	NOUN
ejpam-1677	64	16	x	x	X
ejpam-1677	64	17	,	,	PUNCT
ejpam-1677	64	18	∗	∗	PROPN
ejpam-1677	64	19	y	y	PROPN
ejpam-1677	64	20	,	,	PUNCT
ejpam-1677	64	21	∗	∗	PROPN
ejpam-1677	64	22	z	z	PROPN
ejpam-1677	64	23	,	,	PUNCT
ejpam-1677	64	24	∗	∗	NOUN
ejpam-1677	64	25	u	u	NOUN
ejpam-1677	64	26	,	,	PUNCT
ejpam-1677	64	27	∗	∗	PROPN
ejpam-1677	64	28	v∈	v∈	PROPN
ejpam-1677	64	29	χ(m2	χ(m2	PROPN
ejpam-1677	64	30	)	)	PUNCT
ejpam-1677	64	31	,	,	PUNCT
ejpam-1677	64	32	then	then	ADV
ejpam-1677	64	33	we	we	PRON
ejpam-1677	64	34	have	have	VERB
ejpam-1677	64	35	the	the	DET
ejpam-1677	64	36	following	follow	VERB
ejpam-1677	64	37	relations	relation	NOUN
ejpam-1677	64	38	:	:	PUNCT
ejpam-1677	65	1	r	r	X
ejpam-1677	65	2	(	(	PUNCT
ejpam-1677	65	3	∗	∗	NOUN
ejpam-1677	65	4	x	x	X
ejpam-1677	65	5	,	,	PUNCT
ejpam-1677	65	6	ỹ	ỹ	PROPN
ejpam-1677	65	7	,	,	PUNCT
ejpam-1677	65	8	z̃	z̃	PROPN
ejpam-1677	65	9	,	,	PUNCT
ejpam-1677	65	10	ũ	ũ	PROPN
ejpam-1677	65	11	)	)	PUNCT
ejpam-1677	65	12	=	=	SYM
ejpam-1677	65	13	0=	0=	NUM
ejpam-1677	66	1	r(x̃	r(x̃	NOUN
ejpam-1677	66	2	,	,	PUNCT
ejpam-1677	66	3	∗	∗	NOUN
ejpam-1677	66	4	y	y	PROPN
ejpam-1677	66	5	,	,	PUNCT
ejpam-1677	66	6	z̃	z̃	PROPN
ejpam-1677	66	7	,	,	PUNCT
ejpam-1677	66	8	∗	∗	NOUN
ejpam-1677	66	9	u	u	NOUN
ejpam-1677	66	10	)	)	PUNCT
ejpam-1677	66	11	=	=	SYM
ejpam-1677	66	12	r(x̃	r(x̃	NOUN
ejpam-1677	66	13	,	,	PUNCT
ejpam-1677	66	14	∗	∗	PROPN
ejpam-1677	66	15	y	y	PROPN
ejpam-1677	66	16	,	,	PUNCT
ejpam-1677	66	17	∗	∗	PROPN
ejpam-1677	66	18	z	z	PROPN
ejpam-1677	66	19	,	,	PUNCT
ejpam-1677	66	20	∗	∗	X
ejpam-1677	66	21	u	u	NOUN
ejpam-1677	66	22	)	)	PUNCT
ejpam-1677	66	23	,	,	PUNCT
ejpam-1677	66	24	(	(	PUNCT
ejpam-1677	66	25	∇	∇	X
ejpam-1677	66	26	∗	∗	X
ejpam-1677	66	27	x	x	SYM
ejpam-1677	66	28	r)(ỹ	r)(ỹ	NUM
ejpam-1677	66	29	,	,	PUNCT
ejpam-1677	66	30	z̃	z̃	PROPN
ejpam-1677	66	31	,	,	PUNCT
ejpam-1677	66	32	ũ	ũ	PROPN
ejpam-1677	66	33	,	,	PUNCT
ejpam-1677	66	34	ṽ	ṽ	PROPN
ejpam-1677	66	35	)	)	PUNCT
ejpam-1677	66	36	=	=	PUNCT
ejpam-1677	67	1	0=	0=	PUNCT
ejpam-1677	67	2	(	(	PUNCT
ejpam-1677	67	3	∇x̃	∇x̃	X
ejpam-1677	67	4	r)(ỹ	r)(ỹ	NUM
ejpam-1677	67	5	,	,	PUNCT
ejpam-1677	67	6	∗	∗	PROPN
ejpam-1677	67	7	z	z	PROPN
ejpam-1677	67	8	,	,	PUNCT
ejpam-1677	67	9	ũ	ũ	PROPN
ejpam-1677	67	10	,	,	PUNCT
ejpam-1677	67	11	∗	∗	NOUN
ejpam-1677	67	12	v	v	NOUN
ejpam-1677	67	13	)	)	PUNCT
ejpam-1677	67	14	=	=	PUNCT
ejpam-1677	67	15	(	(	PUNCT
ejpam-1677	67	16	∇	∇	X
ejpam-1677	67	17	∗	∗	X
ejpam-1677	67	18	x	x	SYM
ejpam-1677	67	19	r)(ỹ	r)(ỹ	PROPN
ejpam-1677	67	20	,	,	PUNCT
ejpam-1677	67	21	∗	∗	NOUN
ejpam-1677	67	22	z	z	NOUN
ejpam-1677	67	23	,	,	PUNCT
ejpam-1677	67	24	ũ	ũ	PROPN
ejpam-1677	67	25	,	,	PUNCT
ejpam-1677	67	26	∗	∗	NOUN
ejpam-1677	67	27	v	v	NOUN
ejpam-1677	67	28	)	)	PUNCT
ejpam-1677	67	29	,	,	PUNCT
ejpam-1677	67	30	r(x̃	r(x̃	NOUN
ejpam-1677	67	31	,	,	PUNCT
ejpam-1677	67	32	ỹ	ỹ	PROPN
ejpam-1677	67	33	,	,	PUNCT
ejpam-1677	67	34	z̃	z̃	PROPN
ejpam-1677	67	35	,	,	PUNCT
ejpam-1677	67	36	ũ	ũ	PROPN
ejpam-1677	67	37	)	)	PUNCT
ejpam-1677	67	38	=	=	NOUN
ejpam-1677	67	39	r̃(x̃	r̃(x̃	NOUN
ejpam-1677	67	40	,	,	PUNCT
ejpam-1677	67	41	ỹ	ỹ	PROPN
ejpam-1677	67	42	,	,	PUNCT
ejpam-1677	67	43	z̃	z̃	PROPN
ejpam-1677	67	44	,	,	PUNCT
ejpam-1677	67	45	ũ	ũ	PROPN
ejpam-1677	67	46	)	)	PUNCT
ejpam-1677	67	47	;	;	PUNCT
ejpam-1677	68	1	r	r	X
ejpam-1677	68	2	(	(	PUNCT
ejpam-1677	68	3	∗	∗	NOUN
ejpam-1677	68	4	x	x	PUNCT
ejpam-1677	68	5	,	,	PUNCT
ejpam-1677	68	6	∗	∗	PROPN
ejpam-1677	68	7	y	y	PROPN
ejpam-1677	68	8	,	,	PUNCT
ejpam-1677	68	9	∗	∗	PROPN
ejpam-1677	68	10	z	z	PROPN
ejpam-1677	68	11	,	,	PUNCT
ejpam-1677	68	12	∗	∗	X
ejpam-1677	68	13	u	u	NOUN
ejpam-1677	68	14	)	)	PUNCT
ejpam-1677	68	15	=	=	SYM
ejpam-1677	68	16	∗	∗	NOUN
ejpam-1677	68	17	r	r	NOUN
ejpam-1677	68	18	(	(	PUNCT
ejpam-1677	68	19	∗	∗	NOUN
ejpam-1677	68	20	x	x	SYM
ejpam-1677	68	21	,	,	PUNCT
ejpam-1677	68	22	∗	∗	PROPN
ejpam-1677	68	23	y	y	PROPN
ejpam-1677	68	24	,	,	PUNCT
ejpam-1677	68	25	∗	∗	PROPN
ejpam-1677	68	26	z	z	PROPN
ejpam-1677	68	27	,	,	PUNCT
ejpam-1677	68	28	∗	∗	X
ejpam-1677	68	29	u	u	NOUN
ejpam-1677	68	30	)	)	PUNCT
ejpam-1677	68	31	,	,	PUNCT
ejpam-1677	68	32	s(x̃	s(x̃	PROPN
ejpam-1677	68	33	,	,	PUNCT
ejpam-1677	68	34	ỹ	ỹ	PROPN
ejpam-1677	68	35	)	)	PUNCT
ejpam-1677	69	1	=	=	NOUN
ejpam-1677	69	2	s̃(x̃	s̃(x̃	NOUN
ejpam-1677	69	3	,	,	PUNCT
ejpam-1677	69	4	ỹ	ỹ	PROPN
ejpam-1677	69	5	)	)	PUNCT
ejpam-1677	69	6	;	;	PUNCT
ejpam-1677	69	7	s	s	X
ejpam-1677	69	8	(	(	PUNCT
ejpam-1677	69	9	∗	∗	NOUN
ejpam-1677	69	10	x	x	SYM
ejpam-1677	69	11	,	,	PUNCT
ejpam-1677	69	12	∗	∗	PROPN
ejpam-1677	69	13	y	y	NOUN
ejpam-1677	69	14	)	)	PUNCT
ejpam-1677	70	1	=	=	SYM
ejpam-1677	71	1	∗	∗	NOUN
ejpam-1677	71	2	s	s	X
ejpam-1677	71	3	(	(	PUNCT
ejpam-1677	71	4	∗	∗	NOUN
ejpam-1677	71	5	x	x	SYM
ejpam-1677	71	6	,	,	PUNCT
ejpam-1677	71	7	∗	∗	PROPN
ejpam-1677	71	8	y	y	PROPN
ejpam-1677	71	9	)	)	PUNCT
ejpam-1677	71	10	,	,	PUNCT
ejpam-1677	71	11	(	(	PUNCT
ejpam-1677	71	12	∇x̃	∇x̃	NUM
ejpam-1677	71	13	s)(ỹ	s)(ỹ	NUM
ejpam-1677	71	14	,	,	PUNCT
ejpam-1677	71	15	z̃	z̃	PROPN
ejpam-1677	71	16	)	)	PUNCT
ejpam-1677	71	17	=	=	PUNCT
ejpam-1677	71	18	(	(	PUNCT
ejpam-1677	71	19	∇̃x̃	∇̃x̃	PROPN
ejpam-1677	71	20	s)(ỹ	s)(ỹ	PROPN
ejpam-1677	71	21	,	,	PUNCT
ejpam-1677	71	22	z̃	z̃	PROPN
ejpam-1677	71	23	)	)	PUNCT
ejpam-1677	71	24	;	;	PUNCT
ejpam-1677	71	25	(	(	PUNCT
ejpam-1677	71	26	∇	∇	X
ejpam-1677	71	27	∗	∗	X
ejpam-1677	71	28	x	x	SYM
ejpam-1677	71	29	s	s	X
ejpam-1677	71	30	)	)	PUNCT
ejpam-1677	71	31	(	(	PUNCT
ejpam-1677	71	32	∗	∗	NOUN
ejpam-1677	71	33	y	y	PROPN
ejpam-1677	71	34	,	,	PUNCT
ejpam-1677	71	35	∗	∗	PROPN
ejpam-1677	71	36	z	z	NOUN
ejpam-1677	71	37	)	)	PUNCT
ejpam-1677	71	38	=	=	SYM
ejpam-1677	71	39	(	(	PUNCT
ejpam-1677	71	40	∗	∗	X
ejpam-1677	71	41	∇	∇	PROPN
ejpam-1677	71	42	∗	∗	X
ejpam-1677	71	43	x	x	SYM
ejpam-1677	71	44	s	s	X
ejpam-1677	71	45	)	)	PUNCT
ejpam-1677	71	46	(	(	PUNCT
ejpam-1677	71	47	∗	∗	NOUN
ejpam-1677	71	48	y	y	PROPN
ejpam-1677	71	49	,	,	PUNCT
ejpam-1677	71	50	∗	∗	PROPN
ejpam-1677	71	51	z	z	NOUN
ejpam-1677	71	52	)	)	PUNCT
ejpam-1677	71	53	,	,	PUNCT
ejpam-1677	71	54	and	and	CCONJ
ejpam-1677	71	55	r	r	NOUN
ejpam-1677	71	56	=	=	SYM
ejpam-1677	71	57	r̃+	r̃+	PROPN
ejpam-1677	71	58	∗	∗	NOUN
ejpam-1677	71	59	r	r	NOUN
ejpam-1677	71	60	,	,	PUNCT
ejpam-1677	71	61	where	where	SCONJ
ejpam-1677	71	62	r	r	NOUN
ejpam-1677	71	63	,	,	PUNCT
ejpam-1677	71	64	r̃	r̃	NOUN
ejpam-1677	71	65	,	,	PUNCT
ejpam-1677	71	66	and	and	CCONJ
ejpam-1677	71	67	∗	∗	NOUN
ejpam-1677	71	68	r	r	NOUN
ejpam-1677	71	69	are	be	AUX
ejpam-1677	71	70	the	the	DET
ejpam-1677	71	71	scalar	scalar	ADJ
ejpam-1677	71	72	curvature	curvature	NOUN
ejpam-1677	71	73	of	of	ADP
ejpam-1677	71	74	m	m	PROPN
ejpam-1677	71	75	,	,	PUNCT
ejpam-1677	71	76	m1	m1	PROPN
ejpam-1677	71	77	,	,	PUNCT
ejpam-1677	71	78	m2	m2	PROPN
ejpam-1677	71	79	respectively	respectively	ADV
ejpam-1677	71	80	.	.	PUNCT
ejpam-1677	72	1	in	in	ADP
ejpam-1677	72	2	[	[	X
ejpam-1677	72	3	19	19	NUM
ejpam-1677	72	4	]	]	SYM
ejpam-1677	72	5	yano	yano	PROPN
ejpam-1677	72	6	and	and	CCONJ
ejpam-1677	72	7	kon	kon	PROPN
ejpam-1677	72	8	find	find	VERB
ejpam-1677	72	9	a	a	DET
ejpam-1677	72	10	necessary	necessary	ADJ
ejpam-1677	72	11	and	and	CCONJ
ejpam-1677	72	12	sufficient	sufficient	ADJ
ejpam-1677	72	13	condition	condition	NOUN
ejpam-1677	72	14	that	that	SCONJ
ejpam-1677	72	15	both	both	CCONJ
ejpam-1677	72	16	the	the	DET
ejpam-1677	72	17	decompositions	decomposition	NOUN
ejpam-1677	72	18	of	of	ADP
ejpam-1677	72	19	a	a	DET
ejpam-1677	72	20	decomposable	decomposable	ADJ
ejpam-1677	72	21	riemannian	riemannian	NOUN
ejpam-1677	72	22	manifold	manifold	NOUN
ejpam-1677	72	23	are	be	AUX
ejpam-1677	72	24	einstein	einstein	ADJ
ejpam-1677	72	25	and	and	CCONJ
ejpam-1677	72	26	they	they	PRON
ejpam-1677	72	27	obtained	obtain	VERB
ejpam-1677	72	28	that	that	SCONJ
ejpam-1677	72	29	s.	s.	PROPN
ejpam-1677	72	30	hui	hui	PROPN
ejpam-1677	72	31	/	/	SYM
ejpam-1677	72	32	eur	eur	PROPN
ejpam-1677	72	33	.	.	PUNCT
ejpam-1677	73	1	j.	j.	PROPN
ejpam-1677	73	2	pure	pure	PROPN
ejpam-1677	73	3	appl	appl	PROPN
ejpam-1677	73	4	.	.	PROPN
ejpam-1677	73	5	math	math	PROPN
ejpam-1677	73	6	,	,	PUNCT
ejpam-1677	73	7	5	5	NUM
ejpam-1677	73	8	(	(	PUNCT
ejpam-1677	73	9	2012	2012	NUM
ejpam-1677	73	10	)	)	PUNCT
ejpam-1677	73	11	,	,	PUNCT
ejpam-1677	73	12	365	365	NUM
ejpam-1677	73	13	-	-	SYM
ejpam-1677	73	14	372	372	NUM
ejpam-1677	73	15	368	368	NUM
ejpam-1677	73	16	theorem	theorem	NOUN
ejpam-1677	73	17	2	2	NUM
ejpam-1677	73	18	.	.	PUNCT
ejpam-1677	74	1	in	in	ADP
ejpam-1677	74	2	a	a	DET
ejpam-1677	74	3	decomposable	decomposable	ADJ
ejpam-1677	74	4	riemannian	riemannian	NOUN
ejpam-1677	74	5	manifold	manifold	ADJ
ejpam-1677	74	6	m	m	PROPN
ejpam-1677	74	7	n	n	NOUN
ejpam-1677	74	8	=	=	NOUN
ejpam-1677	74	9	m	m	VERB
ejpam-1677	74	10	p	p	NOUN
ejpam-1677	74	11	1	1	NUM
ejpam-1677	74	12	×	×	NOUN
ejpam-1677	74	13	m	m	NOUN
ejpam-1677	74	14	n−p	n−p	NOUN
ejpam-1677	74	15	2	2	NUM
ejpam-1677	74	16	(	(	PUNCT
ejpam-1677	74	17	2	2	NUM
ejpam-1677	74	18	≤	≤	NOUN
