id	sid	tid	token	lemma	pos
ejpam-1048	1	1	7_1048_yilmaz.dvi	7_1048_yilmaz.dvi	NUM
ejpam-1048	1	2	european	european	PROPN
ejpam-1048	1	3	journal	journal	PROPN
ejpam-1048	1	4	of	of	ADP
ejpam-1048	1	5	pure	pure	ADJ
ejpam-1048	1	6	and	and	CCONJ
ejpam-1048	1	7	applied	apply	VERB
ejpam-1048	1	8	mathematics	mathematic	NOUN
ejpam-1048	1	9	vol	vol	NOUN
ejpam-1048	1	10	.	.	PROPN
ejpam-1048	1	11	4	4	NUM
ejpam-1048	1	12	,	,	PUNCT
ejpam-1048	1	13	no	no	INTJ
ejpam-1048	1	14	.	.	NOUN
ejpam-1048	1	15	2	2	NUM
ejpam-1048	1	16	,	,	PUNCT
ejpam-1048	1	17	2011	2011	NUM
ejpam-1048	1	18	,	,	PUNCT
ejpam-1048	1	19	152	152	NUM
ejpam-1048	1	20	-	-	SYM
ejpam-1048	1	21	161	161	NUM
ejpam-1048	1	22	issn	issn	PROPN
ejpam-1048	1	23	1307	1307	NUM
ejpam-1048	1	24	-	-	SYM
ejpam-1048	1	25	5543	5543	NUM
ejpam-1048	1	26	–	–	PUNCT
ejpam-1048	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1048	1	28	on	on	ADP
ejpam-1048	1	29	a	a	DET
ejpam-1048	1	30	semi	semi	ADJ
ejpam-1048	1	31	symmetric	symmetric	ADJ
ejpam-1048	1	32	metric	metric	ADJ
ejpam-1048	1	33	connection	connection	NOUN
ejpam-1048	1	34	with	with	ADP
ejpam-1048	1	35	a	a	DET
ejpam-1048	1	36	special	special	ADJ
ejpam-1048	1	37	condition	condition	NOUN
ejpam-1048	1	38	on	on	ADP
ejpam-1048	1	39	a	a	DET
ejpam-1048	1	40	riemannian	riemannian	ADJ
ejpam-1048	1	41	manifold	manifold	PROPN
ejpam-1048	1	42	hülya	hülya	PROPN
ejpam-1048	1	43	bağdatlı	bağdatlı	PROPN
ejpam-1048	1	44	yılmaz1,∗	yılmaz1,∗	NOUN
ejpam-1048	1	45	,	,	PUNCT
ejpam-1048	1	46	füsun	füsun	ADJ
ejpam-1048	1	47	özen	özen	NOUN
ejpam-1048	1	48	zengin2	zengin2	NOUN
ejpam-1048	1	49	,	,	PUNCT
ejpam-1048	1	50	and	and	CCONJ
ejpam-1048	1	51	s.	s.	PROPN
ejpam-1048	1	52	aynur	aynur	PROPN
ejpam-1048	1	53	uysal3	uysal3	PROPN
ejpam-1048	1	54	1	1	NUM
ejpam-1048	1	55	department	department	NOUN
ejpam-1048	1	56	of	of	ADP
ejpam-1048	1	57	mathematics	mathematic	NOUN
ejpam-1048	1	58	,	,	PUNCT
ejpam-1048	1	59	faculty	faculty	NOUN
ejpam-1048	1	60	of	of	ADP
ejpam-1048	1	61	sciences	science	NOUN
ejpam-1048	1	62	and	and	CCONJ
ejpam-1048	1	63	letters	letter	NOUN
ejpam-1048	1	64	,	,	PUNCT
ejpam-1048	1	65	marmara	marmara	PROPN
ejpam-1048	1	66	university	university	PROPN
ejpam-1048	1	67	,	,	PUNCT
ejpam-1048	1	68	istanbul	istanbul	PROPN
ejpam-1048	1	69	,	,	PUNCT
ejpam-1048	1	70	turkey	turkey	PROPN
ejpam-1048	1	71	2	2	NUM
ejpam-1048	1	72	department	department	NOUN
ejpam-1048	1	73	of	of	ADP
ejpam-1048	1	74	mathematics	mathematic	NOUN
ejpam-1048	1	75	,	,	PUNCT
ejpam-1048	1	76	faculty	faculty	NOUN
ejpam-1048	1	77	of	of	ADP
ejpam-1048	1	78	sciences	science	NOUN
ejpam-1048	1	79	and	and	CCONJ
ejpam-1048	1	80	letters	letter	NOUN
ejpam-1048	1	81	,	,	PUNCT
ejpam-1048	1	82	istanbul	istanbul	PROPN
ejpam-1048	1	83	technical	technical	PROPN
ejpam-1048	1	84	university	university	PROPN
ejpam-1048	1	85	,	,	PUNCT
ejpam-1048	1	86	istanbul	istanbul	PROPN
ejpam-1048	1	87	,	,	PUNCT
ejpam-1048	1	88	turkey	turkey	PROPN
ejpam-1048	1	89	3	3	NUM
ejpam-1048	1	90	department	department	NOUN
ejpam-1048	1	91	of	of	ADP
ejpam-1048	1	92	mathematics	mathematic	NOUN
ejpam-1048	1	93	,	,	PUNCT
ejpam-1048	1	94	faculty	faculty	NOUN
ejpam-1048	1	95	of	of	ADP
ejpam-1048	1	96	sciences	science	NOUN
ejpam-1048	1	97	and	and	CCONJ
ejpam-1048	1	98	letters	letter	NOUN
ejpam-1048	1	99	,	,	PUNCT
ejpam-1048	1	100	dogus	dogus	PROPN
ejpam-1048	1	101	university	university	PROPN
ejpam-1048	1	102	,	,	PUNCT
ejpam-1048	1	103	istanbul	istanbul	PROPN
ejpam-1048	1	104	,	,	PUNCT
ejpam-1048	1	105	turkey	turkey	PROPN
ejpam-1048	1	106	abstract	abstract	NOUN
ejpam-1048	1	107	.	.	PUNCT
ejpam-1048	2	1	in	in	ADP
ejpam-1048	2	2	this	this	DET
ejpam-1048	2	3	study	study	NOUN
ejpam-1048	2	4	,	,	PUNCT
ejpam-1048	2	5	we	we	PRON
ejpam-1048	2	6	consider	consider	VERB
ejpam-1048	2	7	a	a	DET
ejpam-1048	2	8	manifold	manifold	NOUN
ejpam-1048	2	9	equipped	equip	VERB
ejpam-1048	2	10	with	with	ADP
ejpam-1048	2	11	semi	semi	ADJ
ejpam-1048	2	12	symmetric	symmetric	ADJ
ejpam-1048	2	13	metric	metric	ADJ
ejpam-1048	2	14	connection	connection	NOUN
ejpam-1048	2	15	whose	whose	DET
ejpam-1048	2	16	the	the	DET
ejpam-1048	2	17	torsion	torsion	NOUN
ejpam-1048	2	18	tensor	tensor	NOUN
ejpam-1048	2	19	satisfies	satisfy	VERB
ejpam-1048	2	20	a	a	DET
ejpam-1048	2	21	special	special	ADJ
ejpam-1048	2	22	condition	condition	NOUN
ejpam-1048	2	23	.	.	PUNCT
ejpam-1048	3	1	we	we	PRON
ejpam-1048	3	2	investigate	investigate	VERB
ejpam-1048	3	3	some	some	DET
ejpam-1048	3	4	properties	property	NOUN
ejpam-1048	3	5	of	of	ADP
ejpam-1048	3	6	the	the	DET
ejpam-1048	3	7	ricci	ricci	PROPN
ejpam-1048	3	8	tensor	tensor	NOUN
ejpam-1048	3	9	and	and	CCONJ
ejpam-1048	3	10	the	the	DET
ejpam-1048	3	11	curvature	curvature	NOUN
ejpam-1048	3	12	tensor	tensor	NOUN
ejpam-1048	3	13	of	of	ADP
ejpam-1048	3	14	this	this	DET
ejpam-1048	3	15	manifold	manifold	NOUN
ejpam-1048	3	16	.	.	PUNCT
ejpam-1048	4	1	we	we	PRON
ejpam-1048	4	2	obtain	obtain	VERB
ejpam-1048	4	3	a	a	DET
ejpam-1048	4	4	necessary	necessary	ADJ
ejpam-1048	4	5	and	and	CCONJ
ejpam-1048	4	6	sufficient	sufficient	ADJ
ejpam-1048	4	7	condition	condition	NOUN
ejpam-1048	4	8	for	for	ADP
ejpam-1048	4	9	the	the	DET
ejpam-1048	4	10	mixed	mixed	ADJ
ejpam-1048	4	11	generalized	generalized	ADJ
ejpam-1048	4	12	quasi	quasi	ADJ
ejpam-1048	4	13	-	-	ADJ
ejpam-1048	4	14	constant	constant	ADJ
ejpam-1048	4	15	curvature	curvature	NOUN
ejpam-1048	4	16	of	of	ADP
ejpam-1048	4	17	this	this	DET
ejpam-1048	4	18	manifold	manifold	NOUN
ejpam-1048	4	19	.	.	PUNCT
ejpam-1048	5	1	finally	finally	ADV
ejpam-1048	5	2	,	,	PUNCT
ejpam-1048	5	3	we	we	PRON
ejpam-1048	5	4	prove	prove	VERB
ejpam-1048	5	5	that	that	SCONJ
ejpam-1048	5	6	if	if	SCONJ
ejpam-1048	5	7	the	the	DET
ejpam-1048	5	8	manifold	manifold	NOUN
ejpam-1048	5	9	mentioned	mention	VERB
ejpam-1048	5	10	above	above	ADV
ejpam-1048	5	11	is	be	AUX
ejpam-1048	5	12	conformally	conformally	ADV
ejpam-1048	5	13	flat	flat	ADJ
ejpam-1048	5	14	,	,	PUNCT
ejpam-1048	5	15	then	then	ADV
ejpam-1048	5	16	it	it	PRON
ejpam-1048	5	17	is	be	AUX
ejpam-1048	5	18	a	a	DET
ejpam-1048	5	19	mixed	mixed	ADJ
ejpam-1048	5	20	generalized	generalize	VERB
ejpam-1048	5	21	quasieinstein	quasieinstein	ADJ
ejpam-1048	5	22	manifold	manifold	ADJ
ejpam-1048	5	23	and	and	CCONJ
ejpam-1048	5	24	we	we	PRON
ejpam-1048	5	25	prove	prove	VERB
ejpam-1048	5	26	that	that	SCONJ
ejpam-1048	5	27	if	if	SCONJ
ejpam-1048	5	28	the	the	DET
ejpam-1048	5	29	sectional	sectional	ADJ
ejpam-1048	5	30	curvature	curvature	NOUN
ejpam-1048	5	31	of	of	ADP
ejpam-1048	5	32	a	a	DET
ejpam-1048	5	33	riemannian	riemannian	NOUN
ejpam-1048	5	34	manifold	manifold	NOUN
ejpam-1048	5	35	with	with	ADP
ejpam-1048	5	36	a	a	DET
ejpam-1048	5	37	semi	semi	ADJ
ejpam-1048	5	38	symmetric	symmetric	ADJ
ejpam-1048	5	39	metric	metric	ADJ
ejpam-1048	5	40	connection	connection	NOUN
ejpam-1048	5	41	whose	whose	DET
ejpam-1048	5	42	the	the	DET
ejpam-1048	5	43	special	special	ADJ
ejpam-1048	5	44	torsion	torsion	NOUN
ejpam-1048	5	45	tensor	tensor	NOUN
ejpam-1048	5	46	is	be	AUX
ejpam-1048	5	47	independent	independent	ADJ
ejpam-1048	5	48	from	from	ADP
ejpam-1048	5	49	orientation	orientation	NOUN
ejpam-1048	5	50	chosen	choose	VERB
ejpam-1048	5	51	,	,	PUNCT
ejpam-1048	5	52	then	then	ADV
ejpam-1048	5	53	this	this	DET
ejpam-1048	5	54	manifold	manifold	NOUN
ejpam-1048	5	55	is	be	AUX
ejpam-1048	5	56	of	of	ADP
ejpam-1048	5	57	a	a	DET
ejpam-1048	5	58	mixed	mixed	ADJ
ejpam-1048	5	59	generalized	generalize	VERB
ejpam-1048	5	60	quasi	quasi	ADJ
ejpam-1048	5	61	constant	constant	ADJ
ejpam-1048	5	62	curvature	curvature	NOUN
ejpam-1048	5	63	.	.	PUNCT
ejpam-1048	6	1	2000	2000	NUM
ejpam-1048	6	2	mathematics	mathematic	NOUN
ejpam-1048	6	3	subject	subject	NOUN
ejpam-1048	6	4	classifications	classification	NOUN
ejpam-1048	6	5	:	:	PUNCT
ejpam-1048	6	6	53b15	53b15	NUM
ejpam-1048	6	7	,	,	PUNCT
ejpam-1048	6	8	53b20	53b20	NUM
ejpam-1048	6	9	,	,	PUNCT
ejpam-1048	6	10	53c15	53c15	NUM
ejpam-1048	6	11	key	key	ADJ
ejpam-1048	6	12	words	word	NOUN
ejpam-1048	6	13	and	and	CCONJ
ejpam-1048	6	14	phrases	phrase	NOUN
ejpam-1048	6	15	:	:	PUNCT
ejpam-1048	6	16	semi	semi	ADV
ejpam-1048	6	17	symmetric	symmetric	ADJ
ejpam-1048	6	18	metric	metric	ADJ
ejpam-1048	6	19	connection	connection	NOUN
ejpam-1048	6	20	,	,	PUNCT
ejpam-1048	6	21	generalized	generalize	VERB
ejpam-1048	6	22	quasi	quasi	NOUN
ejpam-1048	6	23	-einstein	-einstein	PROPN
ejpam-1048	6	24	manifold	manifold	ADJ
ejpam-1048	6	25	,	,	PUNCT
ejpam-1048	6	26	mixed	mixed	ADJ
ejpam-1048	6	27	generalized	generalized	ADJ
ejpam-1048	6	28	quasi	quasi	ADJ
ejpam-1048	6	29	constant	constant	ADJ
ejpam-1048	6	30	curvature	curvature	NOUN
ejpam-1048	6	31	manifold	manifold	ADJ
ejpam-1048	6	32	,	,	PUNCT
ejpam-1048	6	33	mixed	mixed	ADJ
ejpam-1048	6	34	generalized	generalized	ADJ
ejpam-1048	6	35	quasi	quasi	ADJ
ejpam-1048	6	36	-	-	ADJ
ejpam-1048	6	37	einstein	einstein	ADJ
ejpam-1048	6	38	manifold	manifold	ADJ
ejpam-1048	6	39	1	1	NUM
ejpam-1048	6	40	.	.	PUNCT
ejpam-1048	6	41	introduction	introduction	NOUN
ejpam-1048	6	42	the	the	DET
ejpam-1048	6	43	notion	notion	NOUN
ejpam-1048	6	44	of	of	ADP
ejpam-1048	6	45	a	a	DET
ejpam-1048	6	46	generalized	generalize	VERB
ejpam-1048	6	47	quasieinstein	quasieinstein	ADJ
ejpam-1048	6	48	manifold	manifold	NOUN
ejpam-1048	6	49	was	be	AUX
ejpam-1048	6	50	introduced	introduce	VERB
ejpam-1048	6	51	by	by	ADP
ejpam-1048	6	52	de	de	X
ejpam-1048	6	53	and	and	CCONJ
ejpam-1048	6	54	ghosh	ghosh	NOUN
ejpam-1048	7	1	[	[	X
ejpam-1048	7	2	5	5	NUM
ejpam-1048	7	3	]	]	PUNCT
ejpam-1048	7	4	.	.	PUNCT
ejpam-1048	8	1	a	a	DET
ejpam-1048	8	2	non	non	ADJ
ejpam-1048	8	3	-	-	ADJ
ejpam-1048	8	4	flat	flat	ADJ
ejpam-1048	8	5	riemannian	riemannian	NOUN
ejpam-1048	8	6	manifold	manifold	NOUN
ejpam-1048	8	7	m	m	VERB
ejpam-1048	8	8	is	be	AUX
ejpam-1048	8	9	called	call	VERB
ejpam-1048	8	10	a	a	DET
ejpam-1048	8	11	generalized	generalize	VERB
ejpam-1048	8	12	quasi	quasi	NOUN
ejpam-1048	8	13	einstein	einstein	PROPN
ejpam-1048	8	14	manifold	manifold	PROPN
ejpam-1048	8	15	if	if	SCONJ
ejpam-1048	8	16	its	its	PRON
ejpam-1048	8	17	ricci	ricci	PROPN
ejpam-1048	8	18	tensor	tensor	NOUN
ejpam-1048	8	19	rk	rk	PROPN
ejpam-1048	8	20	j	j	PROPN
ejpam-1048	8	21	is	be	AUX
ejpam-1048	8	22	not	not	PART
ejpam-1048	8	23	identically	identically	ADV
ejpam-1048	8	24	zero	zero	NUM
ejpam-1048	8	25	and	and	CCONJ
ejpam-1048	8	26	satisfies	satisfy	VERB
ejpam-1048	8	27	the	the	DET
ejpam-1048	8	28	condition	condition	NOUN
ejpam-1048	8	29	rk	rk	NOUN
ejpam-1048	8	30	j	j	PROPN
ejpam-1048	8	31	=	=	PUNCT
ejpam-1048	9	1	αgk	αgk	ADP
ejpam-1048	9	2	j	j	PROPN
ejpam-1048	9	3	+	+	CCONJ
ejpam-1048	9	4	βuku	βuku	PROPN
ejpam-1048	9	5	j	j	PROPN
ejpam-1048	10	1	+	+	CCONJ
ejpam-1048	10	2	γvkv	γvkv	PROPN
ejpam-1048	10	3	j	j	PROPN
ejpam-1048	10	4	where	where	SCONJ
ejpam-1048	10	5	α	α	X
ejpam-1048	10	6	,	,	PUNCT
ejpam-1048	10	7	β	β	X
ejpam-1048	10	8	,	,	PUNCT
ejpam-1048	10	9	γ	γ	PROPN
ejpam-1048	10	10	are	be	AUX
ejpam-1048	10	11	non	non	ADJ
ejpam-1048	10	12	-	-	ADJ
ejpam-1048	10	13	zero	zero	ADJ
ejpam-1048	10	14	scalars	scalar	NOUN
ejpam-1048	10	15	and	and	CCONJ
ejpam-1048	10	16	uk	uk	PROPN
ejpam-1048	10	17	and	and	CCONJ
ejpam-1048	10	18	vk	vk	PROPN
ejpam-1048	10	19	are	be	AUX
ejpam-1048	10	20	covariant	covariant	ADJ
ejpam-1048	10	21	vectors	vector	NOUN
ejpam-1048	10	22	such	such	ADJ
ejpam-1048	10	23	that	that	SCONJ
ejpam-1048	10	24	uk	uk	PROPN
ejpam-1048	10	25	and	and	CCONJ
ejpam-1048	10	26	vk	vk	PROPN
ejpam-1048	10	27	are	be	AUX
ejpam-1048	10	28	orthogonal	orthogonal	ADJ
ejpam-1048	10	29	to	to	ADP
ejpam-1048	10	30	each	each	DET
ejpam-1048	10	31	other	other	ADJ
ejpam-1048	10	32	vector	vector	NOUN
ejpam-1048	10	33	fields	field	NOUN
ejpam-1048	10	34	on	on	ADP
ejpam-1048	10	35	m	m	PROPN
ejpam-1048	10	36	.	.	PUNCT
ejpam-1048	11	1	the	the	DET
ejpam-1048	11	2	mixed	mixed	ADJ
ejpam-1048	11	3	generalized	generalize	VERB
ejpam-1048	11	4	quasi	quasi	NOUN
ejpam-1048	11	5	einstein	einstein	PROPN
ejpam-1048	11	6	manifold	manifold	PROPN
ejpam-1048	11	7	was	be	AUX
ejpam-1048	11	8	defined	define	VERB
ejpam-1048	11	9	by	by	ADP
ejpam-1048	11	10	bhattacharyya	bhattacharyya	ADJ
ejpam-1048	11	11	and	and	CCONJ
ejpam-1048	11	12	de	de	X
ejpam-1048	12	1	[	[	X
ejpam-1048	12	2	1	1	NUM
ejpam-1048	12	3	]	]	PUNCT
ejpam-1048	12	4	.	.	PUNCT
ejpam-1048	13	1	a	a	DET
ejpam-1048	13	2	non	non	ADJ
ejpam-1048	13	3	-	-	ADJ
ejpam-1048	13	4	flat	flat	ADJ
ejpam-1048	13	5	riemannian	riemannian	NOUN
ejpam-1048	13	6	manifold	manifold	NOUN
ejpam-1048	13	7	m	m	VERB
ejpam-1048	13	8	is	be	AUX
ejpam-1048	13	9	called	call	VERB
ejpam-1048	13	10	a	a	DET
ejpam-1048	13	11	∗corresponding	∗corresponding	NOUN
ejpam-1048	13	12	author	author	NOUN
ejpam-1048	13	13	.	.	PUNCT
ejpam-1048	14	1	email	email	NOUN
ejpam-1048	14	2	addresses	address	NOUN
ejpam-1048	14	3	:	:	PUNCT
ejpam-1048	14	4	hbagdatli�marmara.edu.tr	hbagdatli�marmara.edu.tr	PROPN