ejpam-1677	74	19	p	p	NOUN
ejpam-1677	74	20	≤	≤	NUM
ejpam-1677	74	21	n−	n−	NOUN
ejpam-1677	74	22	2	2	NUM
ejpam-1677	74	23	)	)	PUNCT
ejpam-1677	74	24	,	,	PUNCT
ejpam-1677	74	25	a	a	DET
ejpam-1677	74	26	necessary	necessary	ADJ
ejpam-1677	74	27	and	and	CCONJ
ejpam-1677	74	28	sufficient	sufficient	ADJ
ejpam-1677	74	29	condition	condition	NOUN
ejpam-1677	74	30	that	that	SCONJ
ejpam-1677	74	31	the	the	DET
ejpam-1677	74	32	two	two	NUM
ejpam-1677	74	33	decompositions	decomposition	NOUN
ejpam-1677	74	34	are	be	AUX
ejpam-1677	74	35	both	both	PRON
ejpam-1677	74	36	einstein	einstein	ADJ
ejpam-1677	74	37	is	be	AUX
ejpam-1677	74	38	that	that	SCONJ
ejpam-1677	74	39	the	the	DET
ejpam-1677	74	40	ricci	ricci	PROPN
ejpam-1677	74	41	tensor	tensor	NOUN
ejpam-1677	74	42	of	of	ADP
ejpam-1677	74	43	the	the	DET
ejpam-1677	74	44	manifold	manifold	NOUN
ejpam-1677	74	45	has	have	VERB
ejpam-1677	74	46	the	the	DET
ejpam-1677	74	47	form	form	NOUN
ejpam-1677	74	48	s(x	s(x	NOUN
ejpam-1677	74	49	,	,	PUNCT
ejpam-1677	74	50	y	y	PROPN
ejpam-1677	74	51	)	)	PUNCT
ejpam-1677	75	1	=	=	SYM
ejpam-1677	75	2	ag(x	ag(x	X
ejpam-1677	75	3	,	,	PUNCT
ejpam-1677	75	4	y	y	PROPN
ejpam-1677	75	5	)	)	PUNCT
ejpam-1677	76	1	+	+	CCONJ
ejpam-1677	76	2	bf(x	bf(x	X
ejpam-1677	76	3	,	,	PUNCT
ejpam-1677	76	4	y	y	PROPN
ejpam-1677	76	5	)	)	PUNCT
ejpam-1677	76	6	,	,	PUNCT
ejpam-1677	76	7	(	(	PUNCT
ejpam-1677	76	8	9	9	X
ejpam-1677	76	9	)	)	PUNCT
ejpam-1677	76	10	a	a	PRON
ejpam-1677	76	11	and	and	CCONJ
ejpam-1677	76	12	b	b	NOUN
ejpam-1677	76	13	being	be	AUX
ejpam-1677	76	14	necessarily	necessarily	ADV
ejpam-1677	76	15	constant	constant	ADJ
ejpam-1677	76	16	and	and	CCONJ
ejpam-1677	76	17	f	f	PROPN
ejpam-1677	76	18	is	be	AUX
ejpam-1677	76	19	a	a	DET
ejpam-1677	76	20	(	(	PUNCT
ejpam-1677	76	21	0	0	NUM
ejpam-1677	76	22	,	,	PUNCT
ejpam-1677	76	23	2	2	NUM
ejpam-1677	76	24	)	)	PUNCT
ejpam-1677	76	25	type	type	NOUN
ejpam-1677	76	26	metric	metric	ADJ
ejpam-1677	76	27	tensor	tensor	NOUN
ejpam-1677	76	28	such	such	ADJ
ejpam-1677	76	29	that	that	SCONJ
ejpam-1677	76	30	f(x	f(x	PROPN
ejpam-1677	76	31	,	,	PUNCT
ejpam-1677	76	32	y	y	PROPN
ejpam-1677	76	33	)	)	PUNCT
ejpam-1677	76	34	=	=	NOUN
ejpam-1677	76	35	g̃(x̃	g̃(x̃	NOUN
ejpam-1677	76	36	,	,	PUNCT
ejpam-1677	76	37	ỹ	ỹ	PROPN
ejpam-1677	76	38	)	)	PUNCT
ejpam-1677	77	1	+	+	NUM
ejpam-1677	77	2	∗	∗	NOUN
ejpam-1677	77	3	g	g	PROPN
ejpam-1677	77	4	(	(	PUNCT
ejpam-1677	77	5	∗	∗	NOUN
ejpam-1677	77	6	x	x	SYM
ejpam-1677	77	7	,	,	PUNCT
ejpam-1677	77	8	∗	∗	PROPN
ejpam-1677	77	9	y	y	PROPN
ejpam-1677	77	10	)	)	PUNCT
ejpam-1677	77	11	.	.	PUNCT
ejpam-1677	78	1	(	(	PUNCT
ejpam-1677	78	2	10	10	NUM
ejpam-1677	78	3	)	)	PUNCT
ejpam-1677	78	4	by	by	ADP
ejpam-1677	78	5	virtue	virtue	NOUN
ejpam-1677	78	6	of	of	ADP
ejpam-1677	78	7	theorem	theorem	NOUN
ejpam-1677	78	8	2	2	NUM
ejpam-1677	78	9	,	,	PUNCT
ejpam-1677	78	10	we	we	PRON
ejpam-1677	78	11	can	can	AUX
ejpam-1677	78	12	state	state	VERB
ejpam-1677	78	13	the	the	DET
ejpam-1677	78	14	following	following	NOUN
ejpam-1677	78	15	:	:	PUNCT
ejpam-1677	78	16	theorem	theorem	NOUN
ejpam-1677	78	17	3	3	NUM
ejpam-1677	78	18	.	.	PUNCT
ejpam-1677	79	1	a	a	DET
ejpam-1677	79	2	decomposable	decomposable	ADJ
ejpam-1677	79	3	riemannian	riemannian	NOUN
ejpam-1677	79	4	manifold	manifold	ADJ
ejpam-1677	79	5	m	m	PROPN
ejpam-1677	79	6	n	n	NOUN
ejpam-1677	79	7	=	=	NOUN
ejpam-1677	79	8	m	m	VERB
ejpam-1677	79	9	p	p	NOUN
ejpam-1677	79	10	1	1	NUM
ejpam-1677	79	11	×m	×m	NOUN
ejpam-1677	79	12	n−p	n−p	NOUN
ejpam-1677	79	13	2	2	NUM
ejpam-1677	79	14	(	(	PUNCT
ejpam-1677	79	15	2≤	2≤	NUM
ejpam-1677	79	16	p	p	NOUN
ejpam-1677	79	17	≤	≤	NUM
ejpam-1677	79	18	n−	n−	NOUN
ejpam-1677	79	19	2	2	NUM
ejpam-1677	79	20	)	)	PUNCT
ejpam-1677	79	21	is	be	AUX
ejpam-1677	79	22	nearly	nearly	ADV
ejpam-1677	79	23	quasi	quasi	ADJ
ejpam-1677	79	24	-	-	NOUN
ejpam-1677	79	25	einstein	einstein	ADJ
ejpam-1677	79	26	if	if	SCONJ
ejpam-1677	80	1	and	and	CCONJ
ejpam-1677	80	2	only	only	ADV
ejpam-1677	80	3	if	if	SCONJ
ejpam-1677	80	4	both	both	CCONJ
ejpam-1677	80	5	the	the	DET
ejpam-1677	80	6	decompositions	decomposition	NOUN
ejpam-1677	80	7	are	be	AUX
ejpam-1677	80	8	einstein	einstein	ADJ
ejpam-1677	80	9	.	.	PUNCT
ejpam-1677	81	1	4	4	X
ejpam-1677	81	2	.	.	X
ejpam-1677	81	3	some	some	DET
ejpam-1677	81	4	global	global	ADJ
ejpam-1677	81	5	properties	property	NOUN
ejpam-1677	81	6	of	of	ADP
ejpam-1677	81	7	n(qe)n	n(qe)n	NOUN
ejpam-1677	81	8	this	this	DET
ejpam-1677	81	9	section	section	NOUN
ejpam-1677	81	10	is	be	AUX
ejpam-1677	81	11	concerned	concern	VERB
ejpam-1677	81	12	with	with	ADP
ejpam-1677	81	13	a	a	DET
ejpam-1677	81	14	compact	compact	ADJ
ejpam-1677	81	15	,	,	PUNCT
ejpam-1677	81	16	orientable	orientable	ADJ
ejpam-1677	81	17	n(qe)n(n	n(qe)n(n	PROPN
ejpam-1677	81	18	>	>	X
ejpam-1677	81	19	2	2	NUM
ejpam-1677	81	20	)	)	PUNCT
ejpam-1677	81	21	without	without	ADP
ejpam-1677	81	22	boundary	boundary	NOUN
ejpam-1677	81	23	with	with	ADP
ejpam-1677	81	24	α	α	PROPN
ejpam-1677	81	25	,	,	PUNCT
ejpam-1677	81	26	β	β	X
ejpam-1677	81	27	as	as	ADP
ejpam-1677	81	28	associated	associate	VERB
ejpam-1677	81	29	scalars	scalar	NOUN
ejpam-1677	81	30	and	and	CCONJ
ejpam-1677	81	31	d	d	NOUN
ejpam-1677	81	32	as	as	ADP
ejpam-1677	81	33	the	the	DET
ejpam-1677	81	34	structure	structure	NOUN
ejpam-1677	81	35	tensor	tensor	NOUN
ejpam-1677	81	36	.	.	PUNCT
ejpam-1677	82	1	then	then	ADV
ejpam-1677	82	2	we	we	PRON
ejpam-1677	82	3	prove	prove	VERB
ejpam-1677	82	4	the	the	DET
ejpam-1677	82	5	following	following	NOUN
ejpam-1677	82	6	:	:	PUNCT
ejpam-1677	82	7	theorem	theorem	NOUN
ejpam-1677	82	8	4	4	NUM
ejpam-1677	82	9	.	.	PUNCT
ejpam-1677	83	1	if	if	SCONJ
ejpam-1677	83	2	in	in	ADP
ejpam-1677	83	3	a	a	DET
ejpam-1677	83	4	compact	compact	ADJ
ejpam-1677	83	5	,	,	PUNCT
ejpam-1677	83	6	orientable	orientable	ADJ
ejpam-1677	83	7	n(qe)n(n	n(qe)n(n	PROPN
ejpam-1677	83	8	>	>	X
ejpam-1677	83	9	2	2	NUM
ejpam-1677	83	10	)	)	PUNCT
ejpam-1677	83	11	without	without	ADP
ejpam-1677	83	12	boundary	boundary	NOUN
ejpam-1677	83	13	,	,	PUNCT
ejpam-1677	83	14	the	the	DET
ejpam-1677	83	15	associated	associated	ADJ
ejpam-1677	83	16	scalars	scalar	NOUN
ejpam-1677	83	17	and	and	CCONJ
ejpam-1677	83	18	the	the	DET
ejpam-1677	83	19	structure	structure	NOUN
ejpam-1677	83	20	tensor	tensor	NOUN
ejpam-1677	83	21	are	be	AUX
ejpam-1677	83	22	such	such	ADJ
ejpam-1677	83	23	that	that	SCONJ
ejpam-1677	83	24	α	α	PRON
ejpam-1677	83	25	<	<	X
ejpam-1677	83	26	0	0	PUNCT
ejpam-1677	83	27	and	and	CCONJ
ejpam-1677	83	28	βd(x	βd(x	PUNCT
ejpam-1677	83	29	,	,	PUNCT
ejpam-1677	83	30	x	x	X
ejpam-1677	83	31	)	)	PUNCT
ejpam-1677	83	32	<	<	X
ejpam-1677	83	33	0	0	NUM
ejpam-1677	83	34	,	,	PUNCT
ejpam-1677	83	35	then	then	ADV
ejpam-1677	83	36	there	there	PRON
ejpam-1677	83	37	exists	exist	VERB
ejpam-1677	83	38	no	no	DET
ejpam-1677	83	39	non	non	ADJ
ejpam-1677	83	40	-	-	ADJ
ejpam-1677	83	41	zero	zero	ADJ
ejpam-1677	83	42	killing	kill	VERB
ejpam-1677	83	43	vector	vector	NOUN
ejpam-1677	83	44	field	field	NOUN
ejpam-1677	83	45	in	in	ADP
ejpam-1677	83	46	this	this	DET
ejpam-1677	83	47	manifold	manifold	NOUN
ejpam-1677	83	48	.	.	PUNCT
ejpam-1677	84	1	proof	proof	NOUN
ejpam-1677	84	2	.	.	PUNCT
ejpam-1677	85	1	it	it	PRON
ejpam-1677	85	2	is	be	AUX
ejpam-1677	85	3	known	know	VERB
ejpam-1677	85	4	that	that	SCONJ
ejpam-1677	85	5	[	[	X
ejpam-1677	85	6	17	17	NUM
ejpam-1677	85	7	]	]	PUNCT
ejpam-1677	85	8	for	for	ADP
ejpam-1677	85	9	a	a	DET
ejpam-1677	85	10	vector	vector	NOUN
ejpam-1677	85	11	field	field	NOUN
ejpam-1677	85	12	x	x	PUNCT
ejpam-1677	85	13	in	in	ADP
ejpam-1677	85	14	a	a	DET
ejpam-1677	85	15	riemannian	riemannian	ADJ
ejpam-1677	85	16	manifold	manifold	ADJ
ejpam-1677	85	17	m	m	PROPN
ejpam-1677	85	18	,	,	PUNCT
ejpam-1677	85	19	the	the	DET
ejpam-1677	85	20	following	follow	VERB
ejpam-1677	85	21	relation	relation	NOUN
ejpam-1677	85	22	holds	hold	VERB
ejpam-1677	85	23	∫	∫	PROPN
ejpam-1677	85	24	m	m	PROPN
ejpam-1677	85	25	h	h	PROPN
ejpam-1677	85	26	s(x	s(x	PROPN
ejpam-1677	85	27	,	,	PUNCT
ejpam-1677	85	28	x	x	SYM
ejpam-1677	85	29	)	)	PUNCT
ejpam-1677	86	1	−	−	NOUN
ejpam-1677	86	2	|∇x	|∇x	ADJ
ejpam-1677	86	3	|2−	|2−	NOUN
ejpam-1677	86	4	(	(	PUNCT
ejpam-1677	86	5	div	div	X
ejpam-1677	86	6	x	x	SYM
ejpam-1677	86	7	)	)	PUNCT
ejpam-1677	86	8	2	2	NUM
ejpam-1677	86	9	i	i	PRON
ejpam-1677	86	10	dv	dv	PROPN
ejpam-1677	86	11	≤	≤	PROPN
ejpam-1677	86	12	0	0	NUM
ejpam-1677	86	13	,	,	PUNCT
ejpam-1677	86	14	(	(	PUNCT
ejpam-1677	86	15	11	11	NUM
ejpam-1677	86	16	)	)	PUNCT
ejpam-1677	86	17	where	where	SCONJ
ejpam-1677	86	18	“	"	PUNCT
ejpam-1677	86	19	dv	dv	PROPN
ejpam-1677	86	20	”	"	PUNCT
ejpam-1677	86	21	denotes	denote	VERB
ejpam-1677	86	22	the	the	DET
ejpam-1677	86	23	volume	volume	NOUN
ejpam-1677	86	24	element	element	NOUN
ejpam-1677	86	25	of	of	ADP
ejpam-1677	86	26	m	m	PROPN
ejpam-1677	86	27	.	.	PUNCT
ejpam-1677	87	1	if	if	SCONJ
ejpam-1677	87	2	x	x	PRON
ejpam-1677	87	3	is	be	AUX
ejpam-1677	87	4	a	a	DET
ejpam-1677	87	5	killing	kill	VERB
ejpam-1677	87	6	vector	vector	NOUN
ejpam-1677	87	7	field	field	NOUN
ejpam-1677	87	8	,	,	PUNCT
ejpam-1677	87	9	then	then	ADV
ejpam-1677	87	10	div	div	X
ejpam-1677	87	11	x	x	X
ejpam-1677	88	1	=	=	SYM
ejpam-1677	88	2	0	0	PUNCT
ejpam-1677	89	1	[	[	X
ejpam-1677	89	2	18	18	NUM
ejpam-1677	89	3	]	]	PUNCT
ejpam-1677	89	4	.	.	PUNCT
ejpam-1677	90	1	hence	hence	ADV
ejpam-1677	90	2	(	(	PUNCT
ejpam-1677	90	3	11	11	NUM
ejpam-1677	90	4	)	)	PUNCT
ejpam-1677	90	5	takes	take	VERB
ejpam-1677	90	6	the	the	DET
ejpam-1677	90	7	following	follow	VERB
ejpam-1677	90	8	form	form	NOUN
ejpam-1677	90	9	∫	∫	PROPN
ejpam-1677	90	10	m	m	PROPN
ejpam-1677	90	11	h	h	PROPN
ejpam-1677	90	12	s(x	s(x	PROPN
ejpam-1677	90	13	,	,	PUNCT
ejpam-1677	90	14	x	x	SYM
ejpam-1677	90	15	)	)	PUNCT
ejpam-1677	91	1	−	−	NOUN
ejpam-1677	91	2	|∇x	|∇x	VERB
ejpam-1677	91	3	|2	|2	NUM
ejpam-1677	92	1	i	i	PRON
ejpam-1677	92	2	dv	dv	PROPN
ejpam-1677	92	3	=	=	PROPN
ejpam-1677	92	4	0	0	PROPN
ejpam-1677	92	5	.	.	PUNCT
ejpam-1677	93	1	(	(	PUNCT
ejpam-1677	93	2	12	12	NUM
ejpam-1677	93	3	)	)	PUNCT
ejpam-1677	93	4	let	let	VERB
ejpam-1677	93	5	us	we	PRON
ejpam-1677	93	6	consider	consider	VERB
ejpam-1677	93	7	α	α	PRON
ejpam-1677	93	8	<	<	X
ejpam-1677	93	9	0	0	PUNCT
ejpam-1677	93	10	and	and	CCONJ
ejpam-1677	93	11	βd(x	βd(x	PUNCT
ejpam-1677	93	12	,	,	PUNCT
ejpam-1677	93	13	x	x	X
ejpam-1677	93	14	)	)	PUNCT
ejpam-1677	93	15	<	<	X
ejpam-1677	94	1	0	0	X
ejpam-1677	94	2	.	.	PUNCT
ejpam-1677	94	3	hence	hence	ADV
ejpam-1677	94	4	by	by	ADP
ejpam-1677	94	5	virtue	virtue	NOUN
ejpam-1677	94	6	of	of	ADP
ejpam-1677	94	7	(	(	PUNCT
ejpam-1677	94	8	2	2	X
ejpam-1677	94	9	)	)	PUNCT
ejpam-1677	94	10	we	we	PRON
ejpam-1677	94	11	have	have	VERB
ejpam-1677	94	12	∫	∫	PROPN
ejpam-1677	94	13	m	m	PROPN
ejpam-1677	94	14	=	=	NOUN
ejpam-1677	94	15	n(qe)n	n(qe)n	NOUN
ejpam-1677	94	16	h	h	NOUN
ejpam-1677	94	17	α|x	α|x	X
ejpam-1677	94	18	|2	|2	NUM
ejpam-1677	94	19	+	+	CCONJ
ejpam-1677	94	20	βd(x	βd(x	PUNCT
ejpam-1677	94	21	,	,	PUNCT
ejpam-1677	94	22	x	x	X
ejpam-1677	94	23	)	)	PUNCT
ejpam-1677	94	24	−	−	NOUN
ejpam-1677	94	25	|∇x	|∇x	NOUN
ejpam-1677	94	26	|2	|2	NUM
ejpam-1677	95	1	i	i	PRON
ejpam-1677	95	2	dv	dv	PROPN
ejpam-1677	95	3	≥	≥	PROPN
ejpam-1677	95	4	∫	∫	PROPN
ejpam-1677	95	5	m	m	PROPN
ejpam-1677	95	6	h	h	PROPN
ejpam-1677	95	7	s(x	s(x	PROPN
ejpam-1677	95	8	,	,	PUNCT
ejpam-1677	95	9	x	x	SYM
ejpam-1677	95	10	)	)	PUNCT
ejpam-1677	95	11	−	−	NOUN
ejpam-1677	95	12	|∇x	|∇x	VERB
ejpam-1677	95	13	|2	|2	NUM
ejpam-1677	96	1	i	i	PRON
ejpam-1677	96	2	dv	dv	PROPN
ejpam-1677	96	3	,	,	PUNCT
ejpam-1677	96	4	which	which	PRON
ejpam-1677	96	5	yields	yield	VERB
ejpam-1677	96	6	by	by	ADP
ejpam-1677	96	7	virtue	virtue	NOUN
ejpam-1677	96	8	of	of	ADP
ejpam-1677	96	9	(	(	PUNCT
ejpam-1677	96	10	12	12	NUM
ejpam-1677	96	11	)	)	PUNCT
ejpam-1677	97	1	that	that	PRON
ejpam-1677	97	2	∫	∫	PROPN
ejpam-1677	97	3	m	m	VERB
ejpam-1677	97	4	h	h	PROPN
ejpam-1677	97	5	α|x	α|x	PROPN
ejpam-1677	97	6	|2	|2	NUM
ejpam-1677	97	7	+	+	CCONJ
ejpam-1677	97	8	βd(x	βd(x	PUNCT
ejpam-1677	97	9	,	,	PUNCT
ejpam-1677	97	10	x	x	X
ejpam-1677	97	11	)	)	PUNCT
ejpam-1677	97	12	−	−	NOUN
ejpam-1677	97	13	|∇x	|∇x	NOUN
ejpam-1677	97	14	|2	|2	NUM
ejpam-1677	98	1	i	i	PRON
ejpam-1677	98	2	dv	dv	PROPN
ejpam-1677	98	3	≥	≥	PROPN
ejpam-1677	98	4	0	0	NUM
ejpam-1677	98	5	.	.	PUNCT
ejpam-1677	99	1	s.	s.	PROPN
ejpam-1677	99	2	hui	hui	PROPN
ejpam-1677	99	3	/	/	SYM
ejpam-1677	99	4	eur	eur	PROPN
ejpam-1677	99	5	.	.	PUNCT
ejpam-1677	100	1	j.	j.	PROPN
ejpam-1677	100	2	pure	pure	PROPN
ejpam-1677	100	3	appl	appl	PROPN
ejpam-1677	100	4	.	.	PROPN
ejpam-1677	100	5	math	math	PROPN
ejpam-1677	100	6	,	,	PUNCT
ejpam-1677	100	7	5	5	NUM
ejpam-1677	100	8	(	(	PUNCT
ejpam-1677	100	9	2012	2012	NUM
ejpam-1677	100	10	)	)	PUNCT
ejpam-1677	100	11	,	,	PUNCT
ejpam-1677	100	12	365	365	NUM
ejpam-1677	100	13	-	-	SYM
ejpam-1677	100	14	372	372	NUM
ejpam-1677	100	15	369	369	NUM
ejpam-1677	100	16	if	if	SCONJ
ejpam-1677	100	17	α	α	PRON
ejpam-1677	100	18	<	<	X
ejpam-1677	100	19	0	0	PUNCT
ejpam-1677	100	20	and	and	CCONJ
ejpam-1677	100	21	βd(x	βd(x	PUNCT
ejpam-1677	100	22	,	,	PUNCT
ejpam-1677	100	23	x	x	X
ejpam-1677	100	24	)	)	PUNCT
ejpam-1677	100	25	<	<	X
ejpam-1677	100	26	0	0	NUM
ejpam-1677	100	27	,	,	PUNCT
ejpam-1677	100	28	then	then	ADV
ejpam-1677	100	29	the	the	DET
ejpam-1677	100	30	last	last	ADJ
ejpam-1677	100	31	relation	relation	NOUN
ejpam-1677	100	32	reduces	reduce	VERB
ejpam-1677	100	33	to	to	ADP
ejpam-1677	100	34	∫	∫	PROPN
ejpam-1677	100	35	m	m	PROPN
ejpam-1677	100	36	h	h	PROPN
ejpam-1677	100	37	α|x	α|x	PROPN
ejpam-1677	100	38	|2	|2	NUM
ejpam-1677	101	1	+	+	CCONJ
ejpam-1677	102	1	βd(x	βd(x	PUNCT
ejpam-1677	102	2	,	,	PUNCT
ejpam-1677	102	3	x	x	X
ejpam-1677	102	4	)	)	PUNCT
ejpam-1677	102	5	−	−	NOUN
ejpam-1677	102	6	|∇x	|∇x	VERB
ejpam-1677	102	7	|2	|2	NUM
ejpam-1677	103	1	i	i	PRON
ejpam-1677	103	2	dv	dv	PROPN
ejpam-1677	103	3	=	=	PROPN
ejpam-1677	103	4	0	0	PROPN
ejpam-1677	103	5	.	.	PUNCT
ejpam-1677	104	1	hence	hence	ADV
ejpam-1677	104	2	x	x	X
ejpam-1677	104	3	=	=	NOUN
ejpam-1677	104	4	0	0	PROPN
ejpam-1677	104	5	.	.	PUNCT
ejpam-1677	105	1	this	this	PRON
ejpam-1677	105	2	proves	prove	VERB
ejpam-1677	105	3	the	the	DET
ejpam-1677	105	4	theorem	theorem	NOUN
ejpam-1677	105	5	.	.	PROPN
ejpam-1677	106	1	definition	definition	NOUN
ejpam-1677	106	2	1	1	NUM
ejpam-1677	106	3	.	.	PUNCT
ejpam-1677	107	1	[	[	X
ejpam-1677	107	2	18	18	NUM
ejpam-1677	107	3	]	]	PUNCT
ejpam-1677	107	4	a	a	DET
ejpam-1677	107	5	vector	vector	NOUN
ejpam-1677	107	6	field	field	NOUN
ejpam-1677	107	7	x	x	PUNCT
ejpam-1677	107	8	in	in	ADP
ejpam-1677	107	9	a	a	DET
ejpam-1677	107	10	riemannian	riemannian	ADJ
ejpam-1677	107	11	manifold	manifold	NOUN
ejpam-1677	107	12	(	(	PUNCT
ejpam-1677	107	13	m	m	NOUN
ejpam-1677	107	14	n	n	CCONJ
ejpam-1677	107	15	,	,	PUNCT
ejpam-1677	107	16	g	g	NOUN
ejpam-1677	107	17	)	)	PUNCT
ejpam-1677	107	18	(	(	PUNCT
ejpam-1677	107	19	n	n	CCONJ
ejpam-1677	107	20	>	>	X
ejpam-1677	107	21	2	2	NUM
ejpam-1677	107	22	)	)	PUNCT
ejpam-1677	107	23	is	be	AUX
ejpam-1677	107	24	said	say	VERB
ejpam-1677	107	25	to	to	PART
ejpam-1677	107	26	be	be	AUX
ejpam-1677	107	27	projective	projective	ADJ
ejpam-1677	107	28	killing	kill	VERB
ejpam-1677	107	29	vector	vector	NOUN
ejpam-1677	107	30	field	field	NOUN
ejpam-1677	107	31	if	if	SCONJ
ejpam-1677	107	32	it	it	PRON
ejpam-1677	107	33	satisfies	satisfy	VERB
ejpam-1677	107	34	(	(	PUNCT
ejpam-1677	107	35	$	$	SYM
ejpam-1677	107	36	x	x	SYM
ejpam-1677	107	37	g)(y	g)(y	PROPN
ejpam-1677	107	38	,	,	PUNCT
ejpam-1677	107	39	z	z	NOUN
ejpam-1677	107	40	)	)	PUNCT
ejpam-1677	108	1	=	=	NOUN
ejpam-1677	108	2	ω(y	ω(y	NOUN
ejpam-1677	108	3	)	)	PUNCT
ejpam-1677	108	4	z	z	X
ejpam-1677	109	1	+	+	NOUN
ejpam-1677	109	2	ω(z)y	ω(z)y	VERB
ejpam-1677	109	3	for	for	ADP
ejpam-1677	109	4	any	any	DET
ejpam-1677	109	5	vector	vector	NOUN
ejpam-1677	109	6	fields	field	NOUN
ejpam-1677	109	7	y	y	PROPN
ejpam-1677	109	8	and	and	CCONJ
ejpam-1677	109	9	z	z	PROPN
ejpam-1677	109	10	,	,	PUNCT
ejpam-1677	109	11	ω	ω	NUM
ejpam-1677	109	12	being	be	AUX
ejpam-1677	109	13	a	a	DET
ejpam-1677	109	14	certain	certain	ADJ
ejpam-1677	109	15	1	1	NUM
ejpam-1677	109	16	-	-	PUNCT
ejpam-1677	109	17	form	form	NOUN
ejpam-1677	109	18	and	and	CCONJ
ejpam-1677	109	19	$	$	PRON
ejpam-1677	109	20	is	be	AUX
ejpam-1677	109	21	the	the	DET
ejpam-1677	109	22	operator	operator	NOUN
ejpam-1677	109	23	of	of	ADP
ejpam-1677	109	24	lie	lie	NOUN
ejpam-1677	109	25	differentiation	differentiation	NOUN
ejpam-1677	109	26	.	.	PUNCT
ejpam-1677	110	1	theorem	theorem	NOUN
ejpam-1677	110	2	5	5	NUM
ejpam-1677	110	3	.	.	PUNCT
ejpam-1677	111	1	if	if	SCONJ
ejpam-1677	111	2	in	in	ADP
ejpam-1677	111	3	a	a	DET
ejpam-1677	111	4	compact	compact	ADJ
ejpam-1677	111	5	,	,	PUNCT
ejpam-1677	111	6	orientable	orientable	ADJ
ejpam-1677	111	7	n(qe)n(n	n(qe)n(n	PROPN
ejpam-1677	111	8	>	>	X
ejpam-1677	111	9	2	2	NUM
ejpam-1677	111	10	)	)	PUNCT
ejpam-1677	111	11	without	without	ADP
ejpam-1677	111	12	boundary	boundary	NOUN
ejpam-1677	111	13	,	,	PUNCT
ejpam-1677	111	14	the	the	DET
ejpam-1677	111	15	associated	associated	ADJ
ejpam-1677	111	16	scalars	scalar	NOUN
ejpam-1677	111	17	and	and	CCONJ
ejpam-1677	111	18	the	the	DET
ejpam-1677	111	19	structure	structure	NOUN
ejpam-1677	111	20	tensor	tensor	NOUN
ejpam-1677	111	21	are	be	AUX
ejpam-1677	111	22	such	such	ADJ
ejpam-1677	111	23	that	that	SCONJ
ejpam-1677	111	24	α	α	PROPN
ejpam-1677	111	25	≤	≤	NOUN
ejpam-1677	111	26	0	0	PUNCT
ejpam-1677	111	27	and	and	CCONJ
ejpam-1677	111	28	βd(x	βd(x	PUNCT
ejpam-1677	111	29	,	,	PUNCT
ejpam-1677	111	30	x	x	X
ejpam-1677	111	31	)	)	PUNCT
ejpam-1677	111	32	≤	≤	NUM
ejpam-1677	111	33	0	0	NUM
ejpam-1677	111	34	,	,	PUNCT
ejpam-1677	111	35	then	then	ADV
ejpam-1677	111	36	a	a	DET
ejpam-1677	111	37	projective	projective	ADJ
ejpam-1677	111	38	killing	kill	VERB
ejpam-1677	111	39	vector	vector	NOUN
ejpam-1677	111	40	field	field	NOUN
ejpam-1677	111	41	has	have	AUX
ejpam-1677	111	42	vanishing	vanish	VERB
ejpam-1677	111	43	covariant	covariant	ADJ