ejpam-1048	14	5	(	(	PUNCT
ejpam-1048	14	6	h.	h.	PROPN
ejpam-1048	14	7	yılmaz	yılmaz	PROPN
ejpam-1048	14	8	)	)	PUNCT
ejpam-1048	14	9	,	,	PUNCT
ejpam-1048	14	10	fozen�itu.edu.tr	fozen�itu.edu.tr	PUNCT
ejpam-1048	14	11	(	(	PUNCT
ejpam-1048	14	12	f.	f.	PROPN
ejpam-1048	14	13	zengin),auysal	zengin),auysal	PROPN
ejpam-1048	14	14	�	�	PROPN
ejpam-1048	14	15	dogus.edu.tr	dogus.edu.tr	PROPN
ejpam-1048	14	16	(	(	PUNCT
ejpam-1048	14	17	s.	s.	PROPN
ejpam-1048	14	18	uysal	uysal	PROPN
ejpam-1048	14	19	)	)	PUNCT
ejpam-1048	14	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1048	15	1	152	152	NUM
ejpam-1048	15	2	c	c	X
ejpam-1048	15	3	©	©	PROPN
ejpam-1048	15	4	2011	2011	NUM
ejpam-1048	15	5	ejpam	ejpam	VERB
ejpam-1048	15	6	all	all	DET
ejpam-1048	15	7	rights	right	NOUN
ejpam-1048	15	8	reserved	reserve	VERB
ejpam-1048	15	9	.	.	PUNCT
ejpam-1048	16	1	h.	h.	PROPN
ejpam-1048	16	2	yılmaz	yılmaz	PROPN
ejpam-1048	16	3	,	,	PUNCT
ejpam-1048	16	4	f.	f.	PROPN
ejpam-1048	16	5	zengin	zengin	PROPN
ejpam-1048	16	6	,	,	PUNCT
ejpam-1048	16	7	s.	s.	PROPN
ejpam-1048	16	8	uysal	uysal	PROPN
ejpam-1048	16	9	/	/	SYM
ejpam-1048	16	10	eur	eur	PROPN
ejpam-1048	16	11	.	.	PUNCT
ejpam-1048	17	1	j.	j.	PROPN
ejpam-1048	17	2	pure	pure	PROPN
ejpam-1048	17	3	appl	appl	PROPN
ejpam-1048	17	4	.	.	PROPN
ejpam-1048	17	5	math	math	PROPN
ejpam-1048	17	6	,	,	PUNCT
ejpam-1048	17	7	4	4	NUM
ejpam-1048	17	8	(	(	PUNCT
ejpam-1048	17	9	2011	2011	NUM
ejpam-1048	17	10	)	)	PUNCT
ejpam-1048	17	11	,	,	PUNCT
ejpam-1048	17	12	152	152	NUM
ejpam-1048	17	13	-	-	SYM
ejpam-1048	17	14	161	161	NUM
ejpam-1048	17	15	153	153	NUM
ejpam-1048	17	16	mixed	mixed	ADJ
ejpam-1048	17	17	generalized	generalize	VERB
ejpam-1048	17	18	quasi	quasi	NOUN
ejpam-1048	17	19	einstein	einstein	PROPN
ejpam-1048	17	20	manifold	manifold	PROPN
ejpam-1048	17	21	if	if	SCONJ
ejpam-1048	17	22	its	its	PRON
ejpam-1048	17	23	ricci	ricci	PROPN
ejpam-1048	17	24	tensor	tensor	NOUN
ejpam-1048	17	25	rk	rk	PROPN
ejpam-1048	17	26	j	j	PROPN
ejpam-1048	17	27	is	be	AUX
ejpam-1048	17	28	non	non	ADJ
ejpam-1048	17	29	-	-	ADJ
ejpam-1048	17	30	zero	zero	NUM
ejpam-1048	17	31	and	and	CCONJ
ejpam-1048	17	32	satisfies	satisfy	VERB
ejpam-1048	17	33	the	the	DET
ejpam-1048	17	34	condition	condition	NOUN
ejpam-1048	17	35	rk	rk	NOUN
ejpam-1048	17	36	j	j	PROPN
ejpam-1048	17	37	=	=	PUNCT
ejpam-1048	18	1	αgk	αgk	ADP
ejpam-1048	18	2	j	j	PROPN
ejpam-1048	19	1	+	+	CCONJ
ejpam-1048	19	2	βaka	βaka	ADV
ejpam-1048	19	3	j	j	PROPN
ejpam-1048	20	1	+	+	PROPN
ejpam-1048	20	2	γbk	γbk	PROPN
ejpam-1048	20	3	b	b	PROPN
ejpam-1048	20	4	j	j	PROPN
ejpam-1048	20	5	+	+	PROPN
ejpam-1048	20	6	ϑ	ϑ	PROPN
ejpam-1048	20	7	�	�	PROPN
ejpam-1048	20	8	ak	ak	PROPN
ejpam-1048	20	9	b	b	PROPN
ejpam-1048	20	10	j	j	PROPN
ejpam-1048	20	11	+	+	CCONJ
ejpam-1048	20	12	bka	bka	PROPN
ejpam-1048	20	13	j	j	PROPN
ejpam-1048	20	14	�	�	PROPN
ejpam-1048	20	15	(	(	PUNCT
ejpam-1048	20	16	1	1	NUM
ejpam-1048	20	17	)	)	PUNCT
ejpam-1048	20	18	where	where	SCONJ
ejpam-1048	20	19	α	α	X
ejpam-1048	20	20	,	,	PUNCT
ejpam-1048	20	21	β	β	X
ejpam-1048	20	22	,	,	PUNCT
ejpam-1048	20	23	γ,ϑ	γ,ϑ	NOUN
ejpam-1048	20	24	are	be	AUX
ejpam-1048	20	25	non	non	ADJ
ejpam-1048	20	26	-	-	ADJ
ejpam-1048	20	27	zero	zero	ADJ
ejpam-1048	20	28	scalars	scalar	NOUN
ejpam-1048	20	29	and	and	CCONJ
ejpam-1048	20	30	ak	ak	PROPN
ejpam-1048	20	31	and	and	CCONJ
ejpam-1048	20	32	bk	bk	PROPN
ejpam-1048	20	33	are	be	AUX
ejpam-1048	20	34	covariant	covariant	ADJ
ejpam-1048	20	35	vectors	vector	NOUN
ejpam-1048	20	36	such	such	ADJ
ejpam-1048	20	37	that	that	PRON
ejpam-1048	20	38	ak	ak	PROPN
ejpam-1048	20	39	and	and	CCONJ
ejpam-1048	20	40	bk	bk	PROPN
ejpam-1048	20	41	are	be	AUX
ejpam-1048	20	42	orthogonal	orthogonal	ADJ
ejpam-1048	20	43	unit	unit	NOUN
ejpam-1048	20	44	vector	vector	NOUN
ejpam-1048	20	45	fields	field	NOUN
ejpam-1048	20	46	on	on	ADP
ejpam-1048	20	47	m	m	PROPN
ejpam-1048	20	48	.	.	PUNCT
ejpam-1048	21	1	moreover	moreover	ADV
ejpam-1048	21	2	,	,	PUNCT
ejpam-1048	21	3	it	it	PRON
ejpam-1048	21	4	is	be	AUX
ejpam-1048	21	5	stated	state	VERB
ejpam-1048	21	6	that	that	SCONJ
ejpam-1048	21	7	a	a	DET
ejpam-1048	21	8	riemannian	riemannian	ADJ
ejpam-1048	21	9	manifold	manifold	NOUN
ejpam-1048	21	10	is	be	AUX
ejpam-1048	21	11	of	of	ADP
ejpam-1048	21	12	a	a	DET
ejpam-1048	21	13	mixed	mixed	ADJ
ejpam-1048	21	14	generalized	generalize	VERB
ejpam-1048	21	15	quasi	quasi	ADJ
ejpam-1048	21	16	constant	constant	ADJ
ejpam-1048	21	17	curvature	curvature	NOUN
ejpam-1048	21	18	if	if	SCONJ
ejpam-1048	21	19	the	the	DET
ejpam-1048	21	20	curvature	curvature	NOUN
ejpam-1048	21	21	tensor	tensor	NOUN
ejpam-1048	21	22	of	of	ADP
ejpam-1048	21	23	this	this	DET
ejpam-1048	21	24	manifold	manifold	ADJ
ejpam-1048	21	25	satisfies	satisfie	NOUN
ejpam-1048	21	26	the	the	DET
ejpam-1048	21	27	condition	condition	NOUN
ejpam-1048	22	1	rik	rik	PROPN
ejpam-1048	22	2	jm	jm	PROPN
ejpam-1048	22	3	=	=	PROPN
ejpam-1048	22	4	p	p	PROPN
ejpam-1048	22	5	�	�	PROPN
ejpam-1048	22	6	gk	gk	PROPN
ejpam-1048	22	7	j	j	PROPN
ejpam-1048	22	8	gim−	gim−	PROPN
ejpam-1048	22	9	gi	gi	VERB
ejpam-1048	22	10	j	j	PROPN
ejpam-1048	22	11	gkm	gkm	PROPN
ejpam-1048	22	12	�	�	PROPN
ejpam-1048	22	13	(	(	PUNCT
ejpam-1048	22	14	2	2	NUM
ejpam-1048	22	15	)	)	PUNCT
ejpam-1048	22	16	+	+	CCONJ
ejpam-1048	22	17	q	q	PROPN
ejpam-1048	22	18	�	�	PROPN
ejpam-1048	22	19	gimaka	gimaka	PROPN
ejpam-1048	22	20	j	j	PROPN
ejpam-1048	22	21	−	−	PROPN
ejpam-1048	22	22	gkmaia	gkmaia	PROPN
ejpam-1048	22	23	j	j	PROPN
ejpam-1048	22	24	+	+	CCONJ
ejpam-1048	22	25	gk	gk	PROPN
ejpam-1048	22	26	jaiam−	jaiam−	PROPN
ejpam-1048	22	27	gi	gi	NOUN
ejpam-1048	22	28	jakam	jakam	PROPN
ejpam-1048	22	29	�	�	PROPN
ejpam-1048	22	30	+	+	CCONJ
ejpam-1048	22	31	s	s	PART
ejpam-1048	22	32	�	�	PROPN
ejpam-1048	22	33	gim	gim	PROPN
ejpam-1048	22	34	bk	bk	ADP
ejpam-1048	22	35	b	b	PROPN
ejpam-1048	22	36	j	j	PROPN
ejpam-1048	22	37	−	−	PROPN
ejpam-1048	22	38	gkmbi	gkmbi	PROPN
ejpam-1048	22	39	b	b	PROPN
ejpam-1048	22	40	j	j	PROPN
ejpam-1048	22	41	+	+	CCONJ
ejpam-1048	22	42	gk	gk	PROPN
ejpam-1048	22	43	j	j	PROPN
ejpam-1048	22	44	bi	bi	PROPN
ejpam-1048	22	45	bm−	bm−	PROPN
ejpam-1048	22	46	gi	gi	PROPN
ejpam-1048	22	47	j	j	PROPN
ejpam-1048	22	48	bk	bk	PROPN
ejpam-1048	22	49	bm	bm	PROPN
ejpam-1048	22	50	�	�	PROPN
ejpam-1048	22	51	+	+	CCONJ
ejpam-1048	22	52	t	t	PROPN
ejpam-1048	22	53	�	�	PROPN
ejpam-1048	22	54	¦	¦	PROPN
ejpam-1048	22	55	ak	ak	PROPN
ejpam-1048	22	56	b	b	PROPN
ejpam-1048	22	57	j	j	PROPN
ejpam-1048	22	58	+	+	PROPN
ejpam-1048	22	59	bka	bka	PROPN
ejpam-1048	22	60	j	j	PROPN
ejpam-1048	22	61	©	©	PROPN
ejpam-1048	22	62	gim−	gim−	PROPN
ejpam-1048	23	1	¦	¦	PROPN
ejpam-1048	24	1	ai	ai	VERB
ejpam-1048	24	2	b	b	PROPN
ejpam-1048	24	3	j	j	PROPN
ejpam-1048	24	4	+	+	CCONJ
ejpam-1048	24	5	bia	bia	PROPN
ejpam-1048	24	6	j	j	PROPN
ejpam-1048	24	7	©	©	PROPN
ejpam-1048	24	8	gkm	gkm	PROPN
ejpam-1048	24	9	+	+	CCONJ
ejpam-1048	24	10	�	�	PROPN
ejpam-1048	24	11	ai	ai	PROPN
ejpam-1048	24	12	bm+	bm+	PROPN
ejpam-1048	24	13	biam	biam	PROPN
ejpam-1048	24	14	gk	gk	PROPN
ejpam-1048	24	15	j	j	PROPN
ejpam-1048	24	16	−	−	PROPN
ejpam-1048	24	17	�	�	PROPN
ejpam-1048	24	18	ak	ak	PROPN
ejpam-1048	24	19	bm+	bm+	PROPN
ejpam-1048	24	20	bkam	bkam	PROPN
ejpam-1048	24	21	gi	gi	PROPN
ejpam-1048	24	22	j	j	PROPN
ejpam-1048	24	23	�	�	PROPN
ejpam-1048	24	24	where	where	SCONJ
ejpam-1048	24	25	p	p	X
ejpam-1048	24	26	,	,	PUNCT
ejpam-1048	24	27	q	q	ADJ
ejpam-1048	24	28	,	,	PUNCT
ejpam-1048	24	29	r	r	NOUN
ejpam-1048	24	30	,	,	PUNCT
ejpam-1048	24	31	s	s	PROPN
ejpam-1048	24	32	,	,	PUNCT
ejpam-1048	24	33	t	t	PROPN
ejpam-1048	24	34	are	be	AUX
ejpam-1048	24	35	non	non	ADJ
ejpam-1048	24	36	-	-	ADJ
ejpam-1048	24	37	zero	zero	ADJ
ejpam-1048	24	38	scalars	scalar	NOUN
ejpam-1048	24	39	and	and	CCONJ
ejpam-1048	24	40	ak	ak	PROPN
ejpam-1048	24	41	and	and	CCONJ
ejpam-1048	24	42	bk	bk	PROPN
ejpam-1048	24	43	are	be	AUX
ejpam-1048	24	44	covariant	covariant	ADJ
ejpam-1048	24	45	vectors	vector	NOUN
ejpam-1048	24	46	such	such	ADJ
ejpam-1048	24	47	that	that	PRON
ejpam-1048	24	48	ak	ak	PROPN
ejpam-1048	24	49	and	and	CCONJ
ejpam-1048	24	50	bk	bk	PROPN
ejpam-1048	24	51	are	be	AUX
ejpam-1048	24	52	orthonormal	orthonormal	ADJ
ejpam-1048	24	53	unit	unit	NOUN
ejpam-1048	24	54	vector	vector	NOUN
ejpam-1048	24	55	fields	field	NOUN
ejpam-1048	24	56	on	on	ADP
ejpam-1048	24	57	m	m	PROPN
ejpam-1048	24	58	[	[	X
ejpam-1048	24	59	1	1	NUM
ejpam-1048	24	60	]	]	PUNCT
ejpam-1048	24	61	.	.	PUNCT
ejpam-1048	25	1	let	let	VERB
ejpam-1048	25	2	∇	∇	X
ejpam-1048	25	3	be	be	AUX
ejpam-1048	25	4	a	a	DET
ejpam-1048	25	5	linear	linear	ADJ
ejpam-1048	25	6	connection	connection	NOUN
ejpam-1048	25	7	on	on	ADP
ejpam-1048	25	8	m	m	PROPN
ejpam-1048	25	9	.	.	PUNCT
ejpam-1048	26	1	the	the	DET
ejpam-1048	26	2	torsion	torsion	NOUN
ejpam-1048	26	3	tensor	tensor	NOUN
ejpam-1048	26	4	is	be	AUX
ejpam-1048	26	5	given	give	VERB
ejpam-1048	26	6	by	by	ADP
ejpam-1048	26	7	,	,	PUNCT
ejpam-1048	26	8	t	t	PROPN
ejpam-1048	26	9	(	(	PUNCT
ejpam-1048	26	10	x	x	INTJ
ejpam-1048	26	11	,	,	PUNCT
ejpam-1048	26	12	y	y	PROPN
ejpam-1048	26	13	)	)	PUNCT
ejpam-1048	27	1	=	=	X
ejpam-1048	27	2	∇x	∇x	NOUN
ejpam-1048	27	3	y	y	PUNCT
ejpam-1048	27	4	−∇y	−∇y	NUM
ejpam-1048	27	5	x	x	X
ejpam-1048	27	6	−	−	PUNCT
ejpam-1048	28	1	[	[	X
ejpam-1048	28	2	x	x	X
ejpam-1048	28	3	,	,	PUNCT
ejpam-1048	28	4	y	y	PROPN
ejpam-1048	28	5	]	]	PUNCT
ejpam-1048	28	6	the	the	DET
ejpam-1048	28	7	connection	connection	NOUN
ejpam-1048	28	8	∇	∇	VERB
ejpam-1048	28	9	is	be	AUX
ejpam-1048	28	10	symmetric	symmetric	ADJ
ejpam-1048	28	11	if	if	SCONJ
ejpam-1048	28	12	its	its	PRON
ejpam-1048	28	13	torsion	torsion	NOUN
ejpam-1048	28	14	tensor	tensor	NOUN
ejpam-1048	28	15	t	t	PROPN
ejpam-1048	28	16	vanishes	vanish	VERB
ejpam-1048	28	17	,	,	PUNCT
ejpam-1048	28	18	otherwise	otherwise	ADV
ejpam-1048	28	19	it	it	PRON
ejpam-1048	28	20	is	be	AUX
ejpam-1048	28	21	non	non	ADJ
ejpam-1048	28	22	-	-	ADJ
ejpam-1048	28	23	symmetric	symmetric	ADJ
ejpam-1048	28	24	.	.	PUNCT
ejpam-1048	29	1	if	if	SCONJ
ejpam-1048	29	2	there	there	PRON
ejpam-1048	29	3	is	be	VERB
ejpam-1048	29	4	a	a	DET
ejpam-1048	29	5	riemannian	riemannian	ADJ
ejpam-1048	29	6	metric	metric	ADJ
ejpam-1048	29	7	g	g	NOUN
ejpam-1048	29	8	in	in	ADP
ejpam-1048	29	9	m	m	PRON
ejpam-1048	29	10	such	such	ADJ
ejpam-1048	29	11	that	that	SCONJ
ejpam-1048	29	12	∇g	∇g	ADJ
ejpam-1048	29	13	=	=	SYM
ejpam-1048	29	14	0	0	NUM
ejpam-1048	29	15	(	(	PUNCT
ejpam-1048	29	16	3	3	NUM
ejpam-1048	29	17	)	)	PUNCT
ejpam-1048	29	18	then	then	ADV
ejpam-1048	29	19	the	the	DET
ejpam-1048	29	20	connection	connection	NOUN
ejpam-1048	29	21	∇	∇	VERB
ejpam-1048	29	22	is	be	AUX
ejpam-1048	29	23	a	a	DET
ejpam-1048	29	24	metric	metric	ADJ
ejpam-1048	29	25	connection	connection	NOUN
ejpam-1048	29	26	,	,	PUNCT
ejpam-1048	29	27	otherwise	otherwise	ADV
ejpam-1048	29	28	it	it	PRON
ejpam-1048	29	29	is	be	AUX
ejpam-1048	29	30	non	non	ADJ
ejpam-1048	29	31	-	-	ADJ
ejpam-1048	29	32	metric	metric	ADJ
ejpam-1048	29	33	[	[	X
ejpam-1048	29	34	12	12	NUM
ejpam-1048	29	35	]	]	PUNCT
ejpam-1048	29	36	.	.	PUNCT
ejpam-1048	30	1	a	a	DET
ejpam-1048	30	2	linear	linear	ADJ
ejpam-1048	30	3	connection	connection	NOUN
ejpam-1048	30	4	is	be	AUX
ejpam-1048	30	5	said	say	VERB
ejpam-1048	30	6	to	to	PART
ejpam-1048	30	7	be	be	AUX
ejpam-1048	30	8	a	a	DET
ejpam-1048	30	9	semi	semi	ADJ
ejpam-1048	30	10	symmetric	symmetric	ADJ
ejpam-1048	30	11	connection	connection	NOUN
ejpam-1048	30	12	if	if	SCONJ
ejpam-1048	30	13	its	its	PRON
ejpam-1048	30	14	torsion	torsion	NOUN
ejpam-1048	30	15	tensor	tensor	NOUN
ejpam-1048	30	16	t	t	PROPN
ejpam-1048	30	17	is	be	AUX
ejpam-1048	30	18	of	of	ADP
ejpam-1048	30	19	the	the	DET
ejpam-1048	30	20	form	form	NOUN
ejpam-1048	30	21	t	t	NOUN
ejpam-1048	30	22	(	(	PUNCT
ejpam-1048	30	23	x	x	INTJ
ejpam-1048	30	24	,	,	PUNCT
ejpam-1048	30	25	y	y	PROPN
ejpam-1048	30	26	)	)	PUNCT
ejpam-1048	31	1	=	=	SYM
ejpam-1048	31	2	w(y	w(y	PROPN
ejpam-1048	31	3	)	)	PUNCT
ejpam-1048	31	4	x	x	X
ejpam-1048	31	5	−w(x	−w(x	ADJ
ejpam-1048	31	6	)	)	PUNCT
ejpam-1048	31	7	y	y	PROPN
ejpam-1048	31	8	(	(	PUNCT
ejpam-1048	31	9	4	4	NUM
ejpam-1048	31	10	)	)	PUNCT
ejpam-1048	31	11	where	where	SCONJ
ejpam-1048	31	12	w(x	w(x	NOUN
ejpam-1048	31	13	)	)	PUNCT
ejpam-1048	32	1	=	=	PUNCT
ejpam-1048	32	2	g(x	g(x	PROPN
ejpam-1048	32	3	,	,	PUNCT
ejpam-1048	32	4	u	u	NOUN
ejpam-1048	32	5	)	)	PUNCT
ejpam-1048	32	6	and	and	CCONJ
ejpam-1048	32	7	u	u	NOUN
ejpam-1048	32	8	is	be	AUX
ejpam-1048	32	9	a	a	DET
ejpam-1048	32	10	vector	vector	NOUN
ejpam-1048	32	11	field	field	NOUN
ejpam-1048	32	12	.	.	PUNCT
ejpam-1048	33	1	in	in	ADP
ejpam-1048	33	2	[	[	X
ejpam-1048	33	3	9	9	NUM
ejpam-1048	33	4	]	]	PUNCT
ejpam-1048	33	5	,	,	PUNCT
ejpam-1048	33	6	pak	pak	PROPN
ejpam-1048	33	7	showed	show	VERB
ejpam-1048	33	8	that	that	SCONJ
ejpam-1048	33	9	a	a	DET
ejpam-1048	33	10	hayden	hayden	NOUN
ejpam-1048	33	11	connection	connection	NOUN
ejpam-1048	33	12	with	with	ADP
ejpam-1048	33	13	the	the	DET
ejpam-1048	33	14	torsion	torsion	NOUN
ejpam-1048	33	15	tensor	tensor	NOUN
ejpam-1048	33	16	of	of	ADP
ejpam-1048	33	17	the	the	DET
ejpam-1048	33	18	form	form	NOUN
ejpam-1048	33	19	(	(	PUNCT
ejpam-1048	33	20	4	4	NUM
ejpam-1048	33	21	)	)	PUNCT
ejpam-1048	33	22	is	be	AUX
ejpam-1048	33	23	a	a	DET
ejpam-1048	33	24	semi	semi	ADJ
ejpam-1048	33	25	symmetric	symmetric	ADJ
ejpam-1048	33	26	metric	metric	ADJ
ejpam-1048	33	27	connection	connection	NOUN
ejpam-1048	33	28	.	.	PUNCT
ejpam-1048	34	1	in	in	ADP
ejpam-1048	34	2	[	[	X
ejpam-1048	34	3	11	11	NUM
ejpam-1048	34	4	]	]	PUNCT
ejpam-1048	34	5	,	,	PUNCT
ejpam-1048	34	6	yano	yano	PROPN
ejpam-1048	34	7	proved	prove	VERB
ejpam-1048	34	8	that	that	SCONJ
ejpam-1048	34	9	in	in	ADP
ejpam-1048	34	10	order	order	NOUN
ejpam-1048	34	11	that	that	SCONJ
ejpam-1048	34	12	a	a	DET
ejpam-1048	34	13	riemannian	riemannian	ADJ
ejpam-1048	34	14	manifold	manifold	NOUN
ejpam-1048	34	15	admits	admit	VERB
ejpam-1048	34	16	a	a	DET
ejpam-1048	34	17	semi	semi	ADJ
ejpam-1048	34	18	symmetric	symmetric	ADJ
ejpam-1048	34	19	metric	metric	ADJ
ejpam-1048	34	20	connection	connection	NOUN
ejpam-1048	34	21	whose	whose	DET
ejpam-1048	34	22	curvature	curvature	NOUN
ejpam-1048	34	23	tensor	tensor	NOUN
ejpam-1048	34	24	vanishes	vanish	VERB
ejpam-1048	34	25	,	,	PUNCT
ejpam-1048	34	26	it	it	PRON
ejpam-1048	34	27	is	be	AUX
ejpam-1048	34	28	necessary	necessary	ADJ
ejpam-1048	34	29	and	and	CCONJ
ejpam-1048	34	30	sufficient	sufficient	ADJ
ejpam-1048	34	31	that	that	SCONJ
ejpam-1048	34	32	the	the	DET
ejpam-1048	34	33	riemannian	riemannian	ADJ
ejpam-1048	34	34	manifold	manifold	NOUN
ejpam-1048	34	35	be	be	VERB
ejpam-1048	34	36	conformally	conformally	ADV
ejpam-1048	34	37	flat	flat	ADJ
ejpam-1048	34	38	,	,	PUNCT
ejpam-1048	34	39	for	for	ADP
ejpam-1048	34	40	some	some	DET
ejpam-1048	34	41	properties	property	NOUN
ejpam-1048	34	42	of	of	ADP
ejpam-1048	34	43	riemannian	riemannian	ADJ
ejpam-1048	34	44	manifolds	manifold	NOUN
ejpam-1048	34	45	with	with	ADP
ejpam-1048	34	46	a	a	DET
ejpam-1048	34	47	semi	semi	ADJ
ejpam-1048	34	48	symmetric	symmetric	ADJ
ejpam-1048	34	49	metric	metric	ADJ
ejpam-1048	34	50	connection	connection	NOUN
ejpam-1048	34	51	,	,	PUNCT
ejpam-1048	34	52	see	see	VERB
ejpam-1048	34	53	also	also	ADV
ejpam-1048	34	54	[	[	X
ejpam-1048	34	55	4	4	NUM
ejpam-1048	34	56	,	,	PUNCT
ejpam-1048	34	57	6	6	NUM
ejpam-1048	34	58	,	,	PUNCT
ejpam-1048	34	59	8	8	NUM
ejpam-1048	34	60	,	,	PUNCT
ejpam-1048	34	61	10	10	NUM
ejpam-1048	34	62	]	]	PUNCT
ejpam-1048	34	63	the	the	DET
ejpam-1048	34	64	components	component	NOUN
ejpam-1048	34	65	of	of	ADP
ejpam-1048	34	66	semi	semi	ADJ
ejpam-1048	34	67	symmetric	symmetric	ADJ
ejpam-1048	34	68	metric	metric	ADJ
ejpam-1048	34	69	connection	connection	NOUN
ejpam-1048	34	70	are	be	AUX
ejpam-1048	34	71	given	give	VERB
ejpam-1048	34	72	by	by	ADP
ejpam-1048	34	73	γl	γl	PROPN
ejpam-1048	34	74	ik	ik	PROPN
ejpam-1048	34	75	=	=	SYM
ejpam-1048	34	76	¨	¨	PROPN
ejpam-1048	34	77	l	l	NOUN
ejpam-1048	34	78	ik	ik	X
ejpam-1048	34	79	«	«	PUNCT
ejpam-1048	35	1	+	+	CCONJ
ejpam-1048	35	2	δl	δl	X
ejpam-1048	35	3	i	i	PRON
ejpam-1048	35	4	wk	wk	INTJ
ejpam-1048	35	5	−	−	PROPN
ejpam-1048	35	6	gikw	gikw	PROPN
ejpam-1048	35	7	l	l	NOUN
ejpam-1048	35	8	(	(	PUNCT
ejpam-1048	35	9	5	5	NUM
ejpam-1048	35	10	)	)	PUNCT
ejpam-1048	35	11	where	where	SCONJ
ejpam-1048	35	12	wt	wt	NOUN
ejpam-1048	35	13	and	and	CCONJ
ejpam-1048	35	14	w	w	PROPN
ejpam-1048	35	15	l	l	NOUN
ejpam-1048	35	16	=	=	PUNCT
ejpam-1048	35	17	wt	wt	ADP
ejpam-1048	35	18	g	g	PROPN
ejpam-1048	35	19	t	t	PROPN
ejpam-1048	35	20	l	l	NOUN
ejpam-1048	35	21	are	be	AUX
ejpam-1048	35	22	covariant	covariant	ADJ
ejpam-1048	35	23	and	and	CCONJ
ejpam-1048	35	24	contravariant	contravariant	ADJ
ejpam-1048	35	25	components	component	NOUN
ejpam-1048	35	26	of	of	ADP
ejpam-1048	35	27	a	a	DET
ejpam-1048	35	28	vector	vector	NOUN
ejpam-1048	35	29	field	field	NOUN
ejpam-1048	35	30	,	,	PUNCT
ejpam-1048	35	31	respectively	respectively	ADV
ejpam-1048	35	32	and	and	CCONJ
ejpam-1048	35	33	∇kw	∇kw	PRON
ejpam-1048	35	34	j	j	NOUN
ejpam-1048	36	1	=	=	NOUN
ejpam-1048	36	2	∇kw	∇kw	PROPN
ejpam-1048	36	3	j	j	PROPN
ejpam-1048	36	4	−wkw	−wkw	VERB
ejpam-1048	36	5	j	j	PROPN
ejpam-1048	37	1	+	+	PROPN
ejpam-1048	37	2	wgk	wgk	PROPN
ejpam-1048	37	3	j	j	PROPN
ejpam-1048	37	4	,	,	PUNCT
ejpam-1048	37	5	w	w	PROPN
ejpam-1048	37	6	=	=	PUNCT
ejpam-1048	37	7	wt	wt	PROPN
ejpam-1048	37	8	w	w	PROPN
ejpam-1048	37	9	t	t	PROPN
ejpam-1048	37	10	(	(	PUNCT
ejpam-1048	37	11	6	6	NUM
ejpam-1048	37	12	)	)	PUNCT
ejpam-1048	37	13	h.	h.	PROPN
ejpam-1048	37	14	yılmaz	yılmaz	PROPN
ejpam-1048	37	15	,	,	PUNCT
ejpam-1048	37	16	f.	f.	PROPN
ejpam-1048	37	17	zengin	zengin	PROPN
ejpam-1048	37	18	,	,	PUNCT
ejpam-1048	37	19	s.	s.	PROPN
ejpam-1048	37	20	uysal	uysal	PROPN
ejpam-1048	37	21	/	/	SYM
ejpam-1048	37	22	eur	eur	PROPN
ejpam-1048	37	23	.	.	PUNCT
ejpam-1048	38	1	j.	j.	PROPN
ejpam-1048	38	2	pure	pure	PROPN
ejpam-1048	38	3	appl	appl	PROPN
ejpam-1048	38	4	.	.	PROPN
ejpam-1048	38	5	math	math	PROPN
ejpam-1048	38	6	,	,	PUNCT
ejpam-1048	38	7	4	4	NUM
ejpam-1048	38	8	(	(	PUNCT
ejpam-1048	38	9	2011	2011	NUM
ejpam-1048	38	10	)	)	PUNCT
ejpam-1048	38	11	,	,	PUNCT
ejpam-1048	38	12	152	152	NUM
ejpam-1048	38	13	-	-	SYM
ejpam-1048	38	14	161	161	NUM
ejpam-1048	38	15	154	154	NUM
ejpam-1048	38	16	by	by	ADP
ejpam-1048	38	17	using	use	VERB
ejpam-1048	38	18	(	(	PUNCT
ejpam-1048	38	19	5	5	NUM
ejpam-1048	38	20	)	)	PUNCT
ejpam-1048	38	21	,	,	PUNCT
ejpam-1048	38	22	we	we	PRON
ejpam-1048	38	23	obtain	obtain	VERB
ejpam-1048	38	24	,	,	PUNCT
ejpam-1048	38	25	rik	rik	PROPN
ejpam-1048	38	26	jm	jm	PROPN
ejpam-1048	38	27	=	=	PROPN
ejpam-1048	38	28	rik	rik	PROPN
ejpam-1048	38	29	jm−	jm−	PROPN
ejpam-1048	38	30	gimπk	gimπk	PROPN
ejpam-1048	38	31	j	j	PROPN
ejpam-1048	38	32	+	+	CCONJ
ejpam-1048	38	33	gkmπi	gkmπi	ADJ
ejpam-1048	38	34	j	j	PROPN
ejpam-1048	38	35	−	−	PROPN
ejpam-1048	38	36	gk	gk	PROPN
ejpam-1048	39	1	jπim+	jπim+	AUX
ejpam-1048	39	2	gi	gi	ADP
ejpam-1048	39	3	jπkm	jπkm	PROPN
ejpam-1048	39	4	(	(	PUNCT
ejpam-1048	39	5	7	7	NUM
ejpam-1048	39	6	)	)	PUNCT
ejpam-1048	39	7	where	where	SCONJ
ejpam-1048	39	8	rik	rik	PROPN
ejpam-1048	39	9	jm	jm	PROPN
ejpam-1048	39	10	and	and	CCONJ
ejpam-1048	39	11	rik	rik	PROPN
ejpam-1048	39	12	jm	jm	PROPN
ejpam-1048	39	13	are	be	AUX
ejpam-1048	39	14	the	the	DET
ejpam-1048	39	15	riemannian	riemannian	ADJ
ejpam-1048	39	16	curvature	curvature	NOUN
ejpam-1048	39	17	tensors	tensor	NOUN
ejpam-1048	39	18	of	of	ADP
ejpam-1048	39	19	∇	∇	X
ejpam-1048	39	20	and	and	CCONJ
ejpam-1048	39	21	∇	∇	PROPN
ejpam-1048	39	22	,	,	PUNCT
ejpam-1048	39	23	respectively	respectively	ADV
ejpam-1048	39	24	[	[	X
ejpam-1048	39	25	11	11	NUM
ejpam-1048	39	26	]	]	PUNCT
ejpam-1048	39	27	.	.	PUNCT
ejpam-1048	40	1	and	and	CCONJ
ejpam-1048	40	2	π	π	PROPN
ejpam-1048	40	3	is	be	AUX
ejpam-1048	40	4	a	a	DET
ejpam-1048	40	5	tensor	tensor	NOUN
ejpam-1048	40	6	field	field	NOUN
ejpam-1048	40	7	of	of	ADP
ejpam-1048	40	8	type	type	NOUN
ejpam-1048	40	9	(	(	PUNCT
ejpam-1048	40	10	0,2	0,2	NUM
ejpam-1048	40	11	)	)	PUNCT
ejpam-1048	40	12	defined	define	VERB
ejpam-1048	40	13	by	by	ADP
ejpam-1048	40	14	πk	πk	PROPN
ejpam-1048	40	15	j	j	PROPN
ejpam-1048	40	16	=	=	PROPN
ejpam-1048	40	17	∇kw	∇kw	PROPN
ejpam-1048	40	18	j	j	PROPN
ejpam-1048	40	19	−wkw	−wkw	VERB
ejpam-1048	40	20	j	j	PROPN
ejpam-1048	41	1	+	+	CCONJ
ejpam-1048	41	2	1	1	NUM
ejpam-1048	41	3	2	2	NUM
ejpam-1048	41	4	gk	gk	PROPN
ejpam-1048	41	5	jw	jw	PROPN
ejpam-1048	41	6	(	(	PUNCT
ejpam-1048	41	7	8)	8)	NUM
ejpam-1048	41	8	transvecting	transvecte	VERB
ejpam-1048	41	9	the	the	DET
ejpam-1048	41	10	equation	equation	NOUN
ejpam-1048	41	11	(	(	PUNCT
ejpam-1048	41	12	7	7	NUM
ejpam-1048	41	13	)	)	PUNCT
ejpam-1048	41	14	with	with	ADP
ejpam-1048	41	15	g	g	PROPN
ejpam-1048	41	16	i	i	PRON
ejpam-1048	41	17	m	m	PROPN
ejpam-1048	41	18	,	,	PUNCT
ejpam-1048	41	19	we	we	PRON
ejpam-1048	41	20	get	get	VERB
ejpam-1048	41	21	rk	rk	PRON
ejpam-1048	41	22	j	j	NOUN
ejpam-1048	41	23	=	=	PRON
ejpam-1048	41	24	rk	rk	PROPN
ejpam-1048	42	1	j	j	NOUN
ejpam-1048	42	2	−	−	PROPN
ejpam-1048	43	1	(	(	PUNCT
ejpam-1048	43	2	n−	n−	NOUN
ejpam-1048	43	3	2)πk	2)πk	NUM
ejpam-1048	43	4	j	j	PROPN
ejpam-1048	43	5	−πgk	−πgk	NOUN
ejpam-1048	43	6	j	j	PROPN
ejpam-1048	43	7	(	(	PUNCT
ejpam-1048	43	8	9	9	NUM
ejpam-1048	43	9	)	)	PUNCT
ejpam-1048	43	10	where	where	SCONJ
ejpam-1048	43	11	rk	rk	VERB
ejpam-1048	43	12	j	j	PROPN
ejpam-1048	43	13	and	and	CCONJ
ejpam-1048	43	14	rk	rk	PROPN
ejpam-1048	43	15	j	j	PROPN
ejpam-1048	43	16	are	be	AUX
ejpam-1048	43	17	the	the	DET
ejpam-1048	43	18	ricci	ricci	PROPN
ejpam-1048	43	19	tensors	tensor	NOUN
ejpam-1048	43	20	for	for	ADP
ejpam-1048	43	21	the	the	DET
ejpam-1048	43	22	connections	connection	NOUN
ejpam-1048	43	23	∇	∇	X
ejpam-1048	43	24	and	and	CCONJ
ejpam-1048	43	25	∇	∇	NOUN
ejpam-1048	43	26	,	,	PUNCT
ejpam-1048	43	27	respectively	respectively	ADV
ejpam-1048	43	28	and	and	CCONJ
ejpam-1048	43	29	π=	π=	NUM
ejpam-1048	43	30	πim	πim	PROPN
ejpam-1048	43	31	g	g	PROPN
ejpam-1048	43	32	i	i	PROPN
ejpam-1048	43	33	m.	m.	NOUN
ejpam-1048	43	34	multiplying	multiply	VERB
ejpam-1048	43	35	(	(	PUNCT
ejpam-1048	43	36	9	9	NUM
ejpam-1048	43	37	)	)	PUNCT
ejpam-1048	43	38	by	by	ADP
ejpam-1048	43	39	gk	gk	PROPN
ejpam-1048	43	40	j	j	PROPN
ejpam-1048	43	41	,	,	PUNCT
ejpam-1048	43	42	we	we	PRON
ejpam-1048	43	43	obtain	obtain	VERB
ejpam-1048	43	44	r=	r=	ADJ
ejpam-1048	43	45	r−	r−	PROPN
ejpam-1048	43	46	2(n−	2(n−	PROPN
ejpam-1048	43	47	1)π	1)π	NUM
ejpam-1048	43	48	(	(	PUNCT
ejpam-1048	43	49	10	10	NUM
ejpam-1048	43	50	)	)	PUNCT
ejpam-1048	43	51	where	where	SCONJ
ejpam-1048	43	52	r	r	NOUN
ejpam-1048	43	53	and	and	CCONJ
ejpam-1048	43	54	r	r	NOUN
ejpam-1048	43	55	are	be	AUX
ejpam-1048	43	56	the	the	DET
ejpam-1048	43	57	scalar	scalar	ADJ
ejpam-1048	43	58	curvatures	curvature	NOUN
ejpam-1048	43	59	of	of	ADP
ejpam-1048	43	60	semi	semi	ADJ
ejpam-1048	43	61	symmetric	symmetric	ADJ
ejpam-1048	43	62	metric	metric	ADJ
ejpam-1048	43	63	connection	connection	NOUN
ejpam-1048	43	64	and	and	CCONJ
ejpam-1048	43	65	the	the	DET
ejpam-1048	43	66	levicivita	levicivita	NOUN
ejpam-1048	43	67	connection	connection	NOUN
ejpam-1048	43	68	,	,	PUNCT
ejpam-1048	43	69	respectively	respectively	ADV
ejpam-1048	43	70	.	.	PUNCT
ejpam-1048	44	1	2	2	X
ejpam-1048	44	2	.	.	X
ejpam-1048	44	3	a	a	DET
ejpam-1048	44	4	riemannian	riemannian	ADJ
ejpam-1048	44	5	manifold	manifold	NOUN
ejpam-1048	44	6	admitting	admit	VERB
ejpam-1048	44	7	a	a	DET
ejpam-1048	44	8	special	special	ADJ
ejpam-1048	44	9	semi	semi	ADJ
ejpam-1048	44	10	symmetric	symmetric	ADJ
ejpam-1048	44	11	metric	metric	ADJ
ejpam-1048	44	12	connection	connection	NOUN
ejpam-1048	44	13	de	de	PROPN
ejpam-1048	44	14	and	and	CCONJ
ejpam-1048	44	15	sengupta	sengupta	NOUN
ejpam-1048	44	16	considered	consider	VERB
ejpam-1048	44	17	a	a	DET
ejpam-1048	44	18	semi	semi	ADJ
ejpam-1048	44	19	symmetric	symmetric	ADJ
ejpam-1048	44	20	metric	metric	ADJ
ejpam-1048	44	21	connection	connection	NOUN
ejpam-1048	44	22	and	and	CCONJ
ejpam-1048	44	23	studied	study	VERB
ejpam-1048	44	24	some	some	DET
ejpam-1048	44	25	properties	property	NOUN
ejpam-1048	44	26	of	of	ADP
ejpam-1048	44	27	an	an	DET
ejpam-1048	44	28	almost	almost	ADV
ejpam-1048	44	29	contact	contact	NOUN
ejpam-1048	44	30	manifold	manifold	NOUN
ejpam-1048	44	31	of	of	ADP
ejpam-1048	44	32	a	a	DET
ejpam-1048	44	33	semi	semi	ADJ
ejpam-1048	44	34	symmetric	symmetric	ADJ
ejpam-1048	44	35	metric	metric	ADJ
ejpam-1048	44	36	connection	connection	NOUN
ejpam-1048	44	37	whose	whose	DET
ejpam-1048	44	38	the	the	DET
ejpam-1048	44	39	torsion	torsion	NOUN
ejpam-1048	44	40	tensor	tensor	NOUN
ejpam-1048	44	41	satisfies	satisfy	VERB
ejpam-1048	44	42	a	a	DET
ejpam-1048	44	43	special	special	ADJ
ejpam-1048	44	44	condition	condition	NOUN
ejpam-1048	44	45	different	different	ADJ
ejpam-1048	44	46	from	from	ADP
ejpam-1048	44	47	the	the	DET
ejpam-1048	44	48	following	follow	VERB
ejpam-1048	44	49	condition	condition	NOUN
ejpam-1048	44	50	[	[	X
ejpam-1048	44	51	2	2	NUM
ejpam-1048	44	52	]	]	PUNCT
ejpam-1048	44	53	.	.	PUNCT
ejpam-1048	45	1	in	in	ADP
ejpam-1048	45	2	this	this	DET
ejpam-1048	45	3	section	section	NOUN
ejpam-1048	45	4	,	,	PUNCT
ejpam-1048	45	5	we	we	PRON
ejpam-1048	45	6	consider	consider	VERB
ejpam-1048	45	7	a	a	DET
ejpam-1048	45	8	manifold	manifold	NOUN
ejpam-1048	45	9	equipped	equip	VERB
ejpam-1048	45	10	with	with	ADP
ejpam-1048	45	11	a	a	DET
ejpam-1048	45	12	semi	semi	ADJ
ejpam-1048	45	13	symmetric	symmetric	ADJ
ejpam-1048	45	14	metric	metric	ADJ
ejpam-1048	45	15	connection	connection	NOUN
ejpam-1048	45	16	whose	whose	DET
ejpam-1048	45	17	the	the	DET
ejpam-1048	45	18	torsion	torsion	NOUN
ejpam-1048	45	19	t	t	PROPN