ejpam-1677	111	44	derivative	derivative	NOUN
ejpam-1677	111	45	,	,	PUNCT
ejpam-1677	111	46	and	and	CCONJ
ejpam-1677	111	47	if	if	SCONJ
ejpam-1677	111	48	α	α	PRON
ejpam-1677	111	49	<	<	X
ejpam-1677	111	50	0	0	PUNCT
ejpam-1677	111	51	and	and	CCONJ
ejpam-1677	111	52	βd(x	βd(x	PUNCT
ejpam-1677	111	53	,	,	PUNCT
ejpam-1677	111	54	x	x	X
ejpam-1677	111	55	)	)	PUNCT
ejpam-1677	111	56	<	<	X
ejpam-1677	111	57	0	0	NUM
ejpam-1677	111	58	,	,	PUNCT
ejpam-1677	111	59	then	then	ADV
ejpam-1677	111	60	there	there	PRON
ejpam-1677	111	61	exists	exist	VERB
ejpam-1677	111	62	no	no	DET
ejpam-1677	111	63	non	non	ADJ
ejpam-1677	111	64	-	-	ADJ
ejpam-1677	111	65	zero	zero	NUM
ejpam-1677	111	66	projective	projective	ADJ
ejpam-1677	111	67	killing	kill	VERB
ejpam-1677	111	68	vector	vector	NOUN
ejpam-1677	111	69	field	field	NOUN
ejpam-1677	111	70	in	in	ADP
ejpam-1677	111	71	this	this	DET
ejpam-1677	111	72	manifold	manifold	NOUN
ejpam-1677	111	73	.	.	PUNCT
ejpam-1677	112	1	proof	proof	NOUN
ejpam-1677	112	2	.	.	PUNCT
ejpam-1677	113	1	we	we	PRON
ejpam-1677	113	2	know	know	VERB
ejpam-1677	113	3	that	that	SCONJ
ejpam-1677	114	1	[	[	X
ejpam-1677	114	2	17	17	NUM
ejpam-1677	114	3	]	]	PUNCT
ejpam-1677	114	4	for	for	ADP
ejpam-1677	114	5	a	a	DET
ejpam-1677	114	6	vector	vector	NOUN
ejpam-1677	114	7	field	field	NOUN
ejpam-1677	114	8	x	x	PUNCT
ejpam-1677	114	9	in	in	ADP
ejpam-1677	114	10	a	a	DET
ejpam-1677	114	11	riemannian	riemannian	ADJ
ejpam-1677	114	12	manifold	manifold	ADJ
ejpam-1677	114	13	m	m	PROPN
ejpam-1677	114	14	,	,	PUNCT
ejpam-1677	114	15	the	the	DET
ejpam-1677	114	16	following	follow	VERB
ejpam-1677	114	17	relation	relation	NOUN
ejpam-1677	114	18	holds	hold	VERB
ejpam-1677	114	19	∫	∫	PROPN
ejpam-1677	114	20	m	m	PROPN
ejpam-1677	114	21	h	h	PROPN
ejpam-1677	114	22	s(x	s(x	PROPN
ejpam-1677	114	23	,	,	PUNCT
ejpam-1677	114	24	x	x	SYM
ejpam-1677	114	25	)	)	PUNCT
ejpam-1677	114	26	−	−	PROPN
ejpam-1677	114	27	1	1	NUM
ejpam-1677	114	28	4	4	NUM
ejpam-1677	114	29	|dξ|2−	|dξ|2−	NOUN
ejpam-1677	114	30	n−	n−	NOUN
ejpam-1677	114	31	1	1	NUM
ejpam-1677	114	32	2(n+	2(n+	NOUN
ejpam-1677	114	33	1	1	NUM
ejpam-1677	114	34	)	)	PUNCT
ejpam-1677	114	35	(	(	PUNCT
ejpam-1677	114	36	div	div	X
ejpam-1677	114	37	x	x	SYM
ejpam-1677	114	38	)	)	PUNCT
ejpam-1677	114	39	2	2	NUM
ejpam-1677	114	40	i	i	NOUN
ejpam-1677	114	41	dv	dv	PROPN
ejpam-1677	114	42	=	=	PROPN
ejpam-1677	114	43	0	0	PROPN
ejpam-1677	114	44	,	,	PUNCT
ejpam-1677	114	45	(	(	PUNCT
ejpam-1677	114	46	13	13	NUM
ejpam-1677	114	47	)	)	PUNCT
ejpam-1677	114	48	where	where	SCONJ
ejpam-1677	114	49	ξ	ξ	PROPN
ejpam-1677	114	50	is	be	AUX
ejpam-1677	114	51	an	an	DET
ejpam-1677	114	52	1	1	NUM
ejpam-1677	114	53	-	-	PUNCT
ejpam-1677	114	54	form	form	NOUN
ejpam-1677	114	55	corresponding	correspond	VERB
ejpam-1677	114	56	to	to	ADP
ejpam-1677	114	57	the	the	DET
ejpam-1677	114	58	vector	vector	NOUN
ejpam-1677	114	59	field	field	NOUN
ejpam-1677	115	1	x	x	X
ejpam-1677	115	2	.	.	PUNCT
ejpam-1677	116	1	we	we	PRON
ejpam-1677	116	2	now	now	ADV
ejpam-1677	116	3	assume	assume	VERB
ejpam-1677	116	4	α	α	PRON
ejpam-1677	116	5	≤	≤	NOUN
ejpam-1677	116	6	0	0	PUNCT
ejpam-1677	116	7	and	and	CCONJ
ejpam-1677	116	8	βd(x	βd(x	PUNCT
ejpam-1677	116	9	,	,	PUNCT
ejpam-1677	116	10	x	x	X
ejpam-1677	116	11	)	)	PUNCT
ejpam-1677	116	12	≤	≤	NUM
ejpam-1677	116	13	0	0	X
ejpam-1677	116	14	.	.	PUNCT
ejpam-1677	117	1	therefore	therefore	ADV
ejpam-1677	117	2	(	(	PUNCT
ejpam-1677	117	3	13	13	NUM
ejpam-1677	117	4	)	)	PUNCT
ejpam-1677	117	5	yields	yield	NOUN
ejpam-1677	117	6	s(x	s(x	NOUN
ejpam-1677	117	7	,	,	PUNCT
ejpam-1677	117	8	x	x	SYM
ejpam-1677	117	9	)	)	PUNCT
ejpam-1677	117	10	≤	≤	NOUN
ejpam-1677	117	11	0	0	NUM
ejpam-1677	118	1	and	and	CCONJ
ejpam-1677	118	2	hence	hence	ADV
ejpam-1677	118	3	from	from	ADP
ejpam-1677	118	4	(	(	PUNCT
ejpam-1677	118	5	13	13	NUM
ejpam-1677	118	6	)	)	PUNCT
ejpam-1677	118	7	we	we	PRON
ejpam-1677	118	8	obtain	obtain	VERB
ejpam-1677	118	9	dξ	dξ	PROPN
ejpam-1677	118	10	=	=	NOUN
ejpam-1677	118	11	0	0	PUNCT
ejpam-1677	118	12	and	and	CCONJ
ejpam-1677	118	13	div	div	X
ejpam-1677	118	14	x	x	SYM
ejpam-1677	118	15	=	=	PUNCT
ejpam-1677	118	16	0	0	PROPN
ejpam-1677	118	17	.	.	PUNCT
ejpam-1677	119	1	this	this	PRON
ejpam-1677	119	2	implies	imply	VERB
ejpam-1677	119	3	that	that	SCONJ
ejpam-1677	119	4	x	x	PRON
ejpam-1677	119	5	is	be	AUX
ejpam-1677	119	6	harmonic	harmonic	ADJ
ejpam-1677	119	7	as	as	ADV
ejpam-1677	119	8	well	well	ADV
ejpam-1677	119	9	as	as	ADP
ejpam-1677	119	10	a	a	DET
ejpam-1677	119	11	killing	kill	VERB
ejpam-1677	119	12	vector	vector	NOUN
ejpam-1677	119	13	field	field	NOUN
ejpam-1677	119	14	.	.	PUNCT
ejpam-1677	120	1	consequently	consequently	ADV
ejpam-1677	120	2	its	its	PRON
ejpam-1677	120	3	covariant	covariant	ADJ
ejpam-1677	120	4	derivative	derivative	NOUN
ejpam-1677	120	5	vanishes	vanish	VERB
ejpam-1677	120	6	.	.	PUNCT
ejpam-1677	121	1	this	this	PRON
ejpam-1677	121	2	proves	prove	VERB
ejpam-1677	121	3	the	the	DET
ejpam-1677	121	4	theorem	theorem	NOUN
ejpam-1677	121	5	.	.	PROPN
ejpam-1677	122	1	definition	definition	NOUN
ejpam-1677	122	2	2	2	NUM
ejpam-1677	122	3	.	.	PUNCT
ejpam-1677	123	1	[	[	X
ejpam-1677	123	2	18	18	NUM
ejpam-1677	123	3	]	]	PUNCT
ejpam-1677	123	4	a	a	DET
ejpam-1677	123	5	vector	vector	NOUN
ejpam-1677	123	6	field	field	NOUN
ejpam-1677	123	7	x	x	PUNCT
ejpam-1677	123	8	in	in	ADP
ejpam-1677	123	9	a	a	DET
ejpam-1677	123	10	riemannian	riemannian	ADJ
ejpam-1677	123	11	manifold	manifold	NOUN
ejpam-1677	123	12	(	(	PUNCT
ejpam-1677	123	13	m	m	NOUN
ejpam-1677	123	14	n	n	CCONJ
ejpam-1677	123	15	,	,	PUNCT
ejpam-1677	123	16	g	g	NOUN
ejpam-1677	123	17	)	)	PUNCT
ejpam-1677	123	18	(	(	PUNCT
ejpam-1677	123	19	n	n	CCONJ
ejpam-1677	123	20	>	>	X
ejpam-1677	123	21	2	2	NUM
ejpam-1677	123	22	)	)	PUNCT
ejpam-1677	123	23	is	be	AUX
ejpam-1677	123	24	said	say	VERB
ejpam-1677	123	25	to	to	PART
ejpam-1677	123	26	be	be	AUX
ejpam-1677	123	27	conformal	conformal	ADJ
ejpam-1677	123	28	killing	killing	NOUN
ejpam-1677	123	29	vector	vector	NOUN
ejpam-1677	123	30	field	field	NOUN
ejpam-1677	123	31	if	if	SCONJ
ejpam-1677	123	32	it	it	PRON
ejpam-1677	123	33	satisfies	satisfy	VERB
ejpam-1677	123	34	$	$	SYM
ejpam-1677	123	35	x	x	SYM
ejpam-1677	123	36	g	g	NOUN
ejpam-1677	123	37	=	=	PUNCT
ejpam-1677	123	38	2ρg	2ρg	NOUN
ejpam-1677	123	39	for	for	ADP
ejpam-1677	123	40	any	any	DET
ejpam-1677	123	41	vector	vector	NOUN
ejpam-1677	123	42	field	field	NOUN
ejpam-1677	123	43	x	x	PUNCT
ejpam-1677	123	44	,	,	PUNCT
ejpam-1677	123	45	where	where	SCONJ
ejpam-1677	123	46	ρ	ρ	NOUN
ejpam-1677	123	47	is	be	AUX
ejpam-1677	123	48	given	give	VERB
ejpam-1677	123	49	by	by	ADP
ejpam-1677	123	50	ρ	ρ	PROPN
ejpam-1677	123	51	=	=	SYM
ejpam-1677	123	52	−	−	PROPN
ejpam-1677	123	53	1	1	NUM
ejpam-1677	123	54	n	n	CCONJ
ejpam-1677	123	55	(	(	PUNCT
ejpam-1677	123	56	div	div	X
ejpam-1677	123	57	x	x	SYM
ejpam-1677	123	58	)	)	PUNCT
ejpam-1677	123	59	and	and	CCONJ
ejpam-1677	123	60	$	$	PRON
ejpam-1677	123	61	is	be	AUX
ejpam-1677	123	62	the	the	DET
ejpam-1677	123	63	operator	operator	NOUN
ejpam-1677	123	64	of	of	ADP
ejpam-1677	123	65	lie	lie	NOUN
ejpam-1677	123	66	differentiation	differentiation	NOUN
ejpam-1677	123	67	.	.	PUNCT
ejpam-1677	124	1	theorem	theorem	VERB
ejpam-1677	124	2	6	6	NUM
ejpam-1677	124	3	.	.	PUNCT
ejpam-1677	125	1	if	if	SCONJ
ejpam-1677	125	2	in	in	ADP
ejpam-1677	125	3	a	a	DET
ejpam-1677	125	4	compact	compact	ADJ
ejpam-1677	125	5	,	,	PUNCT
ejpam-1677	125	6	orientable	orientable	ADJ
ejpam-1677	125	7	n(qe)n(n	n(qe)n(n	PROPN
ejpam-1677	125	8	>	>	X
ejpam-1677	125	9	2	2	NUM
ejpam-1677	125	10	)	)	PUNCT
ejpam-1677	125	11	without	without	ADP
ejpam-1677	125	12	boundary	boundary	NOUN
ejpam-1677	125	13	,	,	PUNCT
ejpam-1677	125	14	the	the	DET
ejpam-1677	125	15	associated	associated	ADJ
ejpam-1677	125	16	scalars	scalar	NOUN
ejpam-1677	125	17	and	and	CCONJ
ejpam-1677	125	18	the	the	DET
ejpam-1677	125	19	structure	structure	NOUN
ejpam-1677	125	20	tensor	tensor	NOUN
ejpam-1677	125	21	are	be	AUX
ejpam-1677	125	22	such	such	ADJ
ejpam-1677	125	23	that	that	SCONJ
ejpam-1677	125	24	α	α	PRON
ejpam-1677	125	25	<	<	X
ejpam-1677	125	26	0	0	PUNCT
ejpam-1677	125	27	and	and	CCONJ
ejpam-1677	125	28	βd(x	βd(x	PUNCT
ejpam-1677	125	29	,	,	PUNCT
ejpam-1677	125	30	x	x	X
ejpam-1677	125	31	)	)	PUNCT
ejpam-1677	125	32	<	<	X
ejpam-1677	125	33	0	0	NUM
ejpam-1677	125	34	,	,	PUNCT
ejpam-1677	125	35	then	then	ADV
ejpam-1677	125	36	there	there	PRON
ejpam-1677	125	37	exists	exist	VERB
ejpam-1677	125	38	no	no	DET
ejpam-1677	125	39	non	non	ADJ
ejpam-1677	125	40	-	-	ADJ
ejpam-1677	125	41	zero	zero	ADJ
ejpam-1677	125	42	conformal	conformal	ADJ
ejpam-1677	125	43	killing	kill	VERB
ejpam-1677	125	44	vector	vector	NOUN
ejpam-1677	125	45	field	field	NOUN
ejpam-1677	125	46	in	in	ADP
ejpam-1677	125	47	this	this	DET
ejpam-1677	125	48	manifold	manifold	NOUN
ejpam-1677	125	49	.	.	PUNCT
ejpam-1677	126	1	proof	proof	NOUN
ejpam-1677	126	2	.	.	PUNCT
ejpam-1677	127	1	it	it	PRON
ejpam-1677	127	2	is	be	AUX