ejpam-1048	45	20	satisfies	satisfy	VERB
ejpam-1048	45	21	the	the	DET
ejpam-1048	45	22	following	follow	VERB
ejpam-1048	45	23	condition	condition	NOUN
ejpam-1048	45	24	∇	∇	X
ejpam-1048	45	25	j	j	PROPN
ejpam-1048	45	26	t	t	PROPN
ejpam-1048	45	27	l	l	NOUN
ejpam-1048	46	1	ik	ik	PROPN
ejpam-1048	46	2	=	=	PUNCT
ejpam-1048	46	3	a	a	PRON
ejpam-1048	46	4	j	j	PROPN
ejpam-1048	46	5	t	t	PROPN
ejpam-1048	46	6	l	l	NOUN
ejpam-1048	46	7	ik	ik	PROPN
ejpam-1048	47	1	+	+	PROPN
ejpam-1048	47	2	b	b	PROPN
ejpam-1048	47	3	j	j	PROPN
ejpam-1048	47	4	b	b	PROPN
ejpam-1048	47	5	l	l	NOUN
ejpam-1048	47	6	gik	gik	X
ejpam-1048	47	7	+	+	PROPN
ejpam-1048	47	8	δ	δ	PROPN
ejpam-1048	47	9	l	l	PROPN
ejpam-1048	47	10	j	j	PROPN
ejpam-1048	47	11	biak	biak	PROPN
ejpam-1048	47	12	(	(	PUNCT
ejpam-1048	47	13	11	11	NUM
ejpam-1048	47	14	)	)	PUNCT
ejpam-1048	47	15	where	where	SCONJ
ejpam-1048	47	16	bl	bl	VERB
ejpam-1048	47	17	=	=	PUNCT
ejpam-1048	47	18	bt	bt	PROPN
ejpam-1048	47	19	g	g	PROPN
ejpam-1048	47	20	t	t	PROPN
ejpam-1048	47	21	l	l	NOUN
ejpam-1048	47	22	.	.	PUNCT
ejpam-1048	48	1	the	the	DET
ejpam-1048	48	2	equation	equation	NOUN
ejpam-1048	48	3	(	(	PUNCT
ejpam-1048	48	4	4	4	X
ejpam-1048	48	5	)	)	PUNCT
ejpam-1048	48	6	can	can	AUX
ejpam-1048	48	7	be	be	AUX
ejpam-1048	48	8	written	write	VERB
ejpam-1048	48	9	in	in	ADP
ejpam-1048	48	10	the	the	DET
ejpam-1048	48	11	following	follow	VERB
ejpam-1048	48	12	form	form	NOUN
ejpam-1048	48	13	t	t	PROPN
ejpam-1048	48	14	l	l	NOUN
ejpam-1048	48	15	ik	ik	PROPN
ejpam-1048	48	16	=	=	SYM
ejpam-1048	48	17	δ	δ	X
ejpam-1048	48	18	l	l	NOUN
ejpam-1048	49	1	i	i	PRON
ejpam-1048	49	2	wk	wk	INTJ
ejpam-1048	50	1	−	−	PROPN
ejpam-1048	50	2	δ	δ	PROPN
ejpam-1048	50	3	l	l	NOUN
ejpam-1048	50	4	kwi	kwi	NOUN
ejpam-1048	50	5	contracting	contracting	NOUN
ejpam-1048	50	6	on	on	ADP
ejpam-1048	50	7	l	l	PROPN
ejpam-1048	50	8	and	and	CCONJ
ejpam-1048	50	9	i	i	PRON
ejpam-1048	50	10	in	in	ADP
ejpam-1048	50	11	the	the	DET
ejpam-1048	50	12	last	last	ADJ
ejpam-1048	50	13	equation	equation	NOUN
ejpam-1048	50	14	,	,	PUNCT
ejpam-1048	50	15	we	we	PRON
ejpam-1048	50	16	get	get	VERB
ejpam-1048	50	17	t	t	NOUN
ejpam-1048	50	18	l	l	NOUN
ejpam-1048	50	19	lk	lk	NOUN
ejpam-1048	50	20	=	=	PUNCT
ejpam-1048	50	21	(	(	PUNCT
ejpam-1048	50	22	n−	n−	PROPN
ejpam-1048	50	23	1)wk	1)wk	NUM
ejpam-1048	50	24	(	(	PUNCT
ejpam-1048	50	25	12	12	NUM
ejpam-1048	50	26	)	)	PUNCT
ejpam-1048	50	27	thus	thus	ADV
ejpam-1048	50	28	,	,	PUNCT
ejpam-1048	50	29	we	we	PRON
ejpam-1048	50	30	can	can	AUX
ejpam-1048	50	31	find	find	VERB
ejpam-1048	50	32	∇	∇	PROPN
ejpam-1048	50	33	j	j	PROPN
ejpam-1048	50	34	t	t	PROPN
ejpam-1048	50	35	l	l	NOUN
ejpam-1048	50	36	lk	lk	PROPN
ejpam-1048	51	1	=	=	PUNCT
ejpam-1048	52	1	(	(	PUNCT
ejpam-1048	52	2	n−	n−	NOUN
ejpam-1048	52	3	1)∇	1)∇	NOUN
ejpam-1048	52	4	jwk	jwk	PROPN
ejpam-1048	52	5	(	(	PUNCT
ejpam-1048	52	6	13	13	NUM
ejpam-1048	52	7	)	)	PUNCT
ejpam-1048	52	8	moreover	moreover	ADV
ejpam-1048	52	9	,	,	PUNCT
ejpam-1048	52	10	by	by	ADP
ejpam-1048	52	11	using	use	VERB
ejpam-1048	52	12	(	(	PUNCT
ejpam-1048	52	13	11	11	NUM
ejpam-1048	52	14	)	)	PUNCT
ejpam-1048	52	15	,	,	PUNCT
ejpam-1048	52	16	we	we	PRON
ejpam-1048	52	17	obtain	obtain	VERB
ejpam-1048	52	18	∇	∇	PROPN
ejpam-1048	52	19	j	j	PROPN
ejpam-1048	52	20	t	t	PROPN
ejpam-1048	53	1	l	l	NOUN
ejpam-1048	54	1	lk	lk	PROPN
ejpam-1048	55	1	=	=	PUNCT
ejpam-1048	56	1	a	a	DET
ejpam-1048	56	2	j	j	PROPN
ejpam-1048	56	3	t	t	PROPN
ejpam-1048	56	4	l	l	PROPN
ejpam-1048	56	5	lk+	lk+	PROPN
ejpam-1048	56	6	b	b	PROPN
ejpam-1048	56	7	j	j	NOUN
ejpam-1048	56	8	bk	bk	ADP
ejpam-1048	56	9	+	+	PROPN
ejpam-1048	56	10	b	b	PROPN
ejpam-1048	56	11	jak	jak	PROPN
ejpam-1048	56	12	(	(	PUNCT
ejpam-1048	56	13	14	14	NUM
ejpam-1048	56	14	)	)	PUNCT
ejpam-1048	56	15	h.	h.	PROPN
ejpam-1048	56	16	yılmaz	yılmaz	PROPN
ejpam-1048	56	17	,	,	PUNCT
ejpam-1048	56	18	f.	f.	PROPN
ejpam-1048	56	19	zengin	zengin	PROPN
ejpam-1048	56	20	,	,	PUNCT
ejpam-1048	56	21	s.	s.	PROPN
ejpam-1048	56	22	uysal	uysal	PROPN
ejpam-1048	56	23	/	/	SYM
ejpam-1048	56	24	eur	eur	PROPN
ejpam-1048	56	25	.	.	PUNCT
ejpam-1048	57	1	j.	j.	PROPN
ejpam-1048	57	2	pure	pure	PROPN
ejpam-1048	57	3	appl	appl	PROPN
ejpam-1048	57	4	.	.	PROPN
ejpam-1048	57	5	math	math	PROPN
ejpam-1048	57	6	,	,	PUNCT
ejpam-1048	57	7	4	4	NUM
ejpam-1048	57	8	(	(	PUNCT
ejpam-1048	57	9	2011	2011	NUM
ejpam-1048	57	10	)	)	PUNCT
ejpam-1048	57	11	,	,	PUNCT
ejpam-1048	57	12	152	152	NUM
ejpam-1048	57	13	-	-	SYM
ejpam-1048	57	14	161	161	NUM
ejpam-1048	57	15	155	155	NUM
ejpam-1048	57	16	from	from	ADP
ejpam-1048	57	17	(	(	PUNCT
ejpam-1048	57	18	12)-(14	12)-(14	NUM
ejpam-1048	57	19	)	)	PUNCT
ejpam-1048	57	20	,	,	PUNCT
ejpam-1048	57	21	it	it	PRON
ejpam-1048	57	22	is	be	AUX
ejpam-1048	57	23	found	find	VERB
ejpam-1048	57	24	that	that	SCONJ
ejpam-1048	57	25	∇	∇	NOUN
ejpam-1048	57	26	jwk	jwk	NOUN
ejpam-1048	57	27	=	=	PUNCT
ejpam-1048	57	28	a	a	DET
ejpam-1048	57	29	jwk	jwk	NOUN
ejpam-1048	57	30	+	+	CCONJ
ejpam-1048	57	31	1	1	NUM
ejpam-1048	57	32	n−	n−	NOUN
ejpam-1048	57	33	1	1	NUM
ejpam-1048	57	34	b	b	X
ejpam-1048	57	35	j	j	NOUN
ejpam-1048	57	36	bk	bk	ADP
ejpam-1048	57	37	+	+	NOUN
ejpam-1048	57	38	1	1	NUM
ejpam-1048	57	39	n−	n−	PROPN
ejpam-1048	57	40	1	1	NUM
ejpam-1048	57	41	b	b	NOUN
ejpam-1048	57	42	jak	jak	PROPN
ejpam-1048	57	43	(	(	PUNCT
ejpam-1048	57	44	15	15	NUM
ejpam-1048	57	45	)	)	PUNCT
ejpam-1048	57	46	after	after	ADP
ejpam-1048	57	47	that	that	PRON
ejpam-1048	57	48	,	,	PUNCT
ejpam-1048	57	49	from	from	ADP
ejpam-1048	57	50	the	the	DET
ejpam-1048	57	51	covariant	covariant	ADJ
ejpam-1048	57	52	derivative	derivative	NOUN
ejpam-1048	57	53	of	of	ADP
ejpam-1048	57	54	wk	wk	INTJ
ejpam-1048	57	55	with	with	ADP
ejpam-1048	57	56	respect	respect	NOUN
ejpam-1048	57	57	to	to	ADP
ejpam-1048	57	58	∇	∇	PROPN
ejpam-1048	57	59	,	,	PUNCT
ejpam-1048	57	60	we	we	PRON
ejpam-1048	57	61	get	get	VERB
ejpam-1048	57	62	the	the	DET
ejpam-1048	57	63	following	following	ADJ
ejpam-1048	57	64	∇	∇	X
ejpam-1048	57	65	jwk	jwk	PROPN
ejpam-1048	57	66	=	=	NOUN
ejpam-1048	57	67	∇	∇	X
ejpam-1048	57	68	jwk	jwk	PROPN
ejpam-1048	58	1	+	+	PROPN
ejpam-1048	58	2	wkw	wkw	PROPN
ejpam-1048	58	3	j	j	PROPN
ejpam-1048	58	4	−	−	PROPN
ejpam-1048	58	5	g	g	PROPN
ejpam-1048	58	6	jkw	jkw	INTJ
ejpam-1048	58	7	(	(	PUNCT
ejpam-1048	58	8	16	16	NUM
ejpam-1048	58	9	)	)	PUNCT
ejpam-1048	58	10	substituting	substitute	VERB
ejpam-1048	58	11	(	(	PUNCT
ejpam-1048	58	12	16	16	NUM
ejpam-1048	58	13	)	)	PUNCT
ejpam-1048	58	14	in	in	ADP
ejpam-1048	58	15	(	(	PUNCT
ejpam-1048	58	16	8)	8)	NUM
ejpam-1048	58	17	,	,	PUNCT
ejpam-1048	58	18	we	we	PRON
ejpam-1048	58	19	find	find	VERB
ejpam-1048	58	20	πk	πk	ADP
ejpam-1048	58	21	j	j	PROPN
ejpam-1048	58	22	=	=	PROPN
ejpam-1048	58	23	∇kw	∇kw	PROPN
ejpam-1048	58	24	j	j	NOUN
ejpam-1048	58	25	−	−	NOUN
ejpam-1048	58	26	1	1	NUM
ejpam-1048	58	27	2	2	NUM
ejpam-1048	58	28	gk	gk	PROPN
ejpam-1048	58	29	jw	jw	PROPN
ejpam-1048	58	30	(	(	PUNCT
ejpam-1048	58	31	17	17	NUM
ejpam-1048	58	32	)	)	PUNCT
ejpam-1048	58	33	again	again	ADV
ejpam-1048	58	34	,	,	PUNCT
ejpam-1048	58	35	using	use	VERB
ejpam-1048	58	36	(	(	PUNCT
ejpam-1048	58	37	15	15	NUM
ejpam-1048	58	38	)	)	PUNCT
ejpam-1048	58	39	and	and	CCONJ
ejpam-1048	58	40	(	(	PUNCT
ejpam-1048	58	41	17	17	NUM
ejpam-1048	58	42	)	)	PUNCT
ejpam-1048	58	43	,	,	PUNCT
ejpam-1048	58	44	we	we	PRON
ejpam-1048	58	45	obtain	obtain	VERB
ejpam-1048	58	46	πk	πk	ADP
ejpam-1048	58	47	j	j	PROPN
ejpam-1048	58	48	=	=	PROPN
ejpam-1048	58	49	akw	akw	PROPN
ejpam-1048	58	50	j	j	PROPN
ejpam-1048	59	1	+	+	CCONJ
ejpam-1048	59	2	1	1	NUM
ejpam-1048	59	3	n−	n−	NOUN
ejpam-1048	59	4	1	1	NUM
ejpam-1048	59	5	bk	bk	NOUN
ejpam-1048	59	6	b	b	PROPN
ejpam-1048	59	7	j	j	PROPN
ejpam-1048	59	8	+	+	CCONJ
ejpam-1048	59	9	1	1	NUM
ejpam-1048	59	10	n−	n−	PROPN
ejpam-1048	59	11	1	1	NUM
ejpam-1048	59	12	bka	bka	PROPN
ejpam-1048	59	13	j	j	PROPN
ejpam-1048	59	14	−	−	NOUN
ejpam-1048	59	15	1	1	NUM
ejpam-1048	59	16	2	2	NUM
ejpam-1048	59	17	gk	gk	PROPN
ejpam-1048	59	18	jw	jw	PROPN
ejpam-1048	59	19	(	(	PUNCT
ejpam-1048	59	20	18	18	NUM
ejpam-1048	59	21	)	)	PUNCT
ejpam-1048	59	22	then	then	ADV
ejpam-1048	59	23	,	,	PUNCT
ejpam-1048	59	24	if	if	SCONJ
ejpam-1048	59	25	we	we	PRON
ejpam-1048	59	26	substitute	substitute	VERB
ejpam-1048	59	27	(	(	PUNCT
ejpam-1048	59	28	18	18	NUM
ejpam-1048	59	29	)	)	PUNCT
ejpam-1048	59	30	in	in	ADP
ejpam-1048	59	31	(	(	PUNCT
ejpam-1048	59	32	7	7	NUM
ejpam-1048	59	33	)	)	PUNCT
ejpam-1048	59	34	,	,	PUNCT
ejpam-1048	59	35	we	we	PRON
ejpam-1048	59	36	get	get	VERB
ejpam-1048	59	37	rik	rik	PROPN
ejpam-1048	59	38	jm	jm	PROPN
ejpam-1048	59	39	=	=	PROPN
ejpam-1048	59	40	rik	rik	PROPN
ejpam-1048	59	41	jm	jm	PROPN
ejpam-1048	59	42	(	(	PUNCT
ejpam-1048	59	43	19	19	NUM
ejpam-1048	59	44	)	)	PUNCT
ejpam-1048	59	45	+	+	PROPN
ejpam-1048	59	46	w	w	PROPN
ejpam-1048	59	47	�	�	PROPN
ejpam-1048	59	48	gim	gim	PROPN
ejpam-1048	59	49	gk	gk	PROPN
ejpam-1048	59	50	j	j	PROPN
ejpam-1048	59	51	−	−	PROPN
ejpam-1048	59	52	gkmgi	gkmgi	PROPN
ejpam-1048	59	53	j	j	PROPN
ejpam-1048	59	54	�	�	PROPN
ejpam-1048	59	55	−	−	PROPN
ejpam-1048	59	56	gim	gim	PROPN
ejpam-1048	59	57	�	�	PROPN
ejpam-1048	59	58	akw	akw	PROPN
ejpam-1048	59	59	j	j	PROPN
ejpam-1048	60	1	+	+	CCONJ
ejpam-1048	60	2	1	1	NUM
ejpam-1048	60	3	n−	n−	NOUN
ejpam-1048	60	4	1	1	NUM
ejpam-1048	60	5	bk	bk	NOUN
ejpam-1048	60	6	b	b	PROPN
ejpam-1048	60	7	j	j	PROPN
ejpam-1048	60	8	+	+	CCONJ
ejpam-1048	60	9	1	1	NUM
ejpam-1048	60	10	n−	n−	PROPN
ejpam-1048	60	11	1	1	NUM
ejpam-1048	60	12	bka	bka	PROPN
ejpam-1048	60	13	j	j	PROPN
ejpam-1048	60	14	�	�	PROPN
ejpam-1048	60	15	+	+	CCONJ
ejpam-1048	60	16	gkm	gkm	PROPN
ejpam-1048	60	17	�	�	PROPN
ejpam-1048	60	18	aiw	aiw	PROPN
ejpam-1048	60	19	j	j	PROPN
ejpam-1048	60	20	+	+	CCONJ
ejpam-1048	60	21	1	1	NUM
ejpam-1048	60	22	n−	n−	NOUN
ejpam-1048	60	23	1	1	NUM
ejpam-1048	60	24	bi	bi	PROPN
ejpam-1048	60	25	b	b	PROPN
ejpam-1048	60	26	j	j	PROPN
ejpam-1048	60	27	+	+	CCONJ
ejpam-1048	60	28	1	1	NUM
ejpam-1048	60	29	n−	n−	NOUN
ejpam-1048	60	30	1	1	NUM
ejpam-1048	60	31	bia	bia	PROPN
ejpam-1048	60	32	j	j	PROPN
ejpam-1048	60	33	�	�	PROPN
ejpam-1048	61	1	−	−	PROPN
ejpam-1048	61	2	gk	gk	PROPN
ejpam-1048	61	3	j	j	PROPN
ejpam-1048	61	4	�	�	PROPN
ejpam-1048	61	5	aiwm+	aiwm+	NOUN
ejpam-1048	61	6	1	1	NUM
ejpam-1048	61	7	n−	n−	NOUN
ejpam-1048	61	8	1	1	NUM
ejpam-1048	61	9	bi	bi	PROPN
ejpam-1048	61	10	bm+	bm+	PROPN
ejpam-1048	61	11	1	1	NUM
ejpam-1048	61	12	n−	n−	PROPN
ejpam-1048	61	13	1	1	NUM
ejpam-1048	61	14	biam	biam	NOUN
ejpam-1048	61	15	�	�	PROPN
ejpam-1048	61	16	+	+	CCONJ
ejpam-1048	61	17	gi	gi	PROPN
ejpam-1048	61	18	j	j	PROPN
ejpam-1048	61	19	�	�	PROPN
ejpam-1048	61	20	akwm+	akwm+	AUX
ejpam-1048	61	21	1	1	NUM
ejpam-1048	61	22	n−	n−	NOUN
ejpam-1048	61	23	1	1	NUM
ejpam-1048	61	24	bk	bk	VERB
ejpam-1048	61	25	bm+	bm+	PROPN
ejpam-1048	61	26	1	1	NUM
ejpam-1048	61	27	n−	n−	NOUN
ejpam-1048	61	28	1	1	NUM
ejpam-1048	61	29	bkam	bkam	ADJ
ejpam-1048	61	30	�	�	PROPN
ejpam-1048	61	31	from	from	ADP
ejpam-1048	61	32	(	(	PUNCT
ejpam-1048	61	33	19	19	NUM
ejpam-1048	61	34	)	)	PUNCT
ejpam-1048	61	35	,	,	PUNCT
ejpam-1048	61	36	we	we	PRON
ejpam-1048	61	37	have	have	VERB
ejpam-1048	61	38	the	the	DET
ejpam-1048	61	39	following	follow	VERB
ejpam-1048	61	40	theorem	theorem	NOUN
ejpam-1048	61	41	:	:	PUNCT
ejpam-1048	61	42	theorem	theorem	NOUN
ejpam-1048	61	43	1	1	NUM
ejpam-1048	61	44	.	.	PUNCT
ejpam-1048	62	1	the	the	DET
ejpam-1048	62	2	curvature	curvature	NOUN
ejpam-1048	62	3	tensor	tensor	NOUN
ejpam-1048	62	4	of	of	ADP
ejpam-1048	62	5	a	a	DET
ejpam-1048	62	6	riemannian	riemannian	ADJ
ejpam-1048	62	7	manifold	manifold	NOUN
ejpam-1048	62	8	admitting	admit	VERB
ejpam-1048	62	9	a	a	DET
ejpam-1048	62	10	semi	semi	ADJ
ejpam-1048	62	11	symmetric	symmetric	ADJ
ejpam-1048	62	12	metric	metric	ADJ
ejpam-1048	62	13	connection	connection	NOUN
ejpam-1048	62	14	whose	whose	DET
ejpam-1048	62	15	the	the	DET
ejpam-1048	62	16	torsion	torsion	NOUN
ejpam-1048	62	17	tensor	tensor	NOUN
ejpam-1048	62	18	satisfies	satisfy	VERB
ejpam-1048	62	19	the	the	DET
ejpam-1048	62	20	condition	condition	NOUN
ejpam-1048	62	21	(	(	PUNCT
ejpam-1048	62	22	11	11	NUM
ejpam-1048	62	23	)	)	PUNCT
ejpam-1048	62	24	is	be	AUX
ejpam-1048	62	25	of	of	ADP
ejpam-1048	62	26	the	the	DET
ejpam-1048	62	27	form	form	NOUN
ejpam-1048	62	28	(	(	PUNCT
ejpam-1048	62	29	19	19	NUM
ejpam-1048	62	30	)	)	PUNCT
ejpam-1048	62	31	.	.	PUNCT
ejpam-1048	63	1	now	now	ADV
ejpam-1048	63	2	,	,	PUNCT
ejpam-1048	63	3	we	we	PRON
ejpam-1048	63	4	recall	recall	VERB
ejpam-1048	63	5	some	some	DET
ejpam-1048	63	6	theorems	theorem	NOUN
ejpam-1048	63	7	which	which	PRON
ejpam-1048	63	8	will	will	AUX
ejpam-1048	63	9	be	be	AUX
ejpam-1048	63	10	used	use	VERB
ejpam-1048	63	11	in	in	ADP
ejpam-1048	63	12	this	this	DET
ejpam-1048	63	13	section	section	NOUN
ejpam-1048	63	14	:	:	PUNCT
ejpam-1048	63	15	theorem	theorem	NOUN
ejpam-1048	63	16	2	2	NUM