ejpam-1677	127	3	known	know	VERB
ejpam-1677	127	4	from	from	ADP
ejpam-1677	127	5	[	[	X
ejpam-1677	127	6	17	17	NUM
ejpam-1677	127	7	]	]	PUNCT
ejpam-1677	127	8	that	that	SCONJ
ejpam-1677	127	9	for	for	ADP
ejpam-1677	127	10	a	a	DET
ejpam-1677	127	11	vector	vector	NOUN
ejpam-1677	127	12	field	field	NOUN
ejpam-1677	127	13	x	x	PUNCT
ejpam-1677	127	14	in	in	ADP
ejpam-1677	127	15	a	a	DET
ejpam-1677	127	16	riemannian	riemannian	ADJ
ejpam-1677	127	17	manifold	manifold	ADJ
ejpam-1677	127	18	m	m	PROPN
ejpam-1677	127	19	,	,	PUNCT
ejpam-1677	127	20	the	the	DET
ejpam-1677	127	21	following	follow	VERB
ejpam-1677	127	22	relation	relation	NOUN
ejpam-1677	127	23	holds	hold	VERB
ejpam-1677	127	24	∫	∫	PROPN
ejpam-1677	127	25	m	m	PROPN
ejpam-1677	127	26	h	h	PROPN
ejpam-1677	127	27	s(x	s(x	PROPN
ejpam-1677	127	28	,	,	PUNCT
ejpam-1677	127	29	x	x	SYM
ejpam-1677	127	30	)	)	PUNCT
ejpam-1677	127	31	−	−	NOUN
ejpam-1677	127	32	|∇x	|∇x	ADV
ejpam-1677	128	1	|2−	|2−	NOUN
ejpam-1677	128	2	n−	n−	NOUN
ejpam-1677	128	3	2	2	NUM
ejpam-1677	128	4	n	n	NOUN
ejpam-1677	128	5	(	(	PUNCT
ejpam-1677	128	6	div	div	X
ejpam-1677	128	7	x	x	SYM
ejpam-1677	128	8	)	)	PUNCT
ejpam-1677	128	9	2	2	NUM
ejpam-1677	129	1	i	i	NOUN
ejpam-1677	129	2	dv	dv	PROPN
ejpam-1677	129	3	=	=	PROPN
ejpam-1677	129	4	0	0	PROPN
ejpam-1677	129	5	,	,	PUNCT
ejpam-1677	129	6	(	(	PUNCT
ejpam-1677	129	7	14	14	NUM
ejpam-1677	129	8	)	)	PUNCT
ejpam-1677	129	9	where	where	SCONJ
ejpam-1677	129	10	dv	dv	PROPN
ejpam-1677	129	11	denotes	denote	VERB
ejpam-1677	129	12	the	the	DET
ejpam-1677	129	13	volume	volume	NOUN
ejpam-1677	129	14	element	element	NOUN
ejpam-1677	129	15	of	of	ADP
ejpam-1677	129	16	m	m	PROPN
ejpam-1677	129	17	.	.	PUNCT
ejpam-1677	130	1	now	now	ADV
ejpam-1677	130	2	we	we	PRON
ejpam-1677	130	3	assume	assume	VERB
ejpam-1677	130	4	that	that	SCONJ
ejpam-1677	130	5	the	the	DET
ejpam-1677	130	6	associated	associated	ADJ
ejpam-1677	130	7	scalars	scalar	NOUN
ejpam-1677	130	8	and	and	CCONJ
ejpam-1677	130	9	the	the	DET
ejpam-1677	130	10	structure	structure	NOUN
ejpam-1677	130	11	tensor	tensor	NOUN
ejpam-1677	130	12	are	be	AUX
ejpam-1677	130	13	such	such	ADJ
ejpam-1677	130	14	that	that	SCONJ
ejpam-1677	130	15	α	α	PRON
ejpam-1677	130	16	<	<	X
ejpam-1677	130	17	0	0	PUNCT
ejpam-1677	130	18	and	and	CCONJ
ejpam-1677	130	19	βd(x	βd(x	PUNCT
ejpam-1677	130	20	,	,	PUNCT
ejpam-1677	130	21	x	x	X
ejpam-1677	130	22	)	)	PUNCT
ejpam-1677	130	23	<	<	X
ejpam-1677	131	1	0	0	X
ejpam-1677	131	2	.	.	PUNCT
ejpam-1677	131	3	then	then	ADV
ejpam-1677	131	4	proceeding	proceed	VERB
ejpam-1677	131	5	similarly	similarly	ADV
ejpam-1677	131	6	as	as	SCONJ
ejpam-1677	131	7	before	before	SCONJ
ejpam-1677	131	8	we	we	PRON
ejpam-1677	131	9	obtain	obtain	VERB
ejpam-1677	131	10	∇x	∇x	NOUN
ejpam-1677	131	11	=	=	SYM
ejpam-1677	131	12	0	0	NUM
ejpam-1677	131	13	,	,	PUNCT
ejpam-1677	131	14	div	div	X
ejpam-1677	131	15	x	x	NOUN
ejpam-1677	131	16	=	=	SYM
ejpam-1677	131	17	0	0	PROPN
ejpam-1677	131	18	.	.	PUNCT
ejpam-1677	132	1	this	this	PRON
ejpam-1677	132	2	proves	prove	VERB
ejpam-1677	132	3	the	the	DET
ejpam-1677	132	4	theorem	theorem	NOUN
ejpam-1677	132	5	.	.	PROPN
ejpam-1677	133	1	references	reference	NOUN
ejpam-1677	133	2	370	370	NUM
ejpam-1677	133	3	5	5	NUM
ejpam-1677	133	4	.	.	PUNCT
ejpam-1677	133	5	example	example	NOUN
ejpam-1677	133	6	of	of	ADP
ejpam-1677	133	7	n(qe)n	n(qe)n	NOUN
ejpam-1677	133	8	we	we	PRON
ejpam-1677	133	9	define	define	VERB
ejpam-1677	133	10	a	a	DET
ejpam-1677	133	11	riemannian	riemannian	ADJ
ejpam-1677	133	12	metric	metric	ADJ
ejpam-1677	133	13	g	g	NOUN
ejpam-1677	133	14	on	on	ADP
ejpam-1677	133	15	the	the	DET
ejpam-1677	133	16	n	n	ADV
ejpam-1677	133	17	-	-	PUNCT
ejpam-1677	133	18	dimensional	dimensional	ADJ
ejpam-1677	133	19	real	real	ADJ
ejpam-1677	133	20	number	number	NOUN
ejpam-1677	133	21	space	space	NOUN
ejpam-1677	133	22	rn	rn	NOUN
ejpam-1677	133	23	by	by	ADP
ejpam-1677	133	24	the	the	DET
ejpam-1677	133	25	formula	formula	NOUN
ejpam-1677	133	26	ds2	ds2	PROPN
ejpam-1677	133	27	=	=	SYM
ejpam-1677	133	28	ekx1	ekx1	PROPN
ejpam-1677	134	1	[	[	X
ejpam-1677	134	2	(	(	PUNCT
ejpam-1677	134	3	d	d	PROPN
ejpam-1677	134	4	x1)2	x1)2	PROPN
ejpam-1677	134	5	+	+	NUM
ejpam-1677	134	6	sin2	sin2	NOUN
ejpam-1677	134	7	x3(d	x3(d	X
ejpam-1677	135	1	x2)2	x2)2	X
ejpam-1677	136	1	+	+	CCONJ
ejpam-1677	136	2	(	(	PUNCT
ejpam-1677	136	3	d	d	NOUN
ejpam-1677	136	4	x3)2	x3)2	X
ejpam-1677	136	5	]	]	X
ejpam-1677	137	1	+	+	NUM
ejpam-1677	137	2	f	f	X
ejpam-1677	137	3	(	(	PUNCT
ejpam-1677	137	4	x4)(d	x4)(d	PROPN
ejpam-1677	137	5	x4)2	x4)2	PUNCT
ejpam-1677	138	1	+	+	NUM
ejpam-1677	138	2	n	n	CCONJ
ejpam-1677	138	3	∑	∑	ADV
ejpam-1677	138	4	l=5	l=5	NOUN
ejpam-1677	138	5	(	(	PUNCT
ejpam-1677	138	6	d	d	NOUN
ejpam-1677	138	7	x	x	SYM
ejpam-1677	138	8	l)2	l)2	ADV
ejpam-1677	138	9	,	,	PUNCT
ejpam-1677	138	10	(	(	PUNCT
ejpam-1677	138	11	15	15	NUM
ejpam-1677	138	12	)	)	PUNCT
ejpam-1677	138	13	where	where	SCONJ
ejpam-1677	138	14	x1	x1	PROPN
ejpam-1677	138	15	is	be	AUX
ejpam-1677	138	16	non	non	ADJ
ejpam-1677	138	17	-	-	ADJ
ejpam-1677	138	18	zero	zero	NUM
ejpam-1677	138	19	finite	finite	NOUN
ejpam-1677	138	20	,	,	PUNCT
ejpam-1677	138	21	0	0	PUNCT
ejpam-1677	138	22	<	<	X
ejpam-1677	138	23	x3	x3	ADJ
ejpam-1677	138	24	<	<	X
ejpam-1677	138	25	π	π	PROPN
ejpam-1677	138	26	2	2	NUM
ejpam-1677	138	27	,	,	PUNCT
ejpam-1677	138	28	k	k	PROPN
ejpam-1677	138	29	is	be	AUX
ejpam-1677	138	30	a	a	DET
ejpam-1677	138	31	non	non	ADJ
ejpam-1677	138	32	-	-	ADJ
ejpam-1677	138	33	zero	zero	NUM
ejpam-1677	138	34	finite	finite	NOUN
ejpam-1677	138	35	real	real	ADJ
ejpam-1677	138	36	number	number	NOUN
ejpam-1677	138	37	excepting	except	VERB
ejpam-1677	138	38	±2	±2	NOUN
ejpam-1677	138	39	and	and	CCONJ
ejpam-1677	138	40	f	f	PROPN
ejpam-1677	138	41	is	be	AUX
ejpam-1677	138	42	a	a	DET
ejpam-1677	138	43	positive	positive	ADJ
ejpam-1677	138	44	smooth	smooth	ADJ
ejpam-1677	138	45	function	function	NOUN
ejpam-1677	138	46	of	of	ADP
ejpam-1677	138	47	x4	x4	PROPN
ejpam-1677	138	48	only	only	ADV
ejpam-1677	138	49	.	.	PUNCT
ejpam-1677	139	1	then	then	ADV
ejpam-1677	139	2	the	the	DET
ejpam-1677	139	3	only	only	ADJ
ejpam-1677	139	4	non	non	ADJ
ejpam-1677	139	5	-	-	ADJ
ejpam-1677	139	6	vanishing	vanishing	ADJ
ejpam-1677	139	7	components	component	NOUN
ejpam-1677	139	8	of	of	ADP
ejpam-1677	139	9	the	the	DET
ejpam-1677	139	10	christoffel	christoffel	ADJ
ejpam-1677	139	11	symbols	symbol	NOUN
ejpam-1677	139	12	,	,	PUNCT
ejpam-1677	139	13	the	the	DET
ejpam-1677	139	14	curvature	curvature	NOUN
ejpam-1677	139	15	tensor	tensor	NOUN
ejpam-1677	139	16	,	,	PUNCT
ejpam-1677	139	17	the	the	DET
ejpam-1677	139	18	ricci	ricci	PROPN
ejpam-1677	139	19	tensors	tensor	NOUN
ejpam-1677	139	20	are	be	AUX
ejpam-1677	139	21	given	give	VERB
ejpam-1677	139	22	by	by	ADP
ejpam-1677	139	23	γ1	γ1	PROPN
ejpam-1677	139	24	11	11	NUM
ejpam-1677	139	25	=	=	SYM
ejpam-1677	139	26	k	k	PROPN
ejpam-1677	139	27	2	2	X
ejpam-1677	139	28	=	=	SYM
ejpam-1677	139	29	γ2	γ2	NOUN
ejpam-1677	139	30	12	12	NUM
ejpam-1677	139	31	=	=	SYM
ejpam-1677	139	32	γ	γ	X
ejpam-1677	139	33	3	3	NUM
ejpam-1677	139	34	13	13	NUM
ejpam-1677	139	35	=	=	NOUN
ejpam-1677	139	36	−γ	−γ	ADP
ejpam-1677	139	37	1	1	NUM
ejpam-1677	139	38	33,γ1	33,γ1	NUM
ejpam-1677	139	39	22	22	NUM
ejpam-1677	139	40	=	=	SYM
ejpam-1677	139	41	−	−	PROPN
ejpam-1677	139	42	k	k	SYM
ejpam-1677	139	43	2	2	NUM
ejpam-1677	139	44	sin2	sin2	NOUN
ejpam-1677	139	45	x3	x3	ADJ
ejpam-1677	139	46	,	,	PUNCT
ejpam-1677	139	47	γ3	γ3	NOUN
ejpam-1677	139	48	22	22	NUM
ejpam-1677	139	49	=	=	SYM
ejpam-1677	139	50	−	−	PROPN
ejpam-1677	139	51	sin	sin	NOUN
ejpam-1677	139	52	x3	x3	PROPN
ejpam-1677	139	53	cos	cos	PROPN
ejpam-1677	139	54	x3,γ2	x3,γ2	PROPN
ejpam-1677	139	55	23	23	NUM
ejpam-1677	140	1	=	=	PUNCT
ejpam-1677	140	2	cot	cot	NOUN
ejpam-1677	140	3	x3,γ4	x3,γ4	PROPN
ejpam-1677	140	4	44	44	NUM
ejpam-1677	140	5	=	=	SYM
ejpam-1677	140	6	1	1	NUM
ejpam-1677	140	7	2	2	NUM
ejpam-1677	140	8	f	f	NOUN
ejpam-1677	140	9	′(x4	′(x4	NOUN
ejpam-1677	140	10	)	)	PUNCT
ejpam-1677	140	11	f	f	PROPN
ejpam-1677	140	12	(	(	PUNCT
ejpam-1677	140	13	x4	x4	PROPN
ejpam-1677	140	14	)	)	PUNCT
ejpam-1677	140	15	,	,	PUNCT
ejpam-1677	140	16	r2332	r2332	PROPN
ejpam-1677	140	17	=	=	SYM
ejpam-1677	140	18	�	�	PROPN
ejpam-1677	140	19	k2	k2	NOUN
ejpam-1677	140	20	4	4	NUM
ejpam-1677	140	21	−	−	SYM
ejpam-1677	140	22	1	1	NUM
ejpam-1677	140	23	�	�	PROPN
ejpam-1677	140	24	ekx1	ekx1	PROPN
ejpam-1677	140	25	sin2	sin2	NOUN
ejpam-1677	140	26	x3,s22	x3,s22	PROPN
ejpam-1677	140	27	=	=	SYM
ejpam-1677	140	28	�	�	PROPN
ejpam-1677	140	29	k2	k2	ADJ
ejpam-1677	140	30	4	4	NUM
ejpam-1677	140	31	−	−	SYM
ejpam-1677	140	32	1	1	NUM
ejpam-1677	140	33	�	�	PROPN
ejpam-1677	140	34	sin2	sin2	NOUN
ejpam-1677	140	35	x3,s33	x3,s33	PROPN
ejpam-1677	140	36	=	=	SYM
ejpam-1677	140	37	�	�	PROPN
ejpam-1677	140	38	k2	k2	ADJ
ejpam-1677	140	39	4	4	NUM
ejpam-1677	140	40	−	−	PROPN
ejpam-1677	140	41	1	1	NUM
ejpam-1677	140	42	�	�	PROPN
ejpam-1677	140	43	.	.	PUNCT
ejpam-1677	141	1	here	here	ADV