ejpam-1048	63	17	.	.	PUNCT
ejpam-1048	64	1	[	[	X
ejpam-1048	64	2	3	3	X
ejpam-1048	64	3	]	]	PUNCT
ejpam-1048	64	4	the	the	DET
ejpam-1048	64	5	ricci	ricci	PROPN
ejpam-1048	64	6	tensor	tensor	NOUN
ejpam-1048	64	7	s(x	s(x	PROPN
ejpam-1048	64	8	,	,	PUNCT
ejpam-1048	64	9	y	y	PROPN
ejpam-1048	64	10	)	)	PUNCT
ejpam-1048	64	11	of	of	ADP
ejpam-1048	64	12	a	a	DET
ejpam-1048	64	13	semi	semi	ADJ
ejpam-1048	64	14	symmetric	symmetric	ADJ
ejpam-1048	64	15	metric	metric	ADJ
ejpam-1048	64	16	connection	connection	NOUN
ejpam-1048	64	17	∇	∇	X
ejpam-1048	64	18	with	with	ADP
ejpam-1048	64	19	the	the	DET
ejpam-1048	64	20	associated	associated	ADJ
ejpam-1048	64	21	1	1	NUM
ejpam-1048	64	22	-	-	PUNCT
ejpam-1048	64	23	form	form	NOUN
ejpam-1048	64	24	w	w	NOUN
ejpam-1048	64	25	will	will	AUX
ejpam-1048	64	26	be	be	AUX
ejpam-1048	64	27	symmetric	symmetric	ADJ
ejpam-1048	64	28	if	if	SCONJ
ejpam-1048	65	1	and	and	CCONJ
ejpam-1048	65	2	only	only	ADV
ejpam-1048	65	3	if	if	SCONJ
ejpam-1048	65	4	w	w	NOUN
ejpam-1048	65	5	is	be	AUX
ejpam-1048	65	6	closed	closed	ADJ
ejpam-1048	65	7	.	.	PUNCT
ejpam-1048	66	1	theorem	theorem	NOUN
ejpam-1048	66	2	3	3	NUM
ejpam-1048	66	3	.	.	PUNCT
ejpam-1048	67	1	[	[	X
ejpam-1048	67	2	3	3	X
ejpam-1048	67	3	]	]	X
ejpam-1048	67	4	a	a	DET
ejpam-1048	67	5	necessary	necessary	ADJ
ejpam-1048	67	6	and	and	CCONJ
ejpam-1048	67	7	sufficient	sufficient	ADJ
ejpam-1048	67	8	condition	condition	NOUN
ejpam-1048	67	9	that	that	SCONJ
ejpam-1048	67	10	the	the	DET
ejpam-1048	67	11	ricci	ricci	PROPN
ejpam-1048	67	12	tensor	tensor	NOUN
ejpam-1048	67	13	of	of	ADP
ejpam-1048	67	14	the	the	DET
ejpam-1048	67	15	semi	semi	ADJ
ejpam-1048	67	16	symmetric	symmetric	ADJ
ejpam-1048	67	17	metric	metric	ADJ
ejpam-1048	67	18	connection	connection	NOUN
ejpam-1048	67	19	∇	∇	VERB
ejpam-1048	67	20	to	to	PART
ejpam-1048	67	21	be	be	AUX
ejpam-1048	67	22	symmetric	symmetric	ADJ
ejpam-1048	67	23	is	be	AUX
ejpam-1048	67	24	that	that	SCONJ
ejpam-1048	67	25	the	the	DET
ejpam-1048	67	26	curvature	curvature	NOUN
ejpam-1048	67	27	tensor	tensor	NOUN
ejpam-1048	67	28	r	r	NOUN
ejpam-1048	67	29	of	of	ADP
ejpam-1048	67	30	(	(	PUNCT
ejpam-1048	67	31	0,4	0,4	NOUN
ejpam-1048	67	32	)	)	PUNCT
ejpam-1048	67	33	type	type	NOUN
ejpam-1048	67	34	with	with	ADP
ejpam-1048	67	35	respect	respect	NOUN
ejpam-1048	67	36	to	to	ADP
ejpam-1048	67	37	the	the	DET
ejpam-1048	67	38	connection	connection	NOUN
ejpam-1048	67	39	∇	∇	X
ejpam-1048	67	40	satisfies	satisfy	VERB
ejpam-1048	67	41	one	one	NUM
ejpam-1048	67	42	of	of	ADP
ejpam-1048	67	43	the	the	DET
ejpam-1048	67	44	following	follow	VERB
ejpam-1048	67	45	two	two	NUM
ejpam-1048	67	46	conditions	condition	NOUN
ejpam-1048	67	47	:	:	PUNCT
ejpam-1048	67	48	i	i	PRON
ejpam-1048	67	49	rik	rik	VERB
ejpam-1048	67	50	jm	jm	PROPN
ejpam-1048	67	51	=	=	PUNCT
ejpam-1048	67	52	r	r	PROPN
ejpam-1048	67	53	jmik	jmik	PROPN
ejpam-1048	67	54	h.	h.	PROPN
ejpam-1048	67	55	yılmaz	yılmaz	PROPN
ejpam-1048	67	56	,	,	PUNCT
ejpam-1048	67	57	f.	f.	PROPN
ejpam-1048	67	58	zengin	zengin	PROPN
ejpam-1048	67	59	,	,	PUNCT
ejpam-1048	67	60	s.	s.	PROPN
ejpam-1048	67	61	uysal	uysal	PROPN
ejpam-1048	67	62	/	/	SYM
ejpam-1048	67	63	eur	eur	PROPN
ejpam-1048	67	64	.	.	PUNCT
ejpam-1048	68	1	j.	j.	PROPN
ejpam-1048	68	2	pure	pure	PROPN
ejpam-1048	68	3	appl	appl	PROPN
ejpam-1048	68	4	.	.	PROPN
ejpam-1048	68	5	math	math	PROPN
ejpam-1048	68	6	,	,	PUNCT
ejpam-1048	68	7	4	4	NUM
ejpam-1048	68	8	(	(	PUNCT
ejpam-1048	68	9	2011	2011	NUM
ejpam-1048	68	10	)	)	PUNCT
ejpam-1048	68	11	,	,	PUNCT
ejpam-1048	68	12	152	152	NUM
ejpam-1048	68	13	-	-	SYM
ejpam-1048	68	14	161	161	NUM
ejpam-1048	68	15	156	156	NUM
ejpam-1048	68	16	ii	ii	NOUN
ejpam-1048	68	17	rik	rik	PROPN
ejpam-1048	68	18	jm+	jm+	NOUN
ejpam-1048	68	19	rk	rk	NOUN
ejpam-1048	68	20	jim+	jim+	VERB
ejpam-1048	68	21	r	r	NOUN
ejpam-1048	68	22	jikm	jikm	NOUN
ejpam-1048	69	1	=	=	SYM
ejpam-1048	69	2	0	0	X
ejpam-1048	69	3	.	.	PUNCT
ejpam-1048	70	1	from	from	ADP
ejpam-1048	70	2	(	(	PUNCT
ejpam-1048	70	3	19	19	NUM
ejpam-1048	70	4	)	)	PUNCT
ejpam-1048	70	5	,	,	PUNCT
ejpam-1048	70	6	we	we	PRON
ejpam-1048	70	7	can	can	AUX
ejpam-1048	70	8	write	write	VERB
ejpam-1048	70	9	r	r	NOUN
ejpam-1048	70	10	jmik	jmik	VERB
ejpam-1048	70	11	=	=	PUNCT
ejpam-1048	70	12	r	r	NOUN
ejpam-1048	70	13	jmik	jmik	NOUN
ejpam-1048	70	14	(	(	PUNCT
ejpam-1048	70	15	20	20	NUM
ejpam-1048	70	16	)	)	PUNCT
ejpam-1048	71	1	+	+	PROPN
ejpam-1048	71	2	w	w	PROPN
ejpam-1048	71	3	�	�	PROPN
ejpam-1048	71	4	g	g	PROPN
ejpam-1048	71	5	jk	jk	PROPN
ejpam-1048	71	6	gim−	gim−	PROPN
ejpam-1048	71	7	gmk	gmk	PROPN
ejpam-1048	71	8	g	g	PROPN
ejpam-1048	71	9	ji	ji	PROPN
ejpam-1048	71	10	�	�	PROPN
ejpam-1048	71	11	−	−	PROPN
ejpam-1048	71	12	g	g	PROPN
ejpam-1048	71	13	jk	jk	PROPN
ejpam-1048	71	14	�	�	PROPN
ejpam-1048	71	15	amwi	amwi	PROPN
ejpam-1048	72	1	+	+	CCONJ
ejpam-1048	72	2	1	1	NUM
ejpam-1048	72	3	n−	n−	NOUN
ejpam-1048	72	4	1	1	NUM
ejpam-1048	72	5	bm	bm	PROPN
ejpam-1048	72	6	bi	bi	PROPN
ejpam-1048	72	7	+	+	PROPN
ejpam-1048	72	8	1	1	NUM
ejpam-1048	72	9	n−	n−	NOUN
ejpam-1048	72	10	1	1	NUM
ejpam-1048	72	11	bmai	bmai	NOUN
ejpam-1048	72	12	�	�	PROPN
ejpam-1048	72	13	+	+	CCONJ
ejpam-1048	72	14	gmk	gmk	PROPN
ejpam-1048	72	15	�	�	PROPN
ejpam-1048	72	16	a	a	DET
ejpam-1048	72	17	jwi	jwi	ADJ
ejpam-1048	72	18	+	+	CCONJ
ejpam-1048	72	19	1	1	NUM
ejpam-1048	72	20	n−	n−	NOUN
ejpam-1048	72	21	1	1	NUM
ejpam-1048	72	22	b	b	NOUN
ejpam-1048	72	23	j	j	PROPN
ejpam-1048	72	24	bi	bi	NOUN
ejpam-1048	72	25	+	+	NOUN
ejpam-1048	72	26	1	1	NUM
ejpam-1048	72	27	n−	n−	PROPN
ejpam-1048	72	28	1	1	NUM
ejpam-1048	72	29	b	b	PROPN
ejpam-1048	72	30	jai	jai	PROPN
ejpam-1048	72	31	�	�	PROPN
ejpam-1048	73	1	−	−	PROPN
ejpam-1048	73	2	gmi	gmi	PROPN
ejpam-1048	73	3	�	�	PROPN
ejpam-1048	73	4	a	a	DET
ejpam-1048	73	5	jwk	jwk	NOUN
ejpam-1048	73	6	+	+	CCONJ
ejpam-1048	73	7	1	1	NUM
ejpam-1048	73	8	n−	n−	NOUN
ejpam-1048	73	9	1	1	NUM
ejpam-1048	73	10	b	b	X
ejpam-1048	73	11	j	j	NOUN
ejpam-1048	73	12	bk	bk	ADP
ejpam-1048	73	13	+	+	NOUN
ejpam-1048	73	14	1	1	NUM
ejpam-1048	73	15	n−	n−	PROPN
ejpam-1048	73	16	1	1	NUM
ejpam-1048	73	17	b	b	PROPN
ejpam-1048	73	18	jak	jak	PROPN
ejpam-1048	73	19	�	�	PROPN
ejpam-1048	74	1	+	+	CCONJ
ejpam-1048	74	2	g	g	PROPN
ejpam-1048	74	3	ji	ji	PROPN
ejpam-1048	74	4	�	�	PROPN
ejpam-1048	74	5	amwk	amwk	PROPN
ejpam-1048	74	6	+	+	CCONJ
ejpam-1048	74	7	1	1	NUM
ejpam-1048	74	8	n−	n−	NOUN
ejpam-1048	74	9	1	1	NUM
ejpam-1048	74	10	bm	bm	VERB
ejpam-1048	74	11	bk	bk	ADP
ejpam-1048	74	12	+	+	NOUN
ejpam-1048	74	13	1	1	NUM
ejpam-1048	74	14	n−	n−	NOUN
ejpam-1048	74	15	1	1	NUM
ejpam-1048	74	16	bmak	bmak	PROPN
ejpam-1048	74	17	�	�	PROPN
ejpam-1048	74	18	we	we	PRON
ejpam-1048	74	19	assume	assume	VERB
ejpam-1048	74	20	that	that	SCONJ
ejpam-1048	74	21	the	the	DET
ejpam-1048	74	22	associated	associated	ADJ
ejpam-1048	74	23	1	1	NUM
ejpam-1048	74	24	-	-	PUNCT
ejpam-1048	74	25	form	form	NOUN
ejpam-1048	74	26	w	w	NOUN
ejpam-1048	74	27	of	of	ADP
ejpam-1048	74	28	a	a	DET
ejpam-1048	74	29	riemannian	riemannian	ADJ
ejpam-1048	74	30	manifold	manifold	NOUN
ejpam-1048	74	31	admitting	admit	VERB
ejpam-1048	74	32	a	a	DET
ejpam-1048	74	33	semi	semi	ADJ
ejpam-1048	74	34	symmetric	symmetric	ADJ
ejpam-1048	74	35	metric	metric	ADJ
ejpam-1048	74	36	connection	connection	NOUN
ejpam-1048	74	37	whose	whose	DET
ejpam-1048	74	38	the	the	DET
ejpam-1048	74	39	torsion	torsion	NOUN
ejpam-1048	74	40	tensor	tensor	NOUN
ejpam-1048	74	41	satisfies	satisfy	VERB
ejpam-1048	74	42	the	the	DET
ejpam-1048	74	43	condition	condition	NOUN
ejpam-1048	74	44	(	(	PUNCT
ejpam-1048	74	45	11	11	NUM
ejpam-1048	74	46	)	)	PUNCT
ejpam-1048	74	47	is	be	AUX
ejpam-1048	74	48	closed	close	VERB
ejpam-1048	74	49	.	.	PUNCT
ejpam-1048	75	1	in	in	ADP
ejpam-1048	75	2	virtue	virtue	NOUN
ejpam-1048	75	3	of	of	ADP
ejpam-1048	75	4	theorem	theorem	NOUN
ejpam-1048	75	5	2	2	NUM
ejpam-1048	75	6	,	,	PUNCT
ejpam-1048	75	7	the	the	DET
ejpam-1048	75	8	ricci	ricci	PROPN
ejpam-1048	75	9	tensor	tensor	NOUN
ejpam-1048	75	10	of	of	ADP
ejpam-1048	75	11	a	a	DET
ejpam-1048	75	12	riemannian	riemannian	NOUN
ejpam-1048	75	13	manifold	manifold	NOUN
ejpam-1048	75	14	with	with	ADP
ejpam-1048	75	15	a	a	DET
ejpam-1048	75	16	semi	semi	ADJ
ejpam-1048	75	17	symmetric	symmetric	ADJ
ejpam-1048	75	18	metric	metric	ADJ
ejpam-1048	75	19	connection	connection	NOUN
ejpam-1048	75	20	is	be	AUX
ejpam-1048	75	21	symmetric	symmetric	ADJ
ejpam-1048	75	22	.	.	PUNCT
ejpam-1048	76	1	thus	thus	ADV
ejpam-1048	76	2	,	,	PUNCT
ejpam-1048	76	3	due	due	ADP
ejpam-1048	76	4	to	to	ADP
ejpam-1048	76	5	theorem	theorem	NOUN
ejpam-1048	76	6	3	3	NUM
ejpam-1048	76	7	,	,	PUNCT
ejpam-1048	76	8	we	we	PRON
ejpam-1048	76	9	get	get	VERB
ejpam-1048	76	10	r	r	NOUN
ejpam-1048	76	11	jmik	jmik	VERB
ejpam-1048	76	12	=	=	SYM
ejpam-1048	76	13	rik	rik	PROPN
ejpam-1048	76	14	jm	jm	PROPN
ejpam-1048	76	15	(	(	PUNCT
ejpam-1048	76	16	21	21	NUM
ejpam-1048	76	17	)	)	PUNCT
ejpam-1048	76	18	in	in	ADP
ejpam-1048	76	19	case	case	NOUN
ejpam-1048	76	20	the	the	DET
ejpam-1048	76	21	equation	equation	NOUN
ejpam-1048	76	22	(	(	PUNCT
ejpam-1048	76	23	21	21	NUM
ejpam-1048	76	24	)	)	PUNCT
ejpam-1048	76	25	is	be	AUX
ejpam-1048	76	26	satisfied	satisfied	ADJ
ejpam-1048	76	27	,	,	PUNCT
ejpam-1048	76	28	we	we	PRON
ejpam-1048	76	29	find	find	VERB
ejpam-1048	76	30	0	0	NUM
ejpam-1048	76	31	=	=	ADJ
ejpam-1048	76	32	gim	gim	NOUN
ejpam-1048	76	33	�	�	PROPN
ejpam-1048	76	34	a	a	DET
ejpam-1048	76	35	j	j	PROPN
ejpam-1048	76	36	�	�	PROPN
ejpam-1048	76	37	wk	wk	NOUN
ejpam-1048	76	38	−	−	PROPN
ejpam-1048	76	39	1	1	NUM
ejpam-1048	76	40	n−	n−	NOUN
ejpam-1048	76	41	1	1	NUM
ejpam-1048	76	42	bk	bk	NOUN
ejpam-1048	76	43	�	�	PROPN
ejpam-1048	76	44	−	−	PROPN
ejpam-1048	76	45	ak	ak	PROPN
ejpam-1048	76	46	�	�	PROPN
ejpam-1048	76	47	w	w	PROPN
ejpam-1048	76	48	j	j	PROPN
ejpam-1048	76	49	−	−	NUM
ejpam-1048	76	50	1	1	NUM
ejpam-1048	76	51	n−	n−	NOUN
ejpam-1048	76	52	1	1	NUM
ejpam-1048	76	53	b	b	PROPN
ejpam-1048	76	54	j	j	PROPN
ejpam-1048	76	55	�	�	PROPN
ejpam-1048	76	56	�	�	PROPN
ejpam-1048	76	57	(	(	PUNCT
ejpam-1048	76	58	22	22	NUM
ejpam-1048	76	59	)	)	PUNCT
ejpam-1048	77	1	+	+	CCONJ
ejpam-1048	77	2	gkm	gkm	ADJ
ejpam-1048	77	3	�	�	PROPN
ejpam-1048	77	4	ai	ai	VERB
ejpam-1048	77	5	�	�	PROPN
ejpam-1048	77	6	w	w	PROPN
ejpam-1048	77	7	j	j	PROPN
ejpam-1048	77	8	−	−	NUM
ejpam-1048	77	9	1	1	NUM
ejpam-1048	77	10	n−	n−	NOUN
ejpam-1048	77	11	1	1	NUM
ejpam-1048	77	12	b	b	X
ejpam-1048	77	13	j	j	PROPN
ejpam-1048	77	14	�	�	PROPN
ejpam-1048	77	15	−	−	PROPN
ejpam-1048	77	16	a	a	DET
ejpam-1048	77	17	j	j	PROPN
ejpam-1048	77	18	�	�	PROPN
ejpam-1048	77	19	wi	wi	PROPN
ejpam-1048	77	20	−	−	PROPN
ejpam-1048	77	21	1	1	NUM
ejpam-1048	77	22	n−	n−	NOUN
ejpam-1048	77	23	1	1	NUM
ejpam-1048	77	24	bi	bi	PROPN
ejpam-1048	77	25	�	�	PROPN
ejpam-1048	77	26	�	�	PROPN
ejpam-1048	77	27	+	+	CCONJ
ejpam-1048	77	28	gk	gk	PROPN
ejpam-1048	77	29	j	j	PROPN
ejpam-1048	77	30	�	�	PROPN
ejpam-1048	77	31	am	be	AUX
ejpam-1048	77	32	�	�	PROPN
ejpam-1048	77	33	wi	wi	PROPN
ejpam-1048	77	34	−	−	PROPN
ejpam-1048	77	35	1	1	NUM
ejpam-1048	77	36	n−	n−	NOUN
ejpam-1048	77	37	1	1	NUM
ejpam-1048	77	38	bi	bi	PROPN
ejpam-1048	77	39	�	�	PROPN
ejpam-1048	77	40	−	−	PROPN
ejpam-1048	77	41	ai	ai	VERB
ejpam-1048	77	42	�	�	PROPN
ejpam-1048	77	43	wm	wm	PROPN
ejpam-1048	77	44	−	−	PROPN
ejpam-1048	77	45	1	1	NUM
ejpam-1048	77	46	n−	n−	PROPN
ejpam-1048	77	47	1	1	NUM
ejpam-1048	77	48	bm	bm	PROPN
ejpam-1048	77	49	�	�	PROPN
ejpam-1048	77	50	�	�	PROPN
ejpam-1048	77	51	+	+	CCONJ
ejpam-1048	77	52	gi	gi	PROPN
ejpam-1048	77	53	j	j	PROPN
ejpam-1048	77	54	�	�	PROPN
ejpam-1048	77	55	ak	ak	PROPN
ejpam-1048	77	56	�	�	PROPN
ejpam-1048	77	57	wm	wm	PROPN
ejpam-1048	77	58	−	−	PROPN
ejpam-1048	77	59	1	1	NUM
ejpam-1048	77	60	n−	n−	PROPN
ejpam-1048	77	61	1	1	NUM
ejpam-1048	77	62	bm	bm	PROPN
ejpam-1048	77	63	�	�	PROPN
ejpam-1048	77	64	−	−	PROPN
ejpam-1048	77	65	am	be	AUX
ejpam-1048	77	66	�	�	NOUN
ejpam-1048	77	67	wk	wk	ADP
ejpam-1048	77	68	−	−	PROPN
ejpam-1048	77	69	1	1	NUM
ejpam-1048	77	70	n−	n−	NOUN
ejpam-1048	77	71	1	1	NUM
ejpam-1048	77	72	bk	bk	NOUN
ejpam-1048	77	73	�	�	PROPN
ejpam-1048	77	74	�	�	PROPN
ejpam-1048	77	75	transvecting	transvecting	NOUN
ejpam-1048	77	76	(	(	PUNCT
ejpam-1048	77	77	22	22	NUM
ejpam-1048	77	78	)	)	PUNCT
ejpam-1048	77	79	with	with	ADP
ejpam-1048	77	80	g	g	PROPN
ejpam-1048	77	81	i	i	PRON
ejpam-1048	77	82	m	m	VERB
ejpam-1048	77	83	,	,	PUNCT
ejpam-1048	77	84	we	we	PRON
ejpam-1048	77	85	get	get	VERB
ejpam-1048	77	86	(	(	PUNCT
ejpam-1048	77	87	2−	2−	NUM
ejpam-1048	77	88	n	n	CCONJ
ejpam-1048	77	89	)	)	PUNCT
ejpam-1048	77	90	�	�	PROPN
ejpam-1048	77	91	ak	ak	PROPN
ejpam-1048	77	92	�	�	PROPN
ejpam-1048	77	93	w	w	PROPN
ejpam-1048	77	94	j	j	PROPN
ejpam-1048	77	95	−	−	NUM
ejpam-1048	77	96	1	1	NUM
ejpam-1048	77	97	n−	n−	NOUN
ejpam-1048	77	98	1	1	NUM
ejpam-1048	77	99	b	b	X
ejpam-1048	77	100	j	j	PROPN