ejpam-1677	141	2	the	the	DET
ejpam-1677	141	3	scalar	scalar	ADJ
ejpam-1677	141	4	curvature	curvature	NOUN
ejpam-1677	141	5	of	of	ADP
ejpam-1677	141	6	the	the	DET
ejpam-1677	141	7	manifold	manifold	NOUN
ejpam-1677	141	8	is	be	AUX
ejpam-1677	141	9	r	r	NOUN
ejpam-1677	141	10	=	=	SYM
ejpam-1677	141	11	2	2	NUM
ejpam-1677	141	12	(	(	PUNCT
ejpam-1677	141	13	k2	k2	ADJ
ejpam-1677	141	14	4	4	NUM
ejpam-1677	141	15	−	−	PROPN
ejpam-1677	141	16	1)e−kx1	1)e−kx1	NOUN
ejpam-1677	141	17	6=	6=	ADP
ejpam-1677	141	18	0	0	NUM
ejpam-1677	141	19	.	.	PUNCT
ejpam-1677	142	1	therefore	therefore	ADV
ejpam-1677	142	2	rn	rn	PROPN
ejpam-1677	142	3	with	with	ADP
ejpam-1677	142	4	the	the	DET
ejpam-1677	142	5	considered	consider	VERB
ejpam-1677	142	6	metric	metric	ADJ
ejpam-1677	142	7	is	be	AUX
ejpam-1677	142	8	a	a	DET
ejpam-1677	142	9	rimennian	rimennian	PROPN
ejpam-1677	142	10	manifold	manifold	NOUN
ejpam-1677	142	11	(	(	PUNCT
ejpam-1677	142	12	m	m	PROPN
ejpam-1677	142	13	n	n	CCONJ
ejpam-1677	142	14	,	,	PUNCT
ejpam-1677	142	15	g	g	NOUN
ejpam-1677	142	16	)	)	PUNCT
ejpam-1677	142	17	of	of	ADP
ejpam-1677	142	18	non	non	ADJ
ejpam-1677	142	19	-	-	ADJ
ejpam-1677	142	20	vanishing	vanishing	ADJ
ejpam-1677	142	21	scalar	scalar	ADJ
ejpam-1677	142	22	curvature	curvature	NOUN
ejpam-1677	142	23	.	.	PUNCT
ejpam-1677	143	1	we	we	PRON
ejpam-1677	143	2	shall	shall	AUX
ejpam-1677	143	3	now	now	ADV
ejpam-1677	143	4	show	show	VERB
ejpam-1677	143	5	that	that	SCONJ
ejpam-1677	143	6	this	this	PRON
ejpam-1677	143	7	m	m	VERB
ejpam-1677	143	8	n	n	VERB
ejpam-1677	143	9	is	be	AUX
ejpam-1677	143	10	a	a	DET
ejpam-1677	143	11	nearly	nearly	ADV
ejpam-1677	143	12	quasi	quasi	ADJ
ejpam-1677	143	13	-	-	ADJ
ejpam-1677	143	14	einstein	einstein	ADJ
ejpam-1677	143	15	manifold	manifold	NOUN
ejpam-1677	143	16	,	,	PUNCT
ejpam-1677	143	17	i.e.	i.e.	X
ejpam-1677	143	18	,	,	PUNCT
ejpam-1677	143	19	it	it	PRON
ejpam-1677	143	20	satisfies	satisfy	VERB
ejpam-1677	143	21	(	(	PUNCT
ejpam-1677	143	22	2	2	NUM
ejpam-1677	143	23	)	)	PUNCT
ejpam-1677	143	24	.	.	PUNCT
ejpam-1677	144	1	let	let	VERB
ejpam-1677	144	2	us	we	PRON
ejpam-1677	144	3	now	now	ADV
ejpam-1677	144	4	consider	consider	VERB
ejpam-1677	144	5	the	the	DET
ejpam-1677	144	6	associated	associate	VERB
ejpam-1677	144	7	scalars	scalar	NOUN
ejpam-1677	144	8	and	and	CCONJ
ejpam-1677	144	9	the	the	DET
ejpam-1677	144	10	components	component	NOUN
ejpam-1677	144	11	of	of	ADP
ejpam-1677	144	12	the	the	DET
ejpam-1677	144	13	structure	structure	NOUN
ejpam-1677	144	14	tensor	tensor	NOUN
ejpam-1677	144	15	of	of	ADP
ejpam-1677	144	16	d	d	PROPN
ejpam-1677	144	17	as	as	SCONJ
ejpam-1677	144	18	follows	follow	VERB
ejpam-1677	144	19	:	:	PUNCT
ejpam-1677	144	20	α=	α=	NUM
ejpam-1677	144	21	1	1	NUM
ejpam-1677	144	22	2	2	NUM
ejpam-1677	144	23	�	�	NOUN
ejpam-1677	144	24	k2	k2	ADJ
ejpam-1677	144	25	4	4	NUM
ejpam-1677	144	26	−	−	SYM
ejpam-1677	144	27	1	1	NUM
ejpam-1677	144	28	�	�	PROPN
ejpam-1677	144	29	e−kx1	e−kx1	NOUN
ejpam-1677	144	30	,	,	PUNCT
ejpam-1677	144	31	β	β	NOUN
ejpam-1677	144	32	=	=	NOUN
ejpam-1677	144	33	1	1	NUM
ejpam-1677	144	34	2	2	NUM
ejpam-1677	144	35	�	�	NOUN
ejpam-1677	144	36	k2	k2	ADJ
ejpam-1677	144	37	4	4	NUM
ejpam-1677	144	38	−	−	SYM
ejpam-1677	144	39	1	1	NUM
ejpam-1677	144	40	�	�	PROPN
ejpam-1677	144	41	,	,	PUNCT
ejpam-1677	144	42	(	(	PUNCT
ejpam-1677	144	43	16	16	NUM
ejpam-1677	144	44	)	)	PUNCT
ejpam-1677	144	45	and	and	CCONJ
ejpam-1677	144	46	di	di	NOUN
ejpam-1677	144	47	j(x	j(x	PROPN
ejpam-1677	144	48	)	)	PUNCT
ejpam-1677	144	49	=	=	PUNCT
ejpam-1677	145	1			PROPN
ejpam-1677	145	2			ADP
ejpam-1677	145	3			ADJ
ejpam-1677	145	4	sin2	sin2	NOUN
ejpam-1677	145	5	x3	x3	VERB
ejpam-1677	145	6	for	for	ADP
ejpam-1677	145	7	i	i	PROPN
ejpam-1677	145	8	,	,	PUNCT
ejpam-1677	145	9	j	j	PROPN
ejpam-1677	145	10	=	=	SYM
ejpam-1677	145	11	2,2	2,2	PROPN
ejpam-1677	145	12	,	,	PUNCT
ejpam-1677	145	13	1	1	NUM
ejpam-1677	145	14	for	for	ADP
ejpam-1677	145	15	i	i	PRON
ejpam-1677	145	16	,	,	PUNCT
ejpam-1677	145	17	j	j	PROPN
ejpam-1677	145	18	=	=	SYM
ejpam-1677	145	19	3,3	3,3	PROPN
ejpam-1677	145	20	,	,	PUNCT
ejpam-1677	145	21	0	0	NUM
ejpam-1677	145	22	otherwise	otherwise	ADV
ejpam-1677	145	23	(	(	PUNCT
ejpam-1677	145	24	17	17	NUM
ejpam-1677	145	25	)	)	PUNCT
ejpam-1677	145	26	at	at	ADP
ejpam-1677	145	27	any	any	DET
ejpam-1677	145	28	point	point	NOUN
ejpam-1677	145	29	x	x	PUNCT
ejpam-1677	145	30	∈	∈	NOUN
ejpam-1677	145	31	m	m	VERB
ejpam-1677	145	32	.	.	PUNCT
ejpam-1677	146	1	then	then	ADV
ejpam-1677	146	2	it	it	PRON
ejpam-1677	146	3	can	can	AUX
ejpam-1677	146	4	be	be	AUX
ejpam-1677	146	5	easily	easily	ADV
ejpam-1677	146	6	shown	show	VERB
ejpam-1677	146	7	that	that	SCONJ
ejpam-1677	146	8	the	the	DET
ejpam-1677	146	9	manifold	manifold	NOUN
ejpam-1677	146	10	under	under	ADP
ejpam-1677	146	11	consideration	consideration	NOUN
ejpam-1677	146	12	is	be	AUX
ejpam-1677	146	13	nearly	nearly	ADV
ejpam-1677	146	14	quasi	quasi	ADJ
ejpam-1677	146	15	-	-	ADJ
ejpam-1677	146	16	einstein	einstein	ADJ
ejpam-1677	146	17	manifold	manifold	NOUN
ejpam-1677	146	18	.	.	PUNCT
ejpam-1677	147	1	hence	hence	ADV
ejpam-1677	147	2	we	we	PRON
ejpam-1677	147	3	can	can	AUX
ejpam-1677	147	4	state	state	VERB
ejpam-1677	147	5	the	the	DET
ejpam-1677	147	6	following	following	NOUN
ejpam-1677	147	7	:	:	PUNCT
ejpam-1677	147	8	theorem	theorem	VERB
ejpam-1677	147	9	7	7	NUM
ejpam-1677	147	10	.	.	PUNCT
ejpam-1677	148	1	let	let	AUX
ejpam-1677	148	2	(	(	PUNCT
ejpam-1677	148	3	m	m	VERB
ejpam-1677	148	4	n	n	CCONJ
ejpam-1677	148	5	,	,	PUNCT
ejpam-1677	148	6	g	g	NOUN
ejpam-1677	148	7	)	)	PUNCT
ejpam-1677	148	8	be	be	AUX
ejpam-1677	148	9	a	a	DET
ejpam-1677	148	10	riemannian	riemannian	ADJ
ejpam-1677	148	11	manifold	manifold	NOUN
ejpam-1677	148	12	endowed	endow	VERB
ejpam-1677	148	13	with	with	ADP
ejpam-1677	148	14	the	the	DET
ejpam-1677	148	15	metric	metric	NOUN
ejpam-1677	148	16	given	give	VERB
ejpam-1677	148	17	in	in	ADP
ejpam-1677	148	18	(	(	PUNCT
ejpam-1677	148	19	15	15	NUM
ejpam-1677	148	20	)	)	PUNCT
ejpam-1677	148	21	.	.	PUNCT
ejpam-1677	149	1	then	then	ADV
ejpam-1677	149	2	(	(	PUNCT
ejpam-1677	149	3	m	m	VERB
ejpam-1677	149	4	n	n	CCONJ
ejpam-1677	149	5	,	,	PUNCT
ejpam-1677	149	6	g	g	NOUN
ejpam-1677	149	7	)	)	PUNCT
ejpam-1677	149	8	is	be	AUX
ejpam-1677	149	9	a	a	DET
ejpam-1677	149	10	nearly	nearly	ADV
ejpam-1677	149	11	quasi	quasi	ADJ
ejpam-1677	149	12	-	-	ADJ
ejpam-1677	149	13	einstein	einstein	ADJ
ejpam-1677	149	14	manifold	manifold	NOUN
ejpam-1677	149	15	with	with	ADP
ejpam-1677	149	16	non	non	ADJ
ejpam-1677	149	17	-	-	ADJ
ejpam-1677	149	18	vanishing	vanishing	ADJ
ejpam-1677	149	19	scalar	scalar	ADJ
ejpam-1677	149	20	curvature	curvature	NOUN
ejpam-1677	149	21	,	,	PUNCT
ejpam-1677	149	22	which	which	PRON
ejpam-1677	149	23	is	be	AUX
ejpam-1677	149	24	not	not	PART
ejpam-1677	149	25	quasi	quasi	ADJ
ejpam-1677	149	26	-	-	NOUN
ejpam-1677	149	27	einstein	einstein	NOUN
ejpam-1677	149	28	.	.	PUNCT
ejpam-1677	150	1	references	reference	NOUN
ejpam-1677	150	2	[	[	X
ejpam-1677	150	3	1	1	NUM
ejpam-1677	150	4	]	]	PUNCT
ejpam-1677	150	5	m.	m.	NOUN
ejpam-1677	150	6	c.	c.	PROPN
ejpam-1677	150	7	chaki	chaki	PROPN
ejpam-1677	150	8	and	and	CCONJ
ejpam-1677	150	9	r.	r.	PROPN
ejpam-1677	150	10	k.	k.	PROPN
ejpam-1677	150	11	maity	maity	PROPN
ejpam-1677	150	12	.	.	PUNCT
ejpam-1677	151	1	on	on	ADP
ejpam-1677	151	2	quasi	quasi	ADJ
ejpam-1677	151	3	-	-	ADJ
ejpam-1677	151	4	einstein	einstein	ADJ
ejpam-1677	151	5	manifolds	manifold	NOUN
ejpam-1677	151	6	,	,	PUNCT
ejpam-1677	151	7	publ	publ	NOUN
ejpam-1677	151	8	.	.	PUNCT
ejpam-1677	152	1	math	math	NOUN
ejpam-1677	152	2	.	.	PUNCT
ejpam-1677	153	1	debrecen	debrecen	PROPN
ejpam-1677	153	2	57	57	NUM
ejpam-1677	153	3	,	,	PUNCT
ejpam-1677	153	4	297–306	297–306	NUM
ejpam-1677	153	5	.	.	NOUN
ejpam-1677	153	6	2000	2000	NUM
ejpam-1677	153	7	.	.	PUNCT
ejpam-1677	154	1	references	reference	NOUN
ejpam-1677	154	2	371	371	NUM
ejpam-1677	154	3	[	[	X
ejpam-1677	154	4	2	2	NUM
ejpam-1677	154	5	]	]	X
ejpam-1677	154	6	u.	u.	PROPN
ejpam-1677	154	7	c.	c.	PROPN
ejpam-1677	154	8	de	de	PROPN
ejpam-1677	154	9	and	and	CCONJ
ejpam-1677	154	10	a.	a.	PROPN
ejpam-1677	154	11	k.	k.	PROPN
ejpam-1677	154	12	gaji	gaji	PROPN
ejpam-1677	154	13	.	.	PUNCT
ejpam-1677	155	1	on	on	ADP
ejpam-1677	155	2	nearly	nearly	ADV
ejpam-1677	155	3	quasi	quasi	ADJ
ejpam-1677	155	4	-	-	ADJ
ejpam-1677	155	5	einstein	einstein	ADJ
ejpam-1677	155	6	manifolds	manifolds	PROPN
ejpam-1677	155	7	,	,	PUNCT
ejpam-1677	155	8	novi	novi	PROPN
ejpam-1677	155	9	sad	sad	PROPN
ejpam-1677	155	10	j.	j.	PROPN
ejpam-1677	155	11	math	math	PROPN
ejpam-1677	155	12	.	.	PUNCT
ejpam-1677	155	13	,	,	PUNCT
ejpam-1677	155	14	38(2	38(2	NOUN
ejpam-1677	155	15	)	)	PUNCT
ejpam-1677	155	16	,	,	PUNCT
ejpam-1677	155	17	115–121	115–121	NUM
ejpam-1677	155	18	.	.	NOUN
ejpam-1677	155	19	2008	2008	NUM
ejpam-1677	156	1	[	[	X
ejpam-1677	156	2	3	3	NUM
ejpam-1677	156	3	]	]	X
ejpam-1677	156	4	f.	f.	PROPN
ejpam-1677	156	5	defever	defever	PROPN