ejpam-1048	77	101	�	�	PROPN
ejpam-1048	77	102	−	−	PROPN
ejpam-1048	77	103	a	a	DET
ejpam-1048	77	104	j	j	PROPN
ejpam-1048	77	105	�	�	PROPN
ejpam-1048	77	106	wk	wk	NOUN
ejpam-1048	77	107	−	−	PROPN
ejpam-1048	77	108	1	1	NUM
ejpam-1048	77	109	n−	n−	NOUN
ejpam-1048	77	110	1	1	NUM
ejpam-1048	77	111	bk	bk	NOUN
ejpam-1048	77	112	�	�	PROPN
ejpam-1048	77	113	�	�	PROPN
ejpam-1048	77	114	=	=	SYM
ejpam-1048	77	115	0	0	NUM
ejpam-1048	78	1	(	(	PUNCT
ejpam-1048	78	2	23	23	NUM
ejpam-1048	78	3	)	)	PUNCT
ejpam-1048	78	4	since	since	SCONJ
ejpam-1048	78	5	n	n	CCONJ
ejpam-1048	78	6	>	>	X
ejpam-1048	78	7	2	2	NUM
ejpam-1048	78	8	,	,	PUNCT
ejpam-1048	78	9	we	we	PRON
ejpam-1048	78	10	get	get	VERB
ejpam-1048	78	11	ak	ak	PROPN
ejpam-1048	78	12	�	�	PROPN
ejpam-1048	78	13	w	w	PROPN
ejpam-1048	78	14	j	j	PROPN
ejpam-1048	79	1	−	−	NUM
ejpam-1048	79	2	1	1	NUM
ejpam-1048	79	3	n−	n−	NOUN
ejpam-1048	79	4	1	1	NUM
ejpam-1048	79	5	b	b	X
ejpam-1048	79	6	j	j	PROPN
ejpam-1048	79	7	�	�	PROPN
ejpam-1048	79	8	=	=	PROPN
ejpam-1048	79	9	a	a	DET
ejpam-1048	79	10	j	j	PROPN
ejpam-1048	79	11	�	�	PROPN
ejpam-1048	79	12	wk	wk	NOUN
ejpam-1048	79	13	−	−	PROPN
ejpam-1048	79	14	1	1	NUM
ejpam-1048	79	15	n−	n−	NOUN
ejpam-1048	79	16	1	1	NUM
ejpam-1048	79	17	bk	bk	NOUN
ejpam-1048	79	18	�	�	PROPN
ejpam-1048	79	19	(	(	PUNCT
ejpam-1048	79	20	24	24	NUM
ejpam-1048	79	21	)	)	PUNCT
ejpam-1048	79	22	now	now	ADV
ejpam-1048	79	23	,	,	PUNCT
ejpam-1048	79	24	permutating	permutate	VERB
ejpam-1048	79	25	the	the	DET
ejpam-1048	79	26	indices	index	NOUN
ejpam-1048	79	27	and	and	CCONJ
ejpam-1048	79	28	adding	add	VERB
ejpam-1048	79	29	the	the	DET
ejpam-1048	79	30	three	three	NUM
ejpam-1048	79	31	equations	equation	NOUN
ejpam-1048	79	32	side	side	NOUN
ejpam-1048	79	33	by	by	ADP
ejpam-1048	79	34	side	side	NOUN
ejpam-1048	79	35	,	,	PUNCT
ejpam-1048	79	36	we	we	PRON
ejpam-1048	79	37	obtain	obtain	VERB
ejpam-1048	79	38	rik	rik	NOUN
ejpam-1048	79	39	jm+rk	jm+rk	PROPN
ejpam-1048	79	40	jim+	jim+	VERB
ejpam-1048	79	41	r	r	NOUN
ejpam-1048	79	42	jikm	jikm	NOUN
ejpam-1048	79	43	(	(	PUNCT
ejpam-1048	79	44	25	25	NUM
ejpam-1048	79	45	)	)	PUNCT
ejpam-1048	79	46	h.	h.	PROPN
ejpam-1048	79	47	yılmaz	yılmaz	PROPN
ejpam-1048	79	48	,	,	PUNCT
ejpam-1048	79	49	f.	f.	PROPN
ejpam-1048	79	50	zengin	zengin	PROPN
ejpam-1048	79	51	,	,	PUNCT
ejpam-1048	79	52	s.	s.	PROPN
ejpam-1048	79	53	uysal	uysal	PROPN
ejpam-1048	79	54	/	/	SYM
ejpam-1048	79	55	eur	eur	PROPN
ejpam-1048	79	56	.	.	PUNCT
ejpam-1048	80	1	j.	j.	PROPN
ejpam-1048	80	2	pure	pure	PROPN
ejpam-1048	80	3	appl	appl	PROPN
ejpam-1048	80	4	.	.	PROPN
ejpam-1048	80	5	math	math	PROPN
ejpam-1048	80	6	,	,	PUNCT
ejpam-1048	80	7	4	4	NUM
ejpam-1048	80	8	(	(	PUNCT
ejpam-1048	80	9	2011	2011	NUM
ejpam-1048	80	10	)	)	PUNCT
ejpam-1048	80	11	,	,	PUNCT
ejpam-1048	80	12	152	152	NUM
ejpam-1048	80	13	-	-	SYM
ejpam-1048	80	14	161	161	NUM
ejpam-1048	80	15	157	157	NUM
ejpam-1048	80	16	=	=	SYM
ejpam-1048	80	17	gim	gim	PROPN
ejpam-1048	80	18	�	�	PROPN
ejpam-1048	80	19	a	a	DET
ejpam-1048	80	20	j	j	PROPN
ejpam-1048	80	21	�	�	PROPN
ejpam-1048	80	22	wk	wk	NOUN
ejpam-1048	80	23	−	−	PROPN
ejpam-1048	80	24	1	1	NUM
ejpam-1048	80	25	n−	n−	NOUN
ejpam-1048	80	26	1	1	NUM
ejpam-1048	80	27	bk	bk	NOUN
ejpam-1048	80	28	�	�	PROPN
ejpam-1048	80	29	−	−	PROPN
ejpam-1048	80	30	ak	ak	PROPN
ejpam-1048	80	31	�	�	PROPN
ejpam-1048	80	32	w	w	PROPN
ejpam-1048	80	33	j	j	PROPN
ejpam-1048	80	34	−	−	NUM
ejpam-1048	80	35	1	1	NUM
ejpam-1048	80	36	n−	n−	NOUN
ejpam-1048	80	37	1	1	NUM
ejpam-1048	80	38	b	b	PROPN
ejpam-1048	80	39	j	j	PROPN
ejpam-1048	80	40	�	�	PROPN
ejpam-1048	80	41	�	�	PROPN
ejpam-1048	80	42	+	+	CCONJ
ejpam-1048	80	43	gkm	gkm	PROPN
ejpam-1048	80	44	�	�	PROPN
ejpam-1048	80	45	ai	ai	VERB
ejpam-1048	80	46	�	�	PROPN
ejpam-1048	80	47	w	w	PROPN
ejpam-1048	80	48	j	j	PROPN
ejpam-1048	80	49	−	−	NUM
ejpam-1048	80	50	1	1	NUM
ejpam-1048	80	51	n−	n−	NOUN
ejpam-1048	80	52	1	1	NUM
ejpam-1048	80	53	b	b	X
ejpam-1048	80	54	j	j	PROPN
ejpam-1048	80	55	�	�	PROPN
ejpam-1048	80	56	−	−	PROPN
ejpam-1048	80	57	a	a	DET
ejpam-1048	80	58	j	j	PROPN
ejpam-1048	80	59	�	�	PROPN
ejpam-1048	80	60	wi	wi	PROPN
ejpam-1048	80	61	−	−	PROPN
ejpam-1048	80	62	1	1	NUM
ejpam-1048	80	63	n−	n−	NOUN
ejpam-1048	80	64	1	1	NUM
ejpam-1048	80	65	bi	bi	PROPN
ejpam-1048	80	66	�	�	PROPN
ejpam-1048	80	67	�	�	PROPN
ejpam-1048	80	68	+	+	CCONJ
ejpam-1048	80	69	g	g	PROPN
ejpam-1048	80	70	jm	jm	PROPN
ejpam-1048	80	71	�	�	PROPN
ejpam-1048	80	72	ak	ak	PROPN
ejpam-1048	80	73	�	�	PROPN
ejpam-1048	80	74	wi	wi	PROPN
ejpam-1048	80	75	−	−	PROPN
ejpam-1048	80	76	1	1	NUM
ejpam-1048	80	77	n−	n−	NOUN
ejpam-1048	80	78	1	1	NUM
ejpam-1048	80	79	bi	bi	PROPN
ejpam-1048	80	80	�	�	PROPN
ejpam-1048	80	81	−	−	PROPN
ejpam-1048	80	82	ai	ai	VERB
ejpam-1048	80	83	�	�	PROPN
ejpam-1048	80	84	wk	wk	NOUN
ejpam-1048	80	85	−	−	PROPN
ejpam-1048	80	86	1	1	NUM
ejpam-1048	80	87	n−	n−	NOUN
ejpam-1048	80	88	1	1	NUM
ejpam-1048	80	89	bk	bk	NOUN
ejpam-1048	80	90	�	�	NOUN
ejpam-1048	80	91	�	�	NOUN
ejpam-1048	80	92	conversely	conversely	ADV
ejpam-1048	80	93	,	,	PUNCT
ejpam-1048	80	94	let	let	VERB
ejpam-1048	80	95	us	we	PRON
ejpam-1048	80	96	assume	assume	VERB
ejpam-1048	80	97	that	that	SCONJ
ejpam-1048	80	98	(	(	PUNCT
ejpam-1048	80	99	24	24	NUM
ejpam-1048	80	100	)	)	PUNCT
ejpam-1048	80	101	is	be	AUX
ejpam-1048	80	102	satisfied	satisfied	ADJ
ejpam-1048	80	103	.	.	PUNCT
ejpam-1048	81	1	then	then	ADV
ejpam-1048	81	2	,	,	PUNCT
ejpam-1048	81	3	the	the	DET
ejpam-1048	81	4	expression	expression	NOUN
ejpam-1048	81	5	on	on	ADP
ejpam-1048	81	6	the	the	DET
ejpam-1048	81	7	right	right	ADJ
ejpam-1048	81	8	side	side	NOUN
ejpam-1048	81	9	of	of	ADP
ejpam-1048	81	10	(	(	PUNCT
ejpam-1048	81	11	25	25	NUM
ejpam-1048	81	12	)	)	PUNCT
ejpam-1048	81	13	vanishes	vanish	VERB
ejpam-1048	81	14	.	.	PUNCT
ejpam-1048	82	1	it	it	PRON
ejpam-1048	82	2	means	mean	VERB
ejpam-1048	82	3	that	that	SCONJ
ejpam-1048	82	4	the	the	DET
ejpam-1048	82	5	curvature	curvature	NOUN
ejpam-1048	82	6	tensor	tensor	NOUN
ejpam-1048	82	7	of	of	ADP
ejpam-1048	82	8	the	the	DET
ejpam-1048	82	9	connection	connection	NOUN
ejpam-1048	82	10	∇	∇	X
ejpam-1048	82	11	satisfies	satisfy	VERB
ejpam-1048	82	12	the	the	DET
ejpam-1048	82	13	first	first	ADJ
ejpam-1048	82	14	bianchi	bianchi	NOUN
ejpam-1048	82	15	identity	identity	NOUN
ejpam-1048	82	16	.	.	PUNCT
ejpam-1048	83	1	due	due	ADP
ejpam-1048	83	2	to	to	ADP
ejpam-1048	83	3	theorem	theorem	NOUN
ejpam-1048	83	4	3	3	NUM
ejpam-1048	83	5	,	,	PUNCT
ejpam-1048	83	6	the	the	DET
ejpam-1048	83	7	ricci	ricci	PROPN
ejpam-1048	83	8	tensor	tensor	NOUN
ejpam-1048	83	9	with	with	ADP
ejpam-1048	83	10	respect	respect	NOUN
ejpam-1048	83	11	to	to	ADP
ejpam-1048	83	12	the	the	DET
ejpam-1048	83	13	connection	connection	NOUN
ejpam-1048	83	14	∇	∇	NOUN
ejpam-1048	83	15	is	be	AUX
ejpam-1048	83	16	symmetric	symmetric	ADJ
ejpam-1048	83	17	.	.	PUNCT
ejpam-1048	84	1	because	because	SCONJ
ejpam-1048	84	2	of	of	ADP
ejpam-1048	84	3	theorem	theorem	NOUN
ejpam-1048	84	4	2	2	NUM
ejpam-1048	84	5	,	,	PUNCT
ejpam-1048	84	6	the	the	DET
ejpam-1048	84	7	associated	associated	ADJ
ejpam-1048	84	8	1	1	NUM
ejpam-1048	84	9	-	-	PUNCT
ejpam-1048	84	10	form	form	NOUN
ejpam-1048	84	11	w	w	NOUN
ejpam-1048	84	12	of	of	ADP
ejpam-1048	84	13	a	a	DET
ejpam-1048	84	14	riemannian	riemannian	NOUN
ejpam-1048	84	15	manifold	manifold	NOUN
ejpam-1048	84	16	with	with	ADP
ejpam-1048	84	17	a	a	DET
ejpam-1048	84	18	semi	semi	ADJ
ejpam-1048	84	19	symmetric	symmetric	ADJ
ejpam-1048	84	20	metric	metric	ADJ
ejpam-1048	84	21	connection	connection	NOUN
ejpam-1048	84	22	is	be	AUX
ejpam-1048	84	23	closed	close	VERB
ejpam-1048	84	24	.	.	PUNCT
ejpam-1048	85	1	hence	hence	ADV
ejpam-1048	85	2	,	,	PUNCT
ejpam-1048	85	3	we	we	PRON
ejpam-1048	85	4	can	can	AUX
ejpam-1048	85	5	establish	establish	VERB
ejpam-1048	85	6	the	the	DET
ejpam-1048	85	7	following	follow	VERB
ejpam-1048	85	8	theorem	theorem	NOUN
ejpam-1048	85	9	:	:	PUNCT
ejpam-1048	85	10	theorem	theorem	ADJ
ejpam-1048	85	11	4	4	NUM
ejpam-1048	85	12	.	.	PUNCT
ejpam-1048	86	1	a	a	DET
ejpam-1048	86	2	necessary	necessary	ADJ
ejpam-1048	86	3	and	and	CCONJ
ejpam-1048	86	4	sufficient	sufficient	ADJ
ejpam-1048	86	5	condition	condition	NOUN
ejpam-1048	86	6	that	that	SCONJ
ejpam-1048	86	7	the	the	DET
ejpam-1048	86	8	associated	associated	ADJ
ejpam-1048	86	9	1	1	NUM
ejpam-1048	86	10	-	-	PUNCT
ejpam-1048	86	11	form	form	NOUN
ejpam-1048	86	12	w	w	NOUN
ejpam-1048	86	13	of	of	ADP
ejpam-1048	86	14	a	a	DET
ejpam-1048	86	15	riemannian	riemannian	NOUN
ejpam-1048	86	16	manifold	manifold	NOUN
ejpam-1048	86	17	with	with	ADP
ejpam-1048	86	18	a	a	DET
ejpam-1048	86	19	semi	semi	ADJ
ejpam-1048	86	20	symmetric	symmetric	ADJ
ejpam-1048	86	21	metric	metric	ADJ
ejpam-1048	86	22	connection	connection	NOUN
ejpam-1048	86	23	whose	whose	DET
ejpam-1048	86	24	the	the	DET
ejpam-1048	86	25	torsion	torsion	NOUN
ejpam-1048	86	26	tensor	tensor	NOUN
ejpam-1048	86	27	satisfies	satisfy	VERB
ejpam-1048	86	28	the	the	DET
ejpam-1048	86	29	condition	condition	NOUN
ejpam-1048	86	30	(	(	PUNCT
ejpam-1048	86	31	11	11	NUM
ejpam-1048	86	32	)	)	PUNCT
ejpam-1048	86	33	to	to	PART
ejpam-1048	86	34	be	be	AUX
ejpam-1048	86	35	closed	close	VERB
ejpam-1048	86	36	is	be	AUX
ejpam-1048	86	37	that	that	SCONJ
ejpam-1048	86	38	the	the	DET
ejpam-1048	86	39	condition	condition	NOUN
ejpam-1048	86	40	(	(	PUNCT
ejpam-1048	86	41	24	24	NUM
ejpam-1048	86	42	)	)	PUNCT
ejpam-1048	86	43	is	be	AUX
ejpam-1048	86	44	satisfied	satisfied	ADJ
ejpam-1048	86	45	.	.	PUNCT
ejpam-1048	86	46	suppose	suppose	VERB
ejpam-1048	86	47	that	that	SCONJ
ejpam-1048	86	48	w	w	NOUN
ejpam-1048	86	49	is	be	AUX
ejpam-1048	86	50	closed	closed	ADJ
ejpam-1048	86	51	.	.	PUNCT
ejpam-1048	87	1	substituting	substitute	VERB
ejpam-1048	87	2	(	(	PUNCT
ejpam-1048	87	3	15	15	NUM
ejpam-1048	87	4	)	)	PUNCT
ejpam-1048	87	5	in	in	ADP
ejpam-1048	87	6	(	(	PUNCT
ejpam-1048	87	7	16	16	NUM
ejpam-1048	87	8	)	)	PUNCT
ejpam-1048	87	9	,	,	PUNCT
ejpam-1048	87	10	we	we	PRON
ejpam-1048	87	11	get	get	VERB
ejpam-1048	87	12	∇	∇	NOUN
ejpam-1048	87	13	jwk	jwk	NOUN
ejpam-1048	87	14	=	=	PUNCT
ejpam-1048	87	15	a	a	DET
ejpam-1048	87	16	jwk	jwk	NOUN
ejpam-1048	87	17	+	+	CCONJ
ejpam-1048	87	18	1	1	NUM
ejpam-1048	87	19	n−	n−	NOUN
ejpam-1048	87	20	1	1	NUM
ejpam-1048	87	21	b	b	X
ejpam-1048	87	22	j	j	NOUN
ejpam-1048	87	23	bk	bk	ADP
ejpam-1048	87	24	+	+	NOUN
ejpam-1048	87	25	1	1	NUM
ejpam-1048	87	26	n−	n−	PROPN
ejpam-1048	87	27	1	1	NUM
ejpam-1048	87	28	b	b	NOUN
ejpam-1048	87	29	jak	jak	PROPN
ejpam-1048	88	1	+	+	PROPN
ejpam-1048	88	2	wkw	wkw	PROPN
ejpam-1048	88	3	j	j	PROPN
ejpam-1048	88	4	−	−	PROPN
ejpam-1048	88	5	g	g	PROPN
ejpam-1048	88	6	jkw	jkw	X
ejpam-1048	88	7	(	(	PUNCT
ejpam-1048	88	8	26	26	NUM
ejpam-1048	88	9	)	)	PUNCT
ejpam-1048	88	10	subtracting	subtract	VERB
ejpam-1048	88	11	the	the	DET
ejpam-1048	88	12	corresponding	corresponding	ADJ
ejpam-1048	88	13	equation	equation	NOUN
ejpam-1048	88	14	found	find	VERB
ejpam-1048	88	15	by	by	ADP
ejpam-1048	88	16	interchanging	interchange	VERB
ejpam-1048	88	17	k	k	PROPN
ejpam-1048	88	18	and	and	CCONJ
ejpam-1048	88	19	j	j	PROPN
ejpam-1048	88	20	in	in	ADP
ejpam-1048	88	21	(	(	PUNCT
ejpam-1048	88	22	26	26	NUM
ejpam-1048	88	23	)	)	PUNCT
ejpam-1048	88	24	from	from	ADP
ejpam-1048	88	25	(	(	PUNCT
ejpam-1048	88	26	26	26	NUM
ejpam-1048	88	27	)	)	PUNCT
ejpam-1048	88	28	,	,	PUNCT
ejpam-1048	88	29	we	we	PRON
ejpam-1048	88	30	get	get	VERB
ejpam-1048	88	31	the	the	DET
ejpam-1048	88	32	equation	equation	NOUN
ejpam-1048	88	33	(	(	PUNCT
ejpam-1048	88	34	24	24	NUM
ejpam-1048	88	35	)	)	PUNCT
ejpam-1048	88	36	.	.	PUNCT
ejpam-1048	89	1	thus	thus	ADV
ejpam-1048	89	2	,	,	PUNCT
ejpam-1048	89	3	by	by	ADP
ejpam-1048	89	4	using	use	VERB
ejpam-1048	89	5	theorem	theorem	ADJ
ejpam-1048	89	6	2	2	NUM
ejpam-1048	89	7	,	,	PUNCT
ejpam-1048	89	8	theorem	theorem	VERB
ejpam-1048	89	9	3	3	NUM
ejpam-1048	89	10	and	and	CCONJ
ejpam-1048	89	11	theorem	theorem	VERB
ejpam-1048	89	12	4	4	NUM
ejpam-1048	89	13	,	,	PUNCT
ejpam-1048	89	14	we	we	PRON
ejpam-1048	89	15	have	have	VERB
ejpam-1048	89	16	the	the	DET
ejpam-1048	89	17	following	follow	VERB
ejpam-1048	89	18	theorem	theorem	NOUN
ejpam-1048	89	19	:	:	PUNCT
ejpam-1048	89	20	theorem	theorem	NOUN
ejpam-1048	89	21	5	5	NUM
ejpam-1048	89	22	.	.	PUNCT
ejpam-1048	89	23	in	in	ADP
ejpam-1048	89	24	a	a	DET
ejpam-1048	89	25	riemannian	riemannian	NOUN
ejpam-1048	89	26	manifold	manifold	NOUN
ejpam-1048	89	27	with	with	ADP
ejpam-1048	89	28	a	a	DET
ejpam-1048	89	29	semi	semi	ADJ
ejpam-1048	89	30	symmetric	symmetric	ADJ
ejpam-1048	89	31	metric	metric	ADJ
ejpam-1048	89	32	connection	connection	NOUN
ejpam-1048	89	33	whose	whose	DET
ejpam-1048	89	34	the	the	DET
ejpam-1048	89	35	torsion	torsion	NOUN
ejpam-1048	89	36	tensor	tensor	NOUN
ejpam-1048	89	37	satisfies	satisfy	VERB
ejpam-1048	89	38	the	the	DET
ejpam-1048	89	39	condition	condition	NOUN
ejpam-1048	89	40	(	(	PUNCT
ejpam-1048	89	41	11	11	NUM
ejpam-1048	89	42	)	)	PUNCT
ejpam-1048	89	43	,	,	PUNCT
ejpam-1048	89	44	a	a	DET
ejpam-1048	89	45	necessary	necessary	ADJ
ejpam-1048	89	46	and	and	CCONJ
ejpam-1048	89	47	sufficient	sufficient	ADJ
ejpam-1048	89	48	condition	condition	NOUN
ejpam-1048	89	49	that	that	SCONJ
ejpam-1048	89	50	the	the	DET
ejpam-1048	89	51	condition	condition	NOUN
ejpam-1048	89	52	(	(	PUNCT
ejpam-1048	89	53	24	24	NUM
ejpam-1048	89	54	)	)	PUNCT
ejpam-1048	89	55	to	to	PART
ejpam-1048	89	56	be	be	AUX
ejpam-1048	89	57	satisfied	satisfied	ADJ
ejpam-1048	89	58	is	be	AUX
ejpam-1048	89	59	that	that	SCONJ
ejpam-1048	89	60	it	it	PRON
ejpam-1048	89	61	is	be	AUX
ejpam-1048	89	62	satisfied	satisfied	ADJ
ejpam-1048	89	63	any	any	DET
ejpam-1048	89	64	one	one	NUM
ejpam-1048	89	65	of	of	ADP
ejpam-1048	89	66	the	the	DET
ejpam-1048	89	67	following	follow	VERB
ejpam-1048	89	68	properties	property	NOUN
ejpam-1048	89	69	:	:	PUNCT
ejpam-1048	89	70	i	i	PRON
ejpam-1048	89	71	the	the	DET
ejpam-1048	89	72	curvature	curvature	NOUN
ejpam-1048	89	73	tensor	tensor	NOUN
ejpam-1048	89	74	with	with	ADP
ejpam-1048	89	75	respect	respect	NOUN
ejpam-1048	89	76	to	to	ADP
ejpam-1048	89	77	the	the	DET
ejpam-1048	89	78	connection	connection	NOUN
ejpam-1048	89	79	∇	∇	X
ejpam-1048	89	80	of	of	ADP
ejpam-1048	89	81	this	this	DET
ejpam-1048	89	82	manifold	manifold	NOUN
ejpam-1048	89	83	has	have	VERB
ejpam-1048	89	84	the	the	DET
ejpam-1048	89	85	properity	properity	NOUN
ejpam-1048	89	86	of	of	ADP
ejpam-1048	89	87	block	block	NOUN
ejpam-1048	89	88	symmetry	symmetry	NOUN
ejpam-1048	89	89	,	,	PUNCT
ejpam-1048	89	90	ii	ii	VERB
ejpam-1048	89	91	the	the	DET
ejpam-1048	89	92	curvature	curvature	NOUN
ejpam-1048	89	93	tensor	tensor	NOUN
ejpam-1048	89	94	with	with	ADP
ejpam-1048	89	95	respect	respect	NOUN
ejpam-1048	89	96	to	to	ADP
ejpam-1048	89	97	the	the	DET
ejpam-1048	89	98	connection	connection	NOUN
ejpam-1048	89	99	∇	∇	X
ejpam-1048	89	100	of	of	ADP
ejpam-1048	89	101	this	this	DET
ejpam-1048	89	102	manifold	manifold	ADJ
ejpam-1048	89	103	satisfies	satisfie	NOUN
ejpam-1048	89	104	the	the	DET
ejpam-1048	89	105	first	first	ADJ
ejpam-1048	89	106	bianchi	bianchi	NOUN
ejpam-1048	89	107	identity	identity	NOUN
ejpam-1048	89	108	,	,	PUNCT
ejpam-1048	89	109	iii	iii	X
ejpam-1048	89	110	the	the	DET
ejpam-1048	89	111	ricci	ricci	PROPN
ejpam-1048	89	112	tensor	tensor	NOUN
ejpam-1048	89	113	of	of	ADP
ejpam-1048	89	114	this	this	DET
ejpam-1048	89	115	manifold	manifold	NOUN
ejpam-1048	89	116	is	be	AUX
ejpam-1048	89	117	symmetric	symmetric	ADJ
ejpam-1048	89	118	.	.	PUNCT
ejpam-1048	90	1	3	3	X
ejpam-1048	90	2	.	.	X
ejpam-1048	90	3	conformally	conformally	ADV
ejpam-1048	90	4	flat	flat	ADJ
ejpam-1048	90	5	manifolds	manifold	NOUN
ejpam-1048	90	6	with	with	ADP
ejpam-1048	90	7	semi	semi	ADJ
ejpam-1048	90	8	symmetric	symmetric	ADJ
ejpam-1048	90	9	metric	metric	ADJ
ejpam-1048	90	10	connection	connection	NOUN
ejpam-1048	90	11	satisfying	satisfy	VERB
ejpam-1048	90	12	some	some	DET
ejpam-1048	90	13	special	special	ADJ
ejpam-1048	90	14	condition	condition	NOUN
ejpam-1048	90	15	in	in	ADP
ejpam-1048	90	16	this	this	DET
ejpam-1048	90	17	section	section	NOUN
ejpam-1048	90	18	,	,	PUNCT
ejpam-1048	90	19	we	we	PRON
ejpam-1048	90	20	shall	shall	AUX
ejpam-1048	90	21	investigate	investigate	VERB
ejpam-1048	90	22	a	a	DET
ejpam-1048	90	23	riemannian	riemannian	ADJ
ejpam-1048	90	24	manifold	manifold	NOUN
ejpam-1048	90	25	m	m	AUX
ejpam-1048	90	26	admitting	admit	VERB
ejpam-1048	90	27	a	a	DET
ejpam-1048	90	28	semi	semi	ADJ
ejpam-1048	90	29	symmetric	symmetric	ADJ
ejpam-1048	90	30	metric	metric	ADJ
ejpam-1048	90	31	connection	connection	NOUN
ejpam-1048	90	32	whose	whose	DET
ejpam-1048	90	33	the	the	DET
ejpam-1048	90	34	torsion	torsion	NOUN
ejpam-1048	90	35	tensor	tensor	NOUN
ejpam-1048	90	36	satisfies	satisfy	VERB
ejpam-1048	90	37	a	a	DET
ejpam-1048	90	38	special	special	ADJ
ejpam-1048	90	39	condition	condition	NOUN
ejpam-1048	90	40	in	in	ADP
ejpam-1048	90	41	the	the	DET
ejpam-1048	90	42	case	case	NOUN
ejpam-1048	90	43	of	of	ADP
ejpam-1048	90	44	conformally	conformally	ADV
ejpam-1048	90	45	flat	flat	ADJ
ejpam-1048	90	46	.	.	PUNCT
ejpam-1048	91	1	firstly	firstly	ADV
ejpam-1048	91	2	,	,	PUNCT
ejpam-1048	91	3	we	we	PRON
ejpam-1048	91	4	consider	consider	VERB
ejpam-1048	91	5	the	the	DET
ejpam-1048	91	6	condition	condition	NOUN
ejpam-1048	91	7	(	(	PUNCT
ejpam-1048	91	8	11	11	NUM
ejpam-1048	91	9	)	)	PUNCT
ejpam-1048	91	10	.	.	PUNCT
ejpam-1048	92	1	then	then	ADV
ejpam-1048	92	2	,	,	PUNCT
ejpam-1048	92	3	∇	∇	PROPN
ejpam-1048	92	4	j	j	PROPN
ejpam-1048	92	5	t	t	PROPN
ejpam-1048	92	6	l	l	NOUN
ejpam-1048	92	7	ik	ik	PROPN
ejpam-1048	92	8	=	=	PUNCT
ejpam-1048	92	9	a	a	DET
ejpam-1048	92	10	j	j	PROPN
ejpam-1048	92	11	t	t	PROPN
ejpam-1048	92	12	l	l	NOUN
ejpam-1048	92	13	ik	ik	PROPN
ejpam-1048	92	14	+	+	PROPN
ejpam-1048	92	15	b	b	PROPN
ejpam-1048	92	16	j	j	PROPN
ejpam-1048	92	17	b	b	PROPN
ejpam-1048	92	18	l	l	NOUN
ejpam-1048	92	19	gik	gik	X
ejpam-1048	92	20	+	+	PROPN
ejpam-1048	92	21	δ	δ	PROPN
ejpam-1048	92	22	l	l	PROPN
ejpam-1048	92	23	j	j	PROPN
ejpam-1048	92	24	biak	biak	PROPN
ejpam-1048	92	25	(	(	PUNCT
ejpam-1048	92	26	27	27	NUM
ejpam-1048	92	27	)	)	PUNCT
ejpam-1048	92	28	h.	h.	PROPN
ejpam-1048	92	29	yılmaz	yılmaz	PROPN
ejpam-1048	92	30	,	,	PUNCT
ejpam-1048	92	31	f.	f.	PROPN
ejpam-1048	92	32	zengin	zengin	PROPN
ejpam-1048	92	33	,	,	PUNCT
ejpam-1048	92	34	s.	s.	PROPN
ejpam-1048	92	35	uysal	uysal	PROPN
ejpam-1048	92	36	/	/	SYM
ejpam-1048	92	37	eur	eur	PROPN
ejpam-1048	92	38	.	.	PUNCT
ejpam-1048	93	1	j.	j.	PROPN
ejpam-1048	93	2	pure	pure	PROPN
ejpam-1048	93	3	appl	appl	PROPN
ejpam-1048	93	4	.	.	PROPN
ejpam-1048	93	5	math	math	PROPN
ejpam-1048	93	6	,	,	PUNCT
ejpam-1048	93	7	4	4	NUM
ejpam-1048	93	8	(	(	PUNCT
ejpam-1048	93	9	2011	2011	NUM
ejpam-1048	93	10	)	)	PUNCT
ejpam-1048	93	11	,	,	PUNCT
ejpam-1048	93	12	152	152	NUM
ejpam-1048	93	13	-	-	SYM
ejpam-1048	93	14	161	161	NUM
ejpam-1048	93	15	158	158	NUM
ejpam-1048	93	16	where	where	SCONJ
ejpam-1048	93	17	ak	ak	PROPN
ejpam-1048	93	18	and	and	CCONJ
ejpam-1048	93	19	bk	bk	PROPN
ejpam-1048	93	20	be	be	AUX
ejpam-1048	93	21	orthogonal	orthogonal	ADJ
ejpam-1048	93	22	to	to	ADP
ejpam-1048	93	23	each	each	DET
ejpam-1048	93	24	other	other	ADJ
ejpam-1048	93	25	.	.	PUNCT
ejpam-1048	94	1	the	the	DET
ejpam-1048	94	2	conformal	conformal	ADJ
ejpam-1048	94	3	curvature	curvature	NOUN
ejpam-1048	94	4	tensor	tensor	NOUN
ejpam-1048	94	5	is	be	AUX
ejpam-1048	94	6	given	give	VERB
ejpam-1048	94	7	by	by	ADP
ejpam-1048	94	8	cik	cik	PROPN
ejpam-1048	94	9	jm	jm	PROPN
ejpam-1048	94	10	=	=	PROPN
ejpam-1048	94	11	rik	rik	PROPN
ejpam-1048	94	12	jm−	jm−	PROPN
ejpam-1048	94	13	1	1	NUM
ejpam-1048	94	14	n−	n−	NOUN
ejpam-1048	94	15	2	2	NUM
ejpam-1048	94	16	�	�	PROPN
ejpam-1048	94	17	rimgk	rimgk	VERB
ejpam-1048	94	18	j	j	PROPN
ejpam-1048	94	19	−	−	PROPN
ejpam-1048	94	20	rkmgi	rkmgi	PROPN
ejpam-1048	94	21	j	j	PROPN
ejpam-1048	94	22	+	+	CCONJ
ejpam-1048	94	23	rk	rk	PROPN
ejpam-1048	94	24	j	j	PROPN
ejpam-1048	94	25	gim−	gim−	PROPN
ejpam-1048	94	26	ri	ri	PROPN
ejpam-1048	94	27	j	j	PROPN
ejpam-1048	94	28	gkm	gkm	PROPN
ejpam-1048	94	29	�	�	PROPN
ejpam-1048	94	30	(	(	PUNCT
ejpam-1048	94	31	28	28	NUM
ejpam-1048	94	32	)	)	PUNCT
ejpam-1048	95	1	+	+	CCONJ
ejpam-1048	95	2	r	r	NOUN
ejpam-1048	95	3	(	(	PUNCT
ejpam-1048	95	4	n−	n−	NOUN
ejpam-1048	95	5	1)(n−	1)(n−	PROPN
ejpam-1048	95	6	2	2	NUM
ejpam-1048	95	7	)	)	PUNCT
ejpam-1048	95	8	�	�	PROPN
ejpam-1048	95	9	gim	gim	PROPN
ejpam-1048	95	10	gk	gk	PROPN
ejpam-1048	95	11	j	j	PROPN
ejpam-1048	95	12	−	−	PROPN
ejpam-1048	95	13	gkmgi	gkmgi	PROPN
ejpam-1048	95	14	j	j	PROPN
ejpam-1048	95	15	�	�	PROPN
ejpam-1048	95	16	now	now	ADV
ejpam-1048	95	17	,	,	PUNCT
ejpam-1048	95	18	we	we	PRON
ejpam-1048	95	19	remember	remember	VERB
ejpam-1048	95	20	that	that	SCONJ
ejpam-1048	95	21	it	it	PRON
ejpam-1048	95	22	is	be	AUX
ejpam-1048	95	23	well	well	ADV
ejpam-1048	95	24	known	know	VERB
ejpam-1048	95	25	the	the	DET
ejpam-1048	95	26	following	follow	VERB
ejpam-1048	95	27	theorem	theorem	NOUN
ejpam-1048	95	28	:	:	PUNCT
ejpam-1048	95	29	theorem	theorem	NOUN
ejpam-1048	95	30	6	6	NUM
ejpam-1048	95	31	.	.	PUNCT
ejpam-1048	96	1	[	[	X
ejpam-1048	96	2	11	11	NUM
ejpam-1048	96	3	]	]	PUNCT
ejpam-1048	96	4	in	in	ADP
ejpam-1048	96	5	order	order	NOUN
ejpam-1048	96	6	that	that	SCONJ
ejpam-1048	96	7	a	a	DET
ejpam-1048	96	8	riemannian	riemannian	ADJ
ejpam-1048	96	9	manifold	manifold	NOUN
ejpam-1048	96	10	admits	admit	VERB
ejpam-1048	96	11	a	a	DET
ejpam-1048	96	12	semi	semi	ADJ
ejpam-1048	96	13	symmetric	symmetric	ADJ
ejpam-1048	96	14	metric	metric	ADJ
ejpam-1048	96	15	connection	connection	NOUN
ejpam-1048	96	16	curvature	curvature	NOUN
ejpam-1048	96	17	tensor	tensor	NOUN
ejpam-1048	96	18	vanishes	vanish	VERB
ejpam-1048	96	19	,	,	PUNCT
ejpam-1048	96	20	it	it	PRON
ejpam-1048	96	21	is	be	AUX
ejpam-1048	96	22	necessary	necessary	ADJ
ejpam-1048	96	23	and	and	CCONJ
ejpam-1048	96	24	sufficient	sufficient	ADJ
ejpam-1048	96	25	condition	condition	NOUN
ejpam-1048	96	26	that	that	SCONJ
ejpam-1048	96	27	the	the	DET
ejpam-1048	96	28	riemannian	riemannian	ADJ
ejpam-1048	96	29	manifold	manifold	NOUN
ejpam-1048	96	30	be	be	VERB
ejpam-1048	96	31	conformally	conformally	ADV
ejpam-1048	96	32	flat	flat	ADJ
ejpam-1048	96	33	.	.	PUNCT
ejpam-1048	97	1	suppose	suppose	VERB
ejpam-1048	97	2	that	that	SCONJ
ejpam-1048	97	3	this	this	DET
ejpam-1048	97	4	manifold	manifold	NOUN
ejpam-1048	97	5	is	be	AUX
ejpam-1048	97	6	conformally	conformally	ADV
ejpam-1048	97	7	flat	flat	ADJ
ejpam-1048	97	8	.	.	PUNCT
ejpam-1048	98	1	hence	hence	ADV
ejpam-1048	98	2	,	,	PUNCT
ejpam-1048	98	3	we	we	PRON
ejpam-1048	98	4	can	can	AUX
ejpam-1048	98	5	write	write	VERB
ejpam-1048	98	6	rik	rik	PROPN
ejpam-1048	98	7	jm	jm	PROPN
ejpam-1048	99	1	=	=	SYM
ejpam-1048	99	2	0	0	PROPN
ejpam-1048	100	1	(	(	PUNCT
ejpam-1048	100	2	29	29	NUM
ejpam-1048	100	3	)	)	PUNCT
ejpam-1048	100	4	therefore	therefore	ADV
ejpam-1048	100	5	,	,	PUNCT
ejpam-1048	100	6	due	due	ADP
ejpam-1048	100	7	to	to	ADP
ejpam-1048	100	8	(	(	PUNCT
ejpam-1048	100	9	7	7	NUM
ejpam-1048	100	10	)	)	PUNCT
ejpam-1048	100	11	and	and	CCONJ
ejpam-1048	100	12	(	(	PUNCT
ejpam-1048	100	13	29	29	NUM
ejpam-1048	100	14	)	)	PUNCT
ejpam-1048	100	15	,	,	PUNCT
ejpam-1048	100	16	we	we	PRON
ejpam-1048	100	17	obtain	obtain	VERB
ejpam-1048	100	18	rik	rik	PROPN
ejpam-1048	100	19	jm	jm	PROPN
ejpam-1048	100	20	=	=	PROPN
ejpam-1048	100	21	gimπk	gimπk	PROPN
ejpam-1048	100	22	j	j	PROPN
ejpam-1048	100	23	−	−	PROPN
ejpam-1048	100	24	gkmπi	gkmπi	PROPN
ejpam-1048	100	25	j	j	PROPN
ejpam-1048	100	26	+	+	CCONJ
ejpam-1048	100	27	gk	gk	PROPN
ejpam-1048	100	28	jπim−	jπim−	NOUN
ejpam-1048	100	29	gi	gi	ADP
ejpam-1048	100	30	jπkm	jπkm	PROPN
ejpam-1048	100	31	(	(	PUNCT
ejpam-1048	100	32	30	30	NUM
ejpam-1048	100	33	)	)	PUNCT
ejpam-1048	100	34	multiplying	multiplying	NOUN
ejpam-1048	100	35	(	(	PUNCT
ejpam-1048	100	36	29	29	NUM
ejpam-1048	100	37	)	)	PUNCT
ejpam-1048	100	38	by	by	ADP
ejpam-1048	100	39	g	g	PROPN
ejpam-1048	100	40	i	i	PRON
ejpam-1048	100	41	m	m	PROPN
ejpam-1048	100	42	,	,	PUNCT
ejpam-1048	100	43	we	we	PRON
ejpam-1048	100	44	get	get	VERB
ejpam-1048	100	45	the	the	DET
ejpam-1048	100	46	corresponding	correspond	VERB
ejpam-1048	100	47	identity	identity	NOUN
ejpam-1048	100	48	rk	rk	NOUN
ejpam-1048	100	49	j	j	PROPN
ejpam-1048	100	50	=	=	SYM
ejpam-1048	100	51	0	0	PROPN
ejpam-1048	100	52	(	(	PUNCT
ejpam-1048	100	53	31	31	NUM
ejpam-1048	100	54	)	)	PUNCT
ejpam-1048	100	55	transvecting	transvecte	VERB
ejpam-1048	100	56	(	(	PUNCT
ejpam-1048	100	57	19	19	NUM
ejpam-1048	100	58	)	)	PUNCT
ejpam-1048	100	59	with	with	ADP
ejpam-1048	100	60	g	g	PROPN
ejpam-1048	100	61	i	i	PRON
ejpam-1048	100	62	m	m	VERB
ejpam-1048	100	63	and	and	CCONJ
ejpam-1048	100	64	using	use	VERB
ejpam-1048	100	65	(	(	PUNCT
ejpam-1048	100	66	31	31	NUM
ejpam-1048	100	67	)	)	PUNCT
ejpam-1048	100	68	,	,	PUNCT
ejpam-1048	100	69	we	we	PRON
ejpam-1048	100	70	have	have	VERB
ejpam-1048	100	71	rk	rk	PROPN
ejpam-1048	100	72	j	j	PROPN
ejpam-1048	100	73	=	=	SYM
ejpam-1048	100	74	�	�	PROPN
ejpam-1048	100	75	(	(	PUNCT
ejpam-1048	100	76	1−	1−	NUM
ejpam-1048	100	77	n)w	n)w	X
ejpam-1048	101	1	+	+	CCONJ
ejpam-1048	101	2	�	�	PROPN
ejpam-1048	101	3	amwm+	amwm+	ADP
ejpam-1048	101	4	1	1	NUM
ejpam-1048	101	5	n−	n−	NOUN
ejpam-1048	101	6	1	1	NUM
ejpam-1048	101	7	b+	b+	ADP
ejpam-1048	101	8	1	1	NUM
ejpam-1048	101	9	n−	n−	NOUN
ejpam-1048	101	10	1	1	NUM
ejpam-1048	101	11	bmam	bmam	PROPN
ejpam-1048	101	12	�	�	PROPN
ejpam-1048	101	13	�	�	PROPN
ejpam-1048	101	14	gk	gk	PROPN
ejpam-1048	101	15	j	j	PROPN
ejpam-1048	101	16	(	(	PUNCT
ejpam-1048	101	17	32	32	NUM
ejpam-1048	101	18	)	)	PUNCT
ejpam-1048	101	19	+	+	CCONJ
ejpam-1048	101	20	(	(	PUNCT
ejpam-1048	101	21	n−	n−	NOUN
ejpam-1048	101	22	2	2	NUM