ejpam-1677	156	6	,	,	PUNCT
ejpam-1677	156	7	r.	r.	PROPN
ejpam-1677	156	8	deszcz	deszcz	PROPN
ejpam-1677	156	9	,	,	PUNCT
ejpam-1677	156	10	m.	m.	NOUN
ejpam-1677	156	11	hotloś	hotloś	PROPN
ejpam-1677	156	12	,	,	PUNCT
ejpam-1677	156	13	m.	m.	NOUN
ejpam-1677	156	14	kucharski	kucharski	PROPN
ejpam-1677	156	15	and	and	CCONJ
ejpam-1677	156	16	z.	z.	PROPN
ejpam-1677	156	17	sentürk	sentürk	PROPN
ejpam-1677	156	18	.	.	PUNCT
ejpam-1677	157	1	generalisations	generalisation	NOUN
ejpam-1677	157	2	of	of	ADP
ejpam-1677	157	3	robertson	robertson	PROPN
ejpam-1677	157	4	-	-	PUNCT
ejpam-1677	157	5	walker	walker	PROPN
ejpam-1677	157	6	spaces	space	NOUN
ejpam-1677	157	7	,	,	PUNCT
ejpam-1677	157	8	annales	annale	VERB
ejpam-1677	157	9	univ	univ	PROPN
ejpam-1677	157	10	.	.	PUNCT
ejpam-1677	158	1	sci	sci	PROPN
ejpam-1677	158	2	.	.	PUNCT
ejpam-1677	158	3	budapest	budapest	PROPN
ejpam-1677	158	4	.	.	PUNCT
ejpam-1677	159	1	eötvös	eötvös	ADJ
ejpam-1677	159	2	sect	sect	NOUN
ejpam-1677	159	3	.	.	PUNCT
ejpam-1677	160	1	math	math	NOUN
ejpam-1677	160	2	.	.	PUNCT
ejpam-1677	160	3	,	,	PUNCT
ejpam-1677	160	4	43	43	NUM
ejpam-1677	160	5	,	,	PUNCT
ejpam-1677	160	6	13–24	13–24	NUM
ejpam-1677	160	7	.	.	PUNCT
ejpam-1677	160	8	2000	2000	NUM
ejpam-1677	160	9	.	.	PUNCT
ejpam-1677	161	1	[	[	X
ejpam-1677	161	2	4	4	NUM
ejpam-1677	161	3	]	]	X
ejpam-1677	161	4	r.	r.	PROPN
ejpam-1677	161	5	deszcz	deszcz	PROPN
ejpam-1677	161	6	.	.	PUNCT
ejpam-1677	162	1	on	on	ADP
ejpam-1677	162	2	pseudosymmetric	pseudosymmetric	ADJ
ejpam-1677	162	3	spaces	space	NOUN
ejpam-1677	162	4	,	,	PUNCT
ejpam-1677	162	5	bull	bull	NOUN
ejpam-1677	162	6	.	.	PUNCT
ejpam-1677	163	1	belg	belg	PROPN
ejpam-1677	163	2	.	.	PUNCT
ejpam-1677	164	1	math	math	NOUN
ejpam-1677	164	2	.	.	PUNCT
ejpam-1677	165	1	soc	soc	PROPN
ejpam-1677	165	2	.	.	PUNCT
ejpam-1677	166	1	ser	ser	PROPN
ejpam-1677	166	2	a	a	PRON
ejpam-1677	166	3	,	,	PUNCT
ejpam-1677	166	4	44	44	NUM
ejpam-1677	166	5	,	,	PUNCT
ejpam-1677	166	6	1–34	1–34	NOUN
ejpam-1677	166	7	.	.	NOUN
ejpam-1677	166	8	1992	1992	NUM
ejpam-1677	166	9	.	.	PUNCT
ejpam-1677	167	1	[	[	X
ejpam-1677	167	2	5	5	NUM
ejpam-1677	167	3	]	]	X
ejpam-1677	167	4	r.	r.	PROPN
ejpam-1677	167	5	deszcz	deszcz	PROPN
ejpam-1677	167	6	,	,	PUNCT
ejpam-1677	167	7	f.	f.	PROPN
ejpam-1677	167	8	dillen	dillen	PROPN
ejpam-1677	167	9	,	,	PUNCT
ejpam-1677	167	10	l.	l.	PROPN
ejpam-1677	167	11	verstraelen	verstraelen	PROPN
ejpam-1677	167	12	and	and	CCONJ
ejpam-1677	167	13	l.	l.	PROPN
ejpam-1677	167	14	vrancken	vrancken	PROPN
ejpam-1677	167	15	.	.	PUNCT
ejpam-1677	168	1	quasi	quasi	ADJ
ejpam-1677	168	2	-	-	NOUN
ejpam-1677	168	3	einstein	einstein	ADJ
ejpam-1677	168	4	totally	totally	ADV
ejpam-1677	168	5	real	real	ADJ
ejpam-1677	168	6	submanifolds	submanifold	NOUN
ejpam-1677	168	7	of	of	ADP
ejpam-1677	168	8	s6(1	s6(1	PROPN
ejpam-1677	168	9	)	)	PUNCT
ejpam-1677	168	10	,	,	PUNCT
ejpam-1677	168	11	tohoku	tohoku	PROPN
ejpam-1677	168	12	math	math	PROPN
ejpam-1677	168	13	.	.	PUNCT
ejpam-1677	169	1	j.	j.	PROPN
ejpam-1677	169	2	,	,	PUNCT
ejpam-1677	169	3	51	51	NUM
ejpam-1677	169	4	,	,	PUNCT
ejpam-1677	169	5	461–478	461–478	NUM
ejpam-1677	169	6	.	.	NOUN
ejpam-1677	169	7	1999	1999	NUM
ejpam-1677	169	8	.	.	PUNCT
ejpam-1677	170	1	[	[	X
ejpam-1677	170	2	6	6	NUM
ejpam-1677	170	3	]	]	PUNCT
ejpam-1677	170	4	r.	r.	PROPN
ejpam-1677	170	5	deszcz	deszcz	ADV
ejpam-1677	170	6	and	and	CCONJ
ejpam-1677	170	7	m.	m.	PROPN
ejpam-1677	170	8	glogowska	glogowska	PROPN
ejpam-1677	170	9	.	.	PUNCT
ejpam-1677	171	1	some	some	DET
ejpam-1677	171	2	examples	example	NOUN
ejpam-1677	171	3	of	of	ADP
ejpam-1677	171	4	nonsemisymmetric	nonsemisymmetric	ADJ
ejpam-1677	171	5	ricci	ricci	PROPN
ejpam-1677	171	6	-	-	PUNCT
ejpam-1677	171	7	semisymmetric	semisymmetric	PROPN
ejpam-1677	171	8	hypersurfaces	hypersurface	NOUN
ejpam-1677	171	9	,	,	PUNCT
ejpam-1677	171	10	colloq	colloq	PROPN
ejpam-1677	171	11	.	.	PUNCT
ejpam-1677	171	12	math	math	PROPN
ejpam-1677	171	13	.	.	PUNCT
ejpam-1677	171	14	,	,	PUNCT
ejpam-1677	171	15	94	94	NUM
ejpam-1677	171	16	,	,	PUNCT
ejpam-1677	171	17	87–101	87–101	PROPN
ejpam-1677	171	18	.	.	PUNCT
ejpam-1677	171	19	2000	2000	NUM
ejpam-1677	171	20	.	.	PUNCT
ejpam-1677	172	1	[	[	X
ejpam-1677	172	2	7	7	X
ejpam-1677	172	3	]	]	X
ejpam-1677	172	4	r.	r.	PROPN
ejpam-1677	172	5	deszcz	deszcz	PROPN
ejpam-1677	172	6	,	,	PUNCT
ejpam-1677	172	7	m.	m.	NOUN
ejpam-1677	172	8	glogowska	glogowska	PROPN
ejpam-1677	172	9	,	,	PUNCT
ejpam-1677	172	10	m.	m.	NOUN
ejpam-1677	172	11	hotloś	hotloś	NOUN
ejpam-1677	172	12	and	and	CCONJ
ejpam-1677	172	13	z.	z.	PROPN
ejpam-1677	172	14	sentürk	sentürk	PROPN
ejpam-1677	172	15	,	,	PUNCT
ejpam-1677	172	16	z.	z.	PROPN
ejpam-1677	172	17	on	on	ADP
ejpam-1677	172	18	certain	certain	ADJ
ejpam-1677	172	19	quasi	quasi	ADJ
ejpam-1677	172	20	-	-	ADJ
ejpam-1677	172	21	einstein	einstein	ADJ
ejpam-1677	172	22	semisymmetric	semisymmetric	ADJ
ejpam-1677	172	23	hypersurfaces	hypersurface	NOUN
ejpam-1677	172	24	,	,	PUNCT
ejpam-1677	172	25	annales	annale	VERB
ejpam-1677	172	26	univ	univ	PROPN
ejpam-1677	172	27	.	.	PUNCT
ejpam-1677	173	1	sci	sci	PROPN
ejpam-1677	173	2	.	.	PUNCT
ejpam-1677	173	3	budapest	budapest	PROPN
ejpam-1677	173	4	.	.	PUNCT
ejpam-1677	174	1	eötvös	eötvös	ADJ
ejpam-1677	174	2	sect	sect	NOUN
ejpam-1677	174	3	.	.	PUNCT
ejpam-1677	175	1	math	math	NOUN
ejpam-1677	175	2	.	.	PUNCT
ejpam-1677	175	3	,	,	PUNCT
ejpam-1677	175	4	41	41	NUM
ejpam-1677	175	5	,	,	PUNCT
ejpam-1677	175	6	151–164	151–164	NUM
ejpam-1677	175	7	.	.	NOUN
ejpam-1677	175	8	1998	1998	NUM
ejpam-1677	175	9	.	.	PUNCT
ejpam-1677	176	1	[	[	X
ejpam-1677	176	2	8	8	NUM
ejpam-1677	176	3	]	]	X
ejpam-1677	176	4	r.	r.	PROPN
ejpam-1677	176	5	deszcz	deszcz	ADV
ejpam-1677	176	6	and	and	CCONJ
ejpam-1677	176	7	m.	m.	NOUN
ejpam-1677	176	8	hotloś.	hotloś.	VERB
ejpam-1677	176	9	on	on	ADP
ejpam-1677	176	10	some	some	DET
ejpam-1677	176	11	pseudosymmetry	pseudosymmetry	NOUN
ejpam-1677	176	12	type	type	NOUN
ejpam-1677	176	13	curvature	curvature	NOUN
ejpam-1677	176	14	condition	condition	NOUN
ejpam-1677	176	15	,	,	PUNCT
ejpam-1677	176	16	tsukuba	tsukuba	PROPN
ejpam-1677	176	17	j.	j.	PROPN
ejpam-1677	176	18	math	math	PROPN
ejpam-1677	176	19	.	.	PROPN
ejpam-1677	176	20	,	,	PUNCT
ejpam-1677	176	21	27	27	NUM
ejpam-1677	176	22	,	,	PUNCT
ejpam-1677	176	23	13–30	13–30	NUM
ejpam-1677	176	24	.	.	PUNCT
ejpam-1677	176	25	2003	2003	NUM
ejpam-1677	176	26	.	.	PUNCT
ejpam-1677	177	1	[	[	X
ejpam-1677	177	2	9	9	NUM
ejpam-1677	177	3	]	]	X
ejpam-1677	177	4	r.	r.	PROPN
ejpam-1677	177	5	deszcz	deszcz	ADV
ejpam-1677	177	6	and	and	CCONJ
ejpam-1677	177	7	m.	m.	NOUN
ejpam-1677	177	8	hotloś	hotloś	NOUN
ejpam-1677	177	9	on	on	ADP
ejpam-1677	177	10	hypersurfaces	hypersurface	NOUN
ejpam-1677	177	11	with	with	ADP
ejpam-1677	177	12	type	type	NOUN
ejpam-1677	177	13	number	number	NOUN
ejpam-1677	177	14	two	two	NUM
ejpam-1677	177	15	in	in	ADP
ejpam-1677	177	16	spaces	space	NOUN
ejpam-1677	177	17	of	of	ADP
ejpam-1677	177	18	constant	constant	ADJ
ejpam-1677	177	19	curvature	curvature	NOUN
ejpam-1677	177	20	,	,	PUNCT
ejpam-1677	177	21	annales	annale	VERB
ejpam-1677	177	22	univ	univ	PROPN
ejpam-1677	177	23	.	.	PUNCT
ejpam-1677	178	1	sci	sci	PROPN
ejpam-1677	178	2	.	.	PUNCT
ejpam-1677	178	3	budapest	budapest	PROPN
ejpam-1677	178	4	.	.	PUNCT
ejpam-1677	179	1	eötvös	eötvös	ADJ
ejpam-1677	179	2	sect	sect	NOUN
ejpam-1677	179	3	.	.	PUNCT
ejpam-1677	180	1	math	math	NOUN
ejpam-1677	180	2	.	.	PUNCT
ejpam-1677	180	3	,	,	PUNCT
ejpam-1677	180	4	46	46	NUM
ejpam-1677	180	5	,	,	PUNCT
ejpam-1677	180	6	19–34	19–34	NUM
ejpam-1677	180	7	.	.	NOUN
ejpam-1677	180	8	2003	2003	NUM
ejpam-1677	180	9	.	.	PUNCT
ejpam-1677	181	1	[	[	X
ejpam-1677	181	2	10	10	NUM
ejpam-1677	181	3	]	]	X
ejpam-1677	181	4	r.	r.	PROPN
ejpam-1677	181	5	deszcz	deszcz	ADV
ejpam-1677	181	6	and	and	CCONJ
ejpam-1677	181	7	m.	m.	NOUN
ejpam-1677	181	8	hotloś	hotloś	PROPN
ejpam-1677	181	9	and	and	CCONJ
ejpam-1677	181	10	z.	z.	PROPN
ejpam-1677	181	11	sentürk	sentürk	PROPN
ejpam-1677	181	12	.	.	PUNCT
ejpam-1677	182	1	quasi	quasi	ADJ
ejpam-1677	182	2	-	-	ADJ
ejpam-1677	182	3	einstein	einstein	ADJ
ejpam-1677	182	4	hypersurfaces	hypersurface	NOUN
ejpam-1677	182	5	in	in	ADP
ejpam-1677	182	6	semi	semi	ADJ
ejpam-1677	182	7	-	-	ADJ
ejpam-1677	182	8	riemannian	riemannian	ADJ
ejpam-1677	182	9	space	space	NOUN
ejpam-1677	182	10	forms	form	NOUN
ejpam-1677	182	11	,	,	PUNCT
ejpam-1677	182	12	colloq	colloq	PROPN
ejpam-1677	182	13	.	.	PUNCT
ejpam-1677	182	14	math	math	PROPN
ejpam-1677	182	15	.	.	PUNCT
ejpam-1677	182	16	,	,	PUNCT
ejpam-1677	182	17	81	81	NUM
ejpam-1677	182	18	,	,	PUNCT
ejpam-1677	182	19	81–97	81–97	NUM
ejpam-1677	182	20	.	.	PUNCT
ejpam-1677	182	21	2001	2001	NUM
ejpam-1677	182	22	.	.	PUNCT
ejpam-1677	183	1	[	[	X
ejpam-1677	183	2	11	11	NUM
ejpam-1677	183	3	]	]	X
ejpam-1677	183	4	r.	r.	PROPN
ejpam-1677	183	5	deszcz	deszcz	ADV
ejpam-1677	183	6	and	and	CCONJ
ejpam-1677	183	7	m.	m.	NOUN
ejpam-1677	183	8	hotloś	hotloś	PROPN
ejpam-1677	183	9	and	and	CCONJ
ejpam-1677	183	10	z.	z.	PROPN
ejpam-1677	183	11	sentürk	sentürk	PROPN
ejpam-1677	183	12	.	.	PUNCT
ejpam-1677	184	1	on	on	ADP
ejpam-1677	184	2	curvature	curvature	NOUN
ejpam-1677	184	3	properties	property	NOUN
ejpam-1677	184	4	of	of	ADP
ejpam-1677	184	5	quasi	quasi	ADJ
ejpam-1677	184	6	-	-	ADJ
ejpam-1677	184	7	einstein	einstein	ADJ
ejpam-1677	184	8	hypersurfaces	hypersurface	NOUN
ejpam-1677	184	9	in	in	ADP
ejpam-1677	184	10	semi	semi	ADJ
ejpam-1677	184	11	-	-	ADJ
ejpam-1677	184	12	euclidean	euclidean	ADJ
ejpam-1677	184	13	spaces	space	NOUN
ejpam-1677	184	14	,	,	PUNCT
ejpam-1677	184	15	soochow	soochow	PROPN
ejpam-1677	184	16	j.	j.	PROPN
ejpam-1677	184	17	math	math	PROPN
ejpam-1677	184	18	.	.	PUNCT
ejpam-1677	184	19	,	,	PUNCT
ejpam-1677	184	20	27(4	27(4	PROPN
ejpam-1677	184	21	)	)	PUNCT
ejpam-1677	184	22	,	,	PUNCT
ejpam-1677	184	23	375–389	375–389	NUM
ejpam-1677	184	24	.	.	PUNCT
ejpam-1677	184	25	2001	2001	NUM
ejpam-1677	184	26	.	.	PUNCT
ejpam-1677	185	1	[	[	X
ejpam-1677	185	2	12	12	NUM
ejpam-1677	185	3	]	]	X
ejpam-1677	185	4	r.	r.	PROPN
ejpam-1677	185	5	deszcz	deszcz	PROPN
ejpam-1677	185	6	,	,	PUNCT
ejpam-1677	185	7	p.	p.	NOUN
ejpam-1677	185	8	verheyen	verheyen	PROPN
ejpam-1677	185	9	and	and	CCONJ
ejpam-1677	185	10	l.	l.	PROPN
ejpam-1677	185	11	verstraelen	verstraelen	PROPN
ejpam-1677	185	12	.	.	PUNCT
ejpam-1677	186	1	on	on	ADP
ejpam-1677	186	2	some	some	DET
ejpam-1677	186	3	generalized	generalize	VERB
ejpam-1677	186	4	einstein	einstein	NOUN
ejpam-1677	186	5	metric	metric	ADJ
ejpam-1677	186	6	conditions	condition	NOUN
ejpam-1677	186	7	,	,	PUNCT
ejpam-1677	186	8	publ	publ	NOUN
ejpam-1677	186	9	.	.	PUNCT
ejpam-1677	187	1	inst	inst	PROPN
ejpam-1677	187	2	.	.	PUNCT
ejpam-1677	187	3	math	math	NOUN
ejpam-1677	187	4	.	.	PUNCT
ejpam-1677	188	1	(	(	PUNCT
ejpam-1677	188	2	beograd	beograd	PROPN
ejpam-1677	188	3	)	)	PUNCT
ejpam-1677	188	4	,	,	PUNCT
ejpam-1677	188	5	60:74	60:74	NUM
ejpam-1677	188	6	,	,	PUNCT
ejpam-1677	188	7	108–120	108–120	NUM
ejpam-1677	188	8	.	.	PUNCT
ejpam-1677	188	9	1996	1996	NUM
ejpam-1677	188	10	.	.	PUNCT
ejpam-1677	189	1	[	[	X
ejpam-1677	189	2	13	13	NUM
ejpam-1677	189	3	]	]	X
ejpam-1677	189	4	d.	d.	PROPN
ejpam-1677	189	5	ferus	ferus	PROPN
ejpam-1677	189	6	.	.	PUNCT
ejpam-1677	190	1	a	a	DET
ejpam-1677	190	2	remark	remark	NOUN
ejpam-1677	190	3	on	on	ADP
ejpam-1677	190	4	codazzi	codazzi	NOUN
ejpam-1677	190	5	tensors	tensor	NOUN
ejpam-1677	190	6	on	on	ADP
ejpam-1677	190	7	constant	constant	ADJ
ejpam-1677	190	8	curvature	curvature	NOUN
ejpam-1677	190	9	space	space	NOUN
ejpam-1677	190	10	,	,	PUNCT
ejpam-1677	190	11	lecture	lecture	NOUN
ejpam-1677	190	12	notes	note	VERB
ejpam-1677	190	13	math	math	NOUN
ejpam-1677	190	14	.	.	PUNCT
ejpam-1677	190	15	,	,	PUNCT
ejpam-1677	190	16	838	838	NUM
ejpam-1677	190	17	,	,	PUNCT
ejpam-1677	190	18	global	global	ADJ
ejpam-1677	190	19	differential	differential	NOUN
ejpam-1677	190	20	geometry	geometry	NOUN
ejpam-1677	190	21	and	and	CCONJ
ejpam-1677	190	22	global	global	ADJ
ejpam-1677	190	23	analysis	analysis	NOUN
ejpam-1677	190	24	,	,	PUNCT
ejpam-1677	190	25	springer	springer	NOUN
ejpam-1677	190	26	-	-	PUNCT
ejpam-1677	190	27	verlag	verlag	PROPN
ejpam-1677	190	28	,	,	PUNCT
ejpam-1677	190	29	new	new	PROPN
ejpam-1677	190	30	york	york	PROPN
ejpam-1677	190	31	,	,	PUNCT
ejpam-1677	190	32	1981	1981	NUM
ejpam-1677	190	33	.	.	PUNCT
ejpam-1677	191	1	[	[	X
ejpam-1677	191	2	14	14	NUM
ejpam-1677	191	3	]	]	PUNCT
ejpam-1677	191	4	a.	a.	NOUN
ejpam-1677	191	5	k.	k.	PROPN
ejpam-1677	191	6	gaji	gaji	PROPN
ejpam-1677	191	7	and	and	CCONJ
ejpam-1677	191	8	u.	u.	PROPN
ejpam-1677	191	9	c.	c.	PROPN
ejpam-1677	191	10	de	de	PROPN
ejpam-1677	191	11	.	.	PROPN
ejpam-1677	191	12	on	on	ADP
ejpam-1677	191	13	the	the	DET
ejpam-1677	191	14	existence	existence	NOUN
ejpam-1677	191	15	of	of	ADP
ejpam-1677	191	16	nearly	nearly	ADV
ejpam-1677	191	17	quasi	quasi	ADJ
ejpam-1677	191	18	-	-	ADJ
ejpam-1677	191	19	einstein	einstein	ADJ
ejpam-1677	191	20	manifolds	manifolds	PROPN
ejpam-1677	191	21	,	,	PUNCT
ejpam-1677	191	22	novi	novi	PROPN
ejpam-1677	191	23	sad	sad	PROPN
ejpam-1677	191	24	j.	j.	PROPN
ejpam-1677	191	25	math	math	PROPN
ejpam-1677	191	26	.	.	PUNCT
ejpam-1677	191	27	,	,	PUNCT
ejpam-1677	191	28	39(2	39(2	NUM
ejpam-1677	191	29	)	)	PUNCT
ejpam-1677	191	30	,	,	PUNCT
ejpam-1677	191	31	111–117	111–117	NUM
ejpam-1677	191	32	.	.	PUNCT
ejpam-1677	191	33	2009	2009	NUM
ejpam-1677	191	34	.	.	PUNCT
ejpam-1677	192	1	[	[	X
ejpam-1677	192	2	15	15	NUM
ejpam-1677	192	3	]	]	X
ejpam-1677	192	4	a.	a.	NOUN
ejpam-1677	192	5	a.	a.	NOUN
ejpam-1677	192	6	shaikh	shaikh	PROPN
ejpam-1677	192	7	,	,	PUNCT
ejpam-1677	192	8	y.	y.	PROPN
ejpam-1677	192	9	h.	h.	PROPN
ejpam-1677	192	10	kim	kim	PROPN
ejpam-1677	192	11	and	and	CCONJ
ejpam-1677	192	12	s.	s.	PROPN
ejpam-1677	192	13	k.	k.	PROPN
ejpam-1677	192	14	hui	hui	PROPN
ejpam-1677	192	15	.	.	PUNCT
ejpam-1677	193	1	on	on	ADP
ejpam-1677	193	2	lorentzian	lorentzian	ADJ
ejpam-1677	193	3	quasi	quasi	PROPN
ejpam-1677	193	4	-	-	ADJ
ejpam-1677	193	5	einstein	einstein	ADJ
ejpam-1677	193	6	manifolds	manifolds	PROPN
ejpam-1677	193	7	,	,	PUNCT
ejpam-1677	193	8	j.	j.	PROPN
ejpam-1677	193	9	korean	korean	PROPN
ejpam-1677	193	10	math	math	PROPN
ejpam-1677	193	11	.	.	PUNCT
ejpam-1677	194	1	society	society	NOUN
ejpam-1677	194	2	,	,	PUNCT
ejpam-1677	194	3	48(4	48(4	NUM
ejpam-1677	194	4	)	)	PUNCT
ejpam-1677	194	5	,	,	PUNCT
ejpam-1677	194	6	669–689	669–689	NUM
ejpam-1677	194	7	.	.	PUNCT
ejpam-1677	194	8	2011	2011	NUM
ejpam-1677	194	9	.	.	PUNCT
ejpam-1677	195	1	[	[	X
ejpam-1677	195	2	16	16	NUM
ejpam-1677	195	3	]	]	PUNCT
ejpam-1677	195	4	a.	a.	NOUN
ejpam-1677	195	5	a.	a.	NOUN
ejpam-1677	195	6	shaikh	shaikh	PROPN
ejpam-1677	195	7	,	,	PUNCT
ejpam-1677	195	8	d.	d.	PROPN
ejpam-1677	195	9	w.	w.	PROPN
ejpam-1677	195	10	yoon	yoon	PROPN
ejpam-1677	195	11	and	and	CCONJ
ejpam-1677	195	12	s.	s.	PROPN
ejpam-1677	195	13	k.	k.	PROPN
ejpam-1677	195	14	hui	hui	PROPN
ejpam-1677	195	15	.	.	PUNCT
ejpam-1677	196	1	on	on	ADP
ejpam-1677	196	2	quasi	quasi	ADJ
ejpam-1677	196	3	-	-	ADJ
ejpam-1677	196	4	einstein	einstein	ADJ
ejpam-1677	196	5	spacetimes	spacetime	NOUN
ejpam-1677	196	6	,	,	PUNCT
ejpam-1677	196	7	tsukuba	tsukuba	PROPN
ejpam-1677	196	8	j.	j.	PROPN
ejpam-1677	196	9	math	math	PROPN
ejpam-1677	196	10	.	.	PUNCT
ejpam-1677	196	11	,	,	PUNCT
ejpam-1677	196	12	33(2	33(2	NUM
ejpam-1677	196	13	)	)	PUNCT
ejpam-1677	196	14	,	,	PUNCT
ejpam-1677	196	15	305–326	305–326	NUM
ejpam-1677	196	16	.	.	PUNCT
ejpam-1677	196	17	2009	2009	NUM
ejpam-1677	196	18	.	.	PUNCT
ejpam-1677	197	1	[	[	X
ejpam-1677	197	2	17	17	NUM
ejpam-1677	197	3	]	]	X
ejpam-1677	197	4	y.	y.	PROPN
ejpam-1677	197	5	watanabe	watanabe	PROPN
ejpam-1677	197	6	.	.	PUNCT
ejpam-1677	198	1	integral	integral	ADJ
ejpam-1677	198	2	inequalities	inequality	NOUN
ejpam-1677	198	3	in	in	ADP
ejpam-1677	198	4	compact	compact	ADJ
ejpam-1677	198	5	orientable	orientable	ADJ
ejpam-1677	198	6	manifolds	manifold	NOUN
ejpam-1677	198	7	,	,	PUNCT
ejpam-1677	198	8	riemannian	riemannian	NOUN
ejpam-1677	198	9	or	or	CCONJ
ejpam-1677	198	10	kahlerian	kahlerian	ADJ
ejpam-1677	198	11	,	,	PUNCT
ejpam-1677	198	12	kodai	kodai	PROPN
ejpam-1677	198	13	math	math	PROPN
ejpam-1677	198	14	.	.	PUNCT
ejpam-1677	199	1	sem	sem	PROPN
ejpam-1677	199	2	.	.	PUNCT
ejpam-1677	199	3	rep	rep	PROPN
ejpam-1677	199	4	.	.	PROPN
ejpam-1677	199	5	,	,	PUNCT
ejpam-1677	199	6	20	20	NUM
ejpam-1677	199	7	,	,	PUNCT
ejpam-1677	199	8	261–271	261–271	NUM
ejpam-1677	199	9	.	.	PUNCT
ejpam-1677	199	10	1968	1968	NUM
ejpam-1677	199	11	.	.	PUNCT
ejpam-1677	200	1	references	reference	NOUN
ejpam-1677	200	2	372	372	NUM
ejpam-1677	200	3	[	[	X
ejpam-1677	200	4	18	18	NUM
ejpam-1677	200	5	]	]	PUNCT
ejpam-1677	200	6	k.	k.	PROPN
ejpam-1677	200	7	yano	yano	PROPN
ejpam-1677	200	8	.	.	PUNCT
ejpam-1677	201	1	integral	integral	ADJ
ejpam-1677	201	2	formulas	formula	NOUN
ejpam-1677	201	3	in	in	ADP
ejpam-1677	201	4	riemannian	riemannian	ADJ
ejpam-1677	201	5	geometry	geometry	NOUN
ejpam-1677	201	6	,	,	PUNCT
ejpam-1677	201	7	marcel	marcel	PROPN
ejpam-1677	201	8	dekker	dekker	PROPN
ejpam-1677	201	9	,	,	PUNCT
ejpam-1677	201	10	new	new	PROPN
ejpam-1677	201	11	york	york	PROPN
ejpam-1677	201	12	,	,	PUNCT
ejpam-1677	201	13	1970	1970	NUM
ejpam-1677	201	14	.	.	PUNCT
ejpam-1677	202	1	[	[	X
ejpam-1677	202	2	19	19	NUM
ejpam-1677	202	3	]	]	PUNCT
ejpam-1677	202	4	k.	k.	PROPN
ejpam-1677	202	5	yano	yano	PROPN
ejpam-1677	202	6	and	and	CCONJ
ejpam-1677	202	7	m.	m.	PROPN
ejpam-1677	202	8	kon	kon	PROPN
ejpam-1677	202	9	.	.	PUNCT
ejpam-1677	203	1	structure	structure	NOUN
ejpam-1677	203	2	on	on	ADP
ejpam-1677	203	3	manifolds	manifold	NOUN
ejpam-1677	203	4	,	,	PUNCT
ejpam-1677	203	5	world	world	NOUN
ejpam-1677	203	6	scientific	scientific	ADJ
ejpam-1677	203	7	publ	publ	NOUN
ejpam-1677	203	8	.	.	PUNCT
ejpam-1677	203	9	,	,	PUNCT
ejpam-1677	203	10	singapore	singapore	PROPN
ejpam-1677	203	11	,	,	PUNCT
ejpam-1677	203	12	1984	1984	NUM
ejpam-1677	203	13	.	.	PUNCT