ejpam-1048	101	23	)	)	PUNCT
ejpam-1048	101	24	�	�	PROPN
ejpam-1048	101	25	akw	akw	PROPN
ejpam-1048	101	26	j	j	PROPN
ejpam-1048	101	27	+	+	CCONJ
ejpam-1048	101	28	1	1	NUM
ejpam-1048	101	29	n−	n−	NOUN
ejpam-1048	101	30	1	1	NUM
ejpam-1048	101	31	bk	bk	NOUN
ejpam-1048	101	32	b	b	PROPN
ejpam-1048	101	33	j	j	PROPN
ejpam-1048	101	34	+	+	CCONJ
ejpam-1048	101	35	1	1	NUM
ejpam-1048	101	36	n−	n−	PROPN
ejpam-1048	101	37	1	1	NUM
ejpam-1048	101	38	bka	bka	PROPN
ejpam-1048	101	39	j	j	PROPN
ejpam-1048	101	40	�	�	PROPN
ejpam-1048	101	41	where	where	SCONJ
ejpam-1048	101	42	am	be	AUX
ejpam-1048	101	43	=	=	PRON
ejpam-1048	101	44	ai	ai	VERB
ejpam-1048	101	45	g	g	PROPN
ejpam-1048	101	46	i	i	NOUN
ejpam-1048	101	47	m	m	PROPN
ejpam-1048	101	48	,	,	PUNCT
ejpam-1048	101	49	b	b	X
ejpam-1048	101	50	=	=	PUNCT
ejpam-1048	101	51	bmbm	bmbm	NOUN
ejpam-1048	101	52	6=	6=	ADP
ejpam-1048	101	53	0	0	NUM
ejpam-1048	101	54	.	.	PUNCT
ejpam-1048	102	1	since	since	SCONJ
ejpam-1048	102	2	ak	ak	PROPN
ejpam-1048	102	3	and	and	CCONJ
ejpam-1048	102	4	bk	bk	PROPN
ejpam-1048	102	5	are	be	AUX
ejpam-1048	102	6	the	the	DET
ejpam-1048	102	7	orthogonal	orthogonal	ADJ
ejpam-1048	102	8	vector	vector	NOUN
ejpam-1048	102	9	fields	field	NOUN
ejpam-1048	102	10	,	,	PUNCT
ejpam-1048	102	11	it	it	PRON
ejpam-1048	102	12	can	can	AUX
ejpam-1048	102	13	be	be	AUX
ejpam-1048	102	14	written	write	VERB
ejpam-1048	102	15	rk	rk	NOUN
ejpam-1048	102	16	j	j	PROPN
ejpam-1048	102	17	=	=	SYM
ejpam-1048	102	18	�	�	PROPN
ejpam-1048	102	19	(	(	PUNCT
ejpam-1048	102	20	1−	1−	NUM
ejpam-1048	102	21	n)w	n)w	X
ejpam-1048	103	1	+	+	ADP
ejpam-1048	103	2	φ	φ	NOUN
ejpam-1048	103	3	+	+	SYM
ejpam-1048	103	4	1	1	NUM
ejpam-1048	103	5	n−	n−	NOUN
ejpam-1048	103	6	1	1	NUM
ejpam-1048	103	7	b	b	X
ejpam-1048	103	8	�	�	PROPN
ejpam-1048	103	9	gk	gk	PROPN
ejpam-1048	103	10	j	j	PROPN
ejpam-1048	103	11	+	+	CCONJ
ejpam-1048	103	12	(	(	PUNCT
ejpam-1048	103	13	n−	n−	NOUN
ejpam-1048	103	14	2	2	NUM
ejpam-1048	103	15	)	)	PUNCT
ejpam-1048	103	16	�	�	PROPN
ejpam-1048	103	17	akw	akw	PROPN
ejpam-1048	103	18	j	j	PROPN
ejpam-1048	104	1	+	+	CCONJ
ejpam-1048	104	2	1	1	NUM
ejpam-1048	104	3	n−	n−	NOUN
ejpam-1048	104	4	1	1	NUM
ejpam-1048	104	5	bk	bk	NOUN
ejpam-1048	104	6	b	b	PROPN
ejpam-1048	104	7	j	j	PROPN
ejpam-1048	104	8	+	+	CCONJ
ejpam-1048	104	9	1	1	NUM
ejpam-1048	104	10	n−	n−	PROPN
ejpam-1048	104	11	1	1	NUM
ejpam-1048	104	12	bka	bka	PROPN
ejpam-1048	104	13	j	j	PROPN
ejpam-1048	104	14	�	�	PROPN
ejpam-1048	104	15	(	(	PUNCT
ejpam-1048	104	16	33	33	NUM
ejpam-1048	104	17	)	)	PUNCT
ejpam-1048	104	18	where	where	SCONJ
ejpam-1048	104	19	amwm	amwm	ADJ
ejpam-1048	104	20	=	=	SYM
ejpam-1048	104	21	φ	φ	PROPN
ejpam-1048	104	22	is	be	AUX
ejpam-1048	104	23	a	a	DET
ejpam-1048	104	24	non	non	ADJ
ejpam-1048	104	25	-	-	ADJ
ejpam-1048	104	26	zero	zero	NUM
ejpam-1048	104	27	scalar	scalar	ADJ
ejpam-1048	104	28	function	function	NOUN
ejpam-1048	104	29	.	.	PUNCT
ejpam-1048	105	1	subtracting	subtract	VERB
ejpam-1048	105	2	(	(	PUNCT
ejpam-1048	105	3	33	33	NUM
ejpam-1048	105	4	)	)	PUNCT
ejpam-1048	105	5	from	from	ADP
ejpam-1048	105	6	the	the	DET
ejpam-1048	105	7	corresponding	corresponding	ADJ
ejpam-1048	105	8	equation	equation	NOUN
ejpam-1048	105	9	found	find	VERB
ejpam-1048	105	10	by	by	ADP
ejpam-1048	105	11	interchanging	interchange	VERB
ejpam-1048	105	12	k	k	PROPN
ejpam-1048	105	13	and	and	CCONJ
ejpam-1048	105	14	j	j	PROPN
ejpam-1048	105	15	in	in	ADP
ejpam-1048	105	16	(	(	PUNCT
ejpam-1048	105	17	33	33	NUM
ejpam-1048	105	18	)	)	PUNCT
ejpam-1048	105	19	,	,	PUNCT
ejpam-1048	105	20	we	we	PRON
ejpam-1048	105	21	get	get	VERB
ejpam-1048	105	22	(	(	PUNCT
ejpam-1048	105	23	24	24	NUM
ejpam-1048	105	24	)	)	PUNCT
ejpam-1048	105	25	.	.	PUNCT
ejpam-1048	106	1	transvecting	transvecte	VERB
ejpam-1048	106	2	(	(	PUNCT
ejpam-1048	106	3	24	24	NUM
ejpam-1048	106	4	)	)	PUNCT
ejpam-1048	106	5	with	with	ADP
ejpam-1048	106	6	a	a	DET
ejpam-1048	106	7	j	j	NOUN
ejpam-1048	106	8	bk	bk	INTJ
ejpam-1048	106	9	,	,	PUNCT
ejpam-1048	106	10	we	we	PRON
ejpam-1048	106	11	find	find	VERB
ejpam-1048	106	12	bkwk	bkwk	NOUN
ejpam-1048	106	13	=	=	SYM
ejpam-1048	106	14	ab	ab	PROPN
ejpam-1048	106	15	n−	n−	PROPN
ejpam-1048	106	16	1	1	NUM
ejpam-1048	106	17	(	(	PUNCT
ejpam-1048	106	18	34	34	NUM
ejpam-1048	106	19	)	)	PUNCT
ejpam-1048	106	20	where	where	SCONJ
ejpam-1048	106	21	amam	amam	NOUN
ejpam-1048	106	22	=	=	PUNCT
ejpam-1048	106	23	a	a	PRON
ejpam-1048	106	24	6=	6=	NUM
ejpam-1048	106	25	0	0	NUM
ejpam-1048	106	26	.	.	PUNCT
ejpam-1048	107	1	from	from	ADP
ejpam-1048	107	2	(	(	PUNCT
ejpam-1048	107	3	34	34	NUM
ejpam-1048	107	4	)	)	PUNCT
ejpam-1048	107	5	,	,	PUNCT
ejpam-1048	107	6	it	it	PRON
ejpam-1048	107	7	is	be	AUX
ejpam-1048	107	8	seen	see	VERB
ejpam-1048	107	9	that	that	SCONJ
ejpam-1048	107	10	bk	bk	PRON
ejpam-1048	107	11	can	can	AUX
ejpam-1048	107	12	not	not	PART
ejpam-1048	107	13	be	be	AUX
ejpam-1048	107	14	orthogonal	orthogonal	ADJ
ejpam-1048	107	15	to	to	ADP
ejpam-1048	107	16	wk	wk	PROPN
ejpam-1048	107	17	.	.	PUNCT
ejpam-1048	108	1	again	again	ADV
ejpam-1048	108	2	,	,	PUNCT
ejpam-1048	108	3	multiplying	multiply	VERB
ejpam-1048	108	4	(	(	PUNCT
ejpam-1048	108	5	24	24	NUM
ejpam-1048	108	6	)	)	PUNCT
ejpam-1048	108	7	by	by	ADP
ejpam-1048	108	8	ak	ak	PROPN
ejpam-1048	108	9	,	,	PUNCT
ejpam-1048	108	10	we	we	PRON
ejpam-1048	108	11	get	get	VERB
ejpam-1048	108	12	w	w	PROPN
ejpam-1048	108	13	j	j	PROPN
ejpam-1048	108	14	=	=	SYM
ejpam-1048	108	15	θa	θa	NUM
ejpam-1048	108	16	j	j	NOUN
ejpam-1048	109	1	+	+	CCONJ
ejpam-1048	109	2	1	1	NUM
ejpam-1048	109	3	n−	n−	NOUN
ejpam-1048	109	4	1	1	NUM
ejpam-1048	109	5	b	b	X
ejpam-1048	109	6	j	j	X
ejpam-1048	109	7	(	(	PUNCT
ejpam-1048	109	8	35	35	NUM
ejpam-1048	109	9	)	)	PUNCT
ejpam-1048	109	10	h.	h.	PROPN
ejpam-1048	109	11	yılmaz	yılmaz	PROPN
ejpam-1048	109	12	,	,	PUNCT
ejpam-1048	109	13	f.	f.	PROPN
ejpam-1048	109	14	zengin	zengin	PROPN
ejpam-1048	109	15	,	,	PUNCT
ejpam-1048	109	16	s.	s.	PROPN
ejpam-1048	109	17	uysal	uysal	PROPN
ejpam-1048	109	18	/	/	SYM
ejpam-1048	109	19	eur	eur	PROPN
ejpam-1048	109	20	.	.	PUNCT
ejpam-1048	110	1	j.	j.	PROPN
ejpam-1048	110	2	pure	pure	PROPN
ejpam-1048	110	3	appl	appl	PROPN
ejpam-1048	110	4	.	.	PROPN
ejpam-1048	110	5	math	math	PROPN
ejpam-1048	110	6	,	,	PUNCT
ejpam-1048	110	7	4	4	NUM
ejpam-1048	110	8	(	(	PUNCT
ejpam-1048	110	9	2011	2011	NUM
ejpam-1048	110	10	)	)	PUNCT
ejpam-1048	110	11	,	,	PUNCT
ejpam-1048	110	12	152	152	NUM
ejpam-1048	110	13	-	-	SYM
ejpam-1048	110	14	161	161	NUM
ejpam-1048	110	15	159	159	NUM
ejpam-1048	110	16	where	where	SCONJ
ejpam-1048	110	17	θ	θ	PROPN
ejpam-1048	110	18	=	=	SYM
ejpam-1048	110	19	φ	φ	PROPN
ejpam-1048	110	20	a	a	PRON
ejpam-1048	110	21	6=	6=	NUM
ejpam-1048	110	22	0	0	NUM
ejpam-1048	110	23	.	.	PUNCT
ejpam-1048	111	1	by	by	ADP
ejpam-1048	111	2	using	use	VERB
ejpam-1048	111	3	(	(	PUNCT
ejpam-1048	111	4	35	35	NUM
ejpam-1048	111	5	)	)	PUNCT
ejpam-1048	111	6	,	,	PUNCT
ejpam-1048	111	7	we	we	PRON
ejpam-1048	111	8	find	find	VERB
ejpam-1048	111	9	that	that	SCONJ
ejpam-1048	111	10	a	a	DET
ejpam-1048	111	11	j	j	PROPN
ejpam-1048	111	12	is	be	AUX
ejpam-1048	111	13	not	not	PART
ejpam-1048	111	14	orthogonal	orthogonal	ADJ
ejpam-1048	111	15	to	to	ADP
ejpam-1048	111	16	w	w	PROPN
ejpam-1048	111	17	j	j	PROPN
ejpam-1048	111	18	.	.	PUNCT
ejpam-1048	112	1	substituting	substitute	VERB
ejpam-1048	112	2	(	(	PUNCT
ejpam-1048	112	3	29	29	NUM
ejpam-1048	112	4	)	)	PUNCT
ejpam-1048	112	5	and	and	CCONJ
ejpam-1048	112	6	(	(	PUNCT
ejpam-1048	112	7	35	35	NUM
ejpam-1048	112	8	)	)	PUNCT
ejpam-1048	112	9	in	in	ADP
ejpam-1048	112	10	(	(	PUNCT
ejpam-1048	112	11	19	19	NUM
ejpam-1048	112	12	)	)	PUNCT
ejpam-1048	112	13	,	,	PUNCT
ejpam-1048	112	14	we	we	PRON
ejpam-1048	112	15	obtain	obtain	VERB
ejpam-1048	112	16	rik	rik	PROPN
ejpam-1048	112	17	jm	jm	PROPN
ejpam-1048	112	18	=	=	PROPN
ejpam-1048	112	19	w	w	PROPN
ejpam-1048	112	20	�	�	PROPN
ejpam-1048	112	21	gkmgi	gkmgi	NOUN
ejpam-1048	112	22	j	j	PROPN
ejpam-1048	113	1	−	−	PROPN
ejpam-1048	113	2	gimgk	gimgk	ADP
ejpam-1048	113	3	j	j	PROPN
ejpam-1048	113	4	�	�	PROPN
ejpam-1048	113	5	(	(	PUNCT
ejpam-1048	113	6	36	36	NUM
ejpam-1048	113	7	)	)	PUNCT
ejpam-1048	114	1	+	+	NUM
ejpam-1048	114	2	θ	θ	PROPN
ejpam-1048	114	3	�	�	PROPN
ejpam-1048	114	4	gimaka	gimaka	PROPN
ejpam-1048	114	5	j	j	PROPN
ejpam-1048	115	1	−	−	PROPN
ejpam-1048	115	2	gkmaia	gkmaia	PROPN
ejpam-1048	115	3	j	j	PROPN
ejpam-1048	115	4	+	+	CCONJ
ejpam-1048	115	5	gk	gk	PROPN
ejpam-1048	115	6	jaiam−	jaiam−	PROPN
ejpam-1048	115	7	gi	gi	NOUN
ejpam-1048	115	8	jakam	jakam	PROPN
ejpam-1048	115	9	�	�	PROPN
ejpam-1048	116	1	+	+	CCONJ
ejpam-1048	116	2	1	1	NUM
ejpam-1048	116	3	n−	n−	NOUN
ejpam-1048	116	4	1	1	NUM
ejpam-1048	116	5	�	�	PROPN
ejpam-1048	116	6	gim	gim	VERB
ejpam-1048	116	7	bk	bk	PROPN
ejpam-1048	116	8	b	b	PROPN
ejpam-1048	116	9	j	j	PROPN
ejpam-1048	116	10	−	−	PROPN
ejpam-1048	116	11	gkmbi	gkmbi	PROPN
ejpam-1048	116	12	b	b	PROPN
ejpam-1048	117	1	j	j	PROPN
ejpam-1048	117	2	+	+	CCONJ
ejpam-1048	117	3	gk	gk	PROPN
ejpam-1048	117	4	j	j	PROPN
ejpam-1048	117	5	bi	bi	PROPN
ejpam-1048	117	6	bm−	bm−	PROPN
ejpam-1048	117	7	gi	gi	PROPN
ejpam-1048	117	8	j	j	PROPN
ejpam-1048	117	9	bk	bk	PROPN
ejpam-1048	117	10	bm	bm	PROPN
ejpam-1048	117	11	�	�	PROPN
ejpam-1048	117	12	+	+	CCONJ
ejpam-1048	117	13	1	1	NUM
ejpam-1048	117	14	n−	n−	NOUN
ejpam-1048	117	15	1	1	NUM
ejpam-1048	117	16	�	�	PROPN
ejpam-1048	117	17	gim	gim	PROPN
ejpam-1048	117	18	�	�	PROPN
ejpam-1048	117	19	ak	ak	PROPN
ejpam-1048	117	20	b	b	PROPN
ejpam-1048	118	1	j	j	PROPN
ejpam-1048	118	2	+	+	CCONJ
ejpam-1048	118	3	bka	bka	PROPN
ejpam-1048	118	4	j	j	PROPN
ejpam-1048	118	5	�	�	PROPN
ejpam-1048	118	6	−	−	PROPN
ejpam-1048	118	7	gkm	gkm	PROPN
ejpam-1048	118	8	�	�	PROPN
ejpam-1048	118	9	ai	ai	PROPN
ejpam-1048	118	10	b	b	PROPN
ejpam-1048	118	11	j	j	PROPN
ejpam-1048	118	12	+	+	CCONJ
ejpam-1048	118	13	bia	bia	PROPN
ejpam-1048	118	14	j	j	PROPN
ejpam-1048	118	15	�	�	PROPN
ejpam-1048	118	16	+	+	PROPN
ejpam-1048	118	17	gk	gk	PROPN
ejpam-1048	118	18	j	j	PROPN
ejpam-1048	118	19	�	�	PROPN
ejpam-1048	118	20	ai	ai	PROPN
ejpam-1048	118	21	bm+	bm+	PROPN
ejpam-1048	118	22	biam	biam	PROPN
ejpam-1048	118	23	�	�	PROPN
ejpam-1048	118	24	−	−	PROPN
ejpam-1048	118	25	gi	gi	PROPN
ejpam-1048	118	26	j	j	PROPN
ejpam-1048	118	27	�	�	PROPN
ejpam-1048	118	28	ak	ak	PROPN
ejpam-1048	118	29	bm+	bm+	PROPN
ejpam-1048	118	30	bkam	bkam	PROPN
ejpam-1048	118	31	�	�	PROPN
ejpam-1048	118	32	�	�	PROPN
ejpam-1048	118	33	if	if	SCONJ
ejpam-1048	118	34	w	w	PROPN
ejpam-1048	118	35	=	=	VERB
ejpam-1048	118	36	θφ	θφ	NOUN
ejpam-1048	118	37	+	+	X
ejpam-1048	118	38	ab	ab	PROPN
ejpam-1048	118	39	(	(	PUNCT
ejpam-1048	118	40	n−1)2	n−1)2	PROPN
ejpam-1048	118	41	6=	6=	ADP
ejpam-1048	118	42	0	0	NUM
ejpam-1048	118	43	,	,	PUNCT
ejpam-1048	118	44	and	and	CCONJ
ejpam-1048	119	1	since	since	SCONJ
ejpam-1048	119	2	ak	ak	PROPN
ejpam-1048	119	3	and	and	CCONJ
ejpam-1048	119	4	bk	bk	PROPN
ejpam-1048	119	5	are	be	AUX
ejpam-1048	119	6	the	the	DET
ejpam-1048	119	7	orthogonal	orthogonal	ADJ
ejpam-1048	119	8	vector	vector	NOUN
ejpam-1048	119	9	fields	field	NOUN
ejpam-1048	119	10	,	,	PUNCT
ejpam-1048	119	11	the	the	DET
ejpam-1048	119	12	equation	equation	NOUN
ejpam-1048	119	13	(	(	PUNCT
ejpam-1048	119	14	36	36	NUM
ejpam-1048	119	15	)	)	PUNCT
ejpam-1048	119	16	is	be	AUX
ejpam-1048	119	17	equivalent	equivalent	ADJ
ejpam-1048	119	18	to	to	ADP
ejpam-1048	119	19	(	(	PUNCT
ejpam-1048	119	20	2	2	NUM
ejpam-1048	119	21	)	)	PUNCT
ejpam-1048	119	22	.	.	PUNCT
ejpam-1048	120	1	this	this	PRON
ejpam-1048	120	2	implies	imply	VERB
ejpam-1048	120	3	that	that	SCONJ
ejpam-1048	120	4	such	such	DET
ejpam-1048	120	5	a	a	DET
ejpam-1048	120	6	manifold	manifold	NOUN
ejpam-1048	120	7	is	be	AUX
ejpam-1048	120	8	of	of	ADP
ejpam-1048	120	9	a	a	DET
ejpam-1048	120	10	mixed	mixed	ADJ
ejpam-1048	120	11	generalized	generalize	VERB
ejpam-1048	120	12	quasi	quasi	ADJ
ejpam-1048	120	13	constant	constant	ADJ
ejpam-1048	120	14	curvature	curvature	NOUN
ejpam-1048	120	15	.	.	PUNCT
ejpam-1048	121	1	multiplying	multiplying	NOUN
ejpam-1048	121	2	(	(	PUNCT
ejpam-1048	121	3	36	36	NUM
ejpam-1048	121	4	)	)	PUNCT
ejpam-1048	121	5	by	by	ADP
ejpam-1048	121	6	g	g	PROPN
ejpam-1048	121	7	im	im	PROPN
ejpam-1048	121	8	,	,	PUNCT
ejpam-1048	121	9	we	we	PRON
ejpam-1048	121	10	obtain	obtain	VERB
ejpam-1048	121	11	rk	rk	PRON
ejpam-1048	121	12	j	j	PROPN
ejpam-1048	122	1	=	=	PROPN
ejpam-1048	123	1	µgk	µgk	PROPN
ejpam-1048	124	1	j	j	PROPN
ejpam-1048	125	1	+	+	CCONJ
ejpam-1048	125	2	(	(	PUNCT
ejpam-1048	125	3	n−	n−	PROPN
ejpam-1048	125	4	2)θaka	2)θaka	NUM
ejpam-1048	126	1	j	j	PROPN
ejpam-1048	126	2	+	+	CCONJ
ejpam-1048	126	3	�	�	PROPN
ejpam-1048	126	4	n−	n−	NOUN
ejpam-1048	126	5	2	2	NUM
ejpam-1048	126	6	n−	n−	NOUN
ejpam-1048	126	7	1	1	NUM
ejpam-1048	126	8	�	�	PROPN
ejpam-1048	126	9	�	�	PROPN
ejpam-1048	126	10	bk	bk	ADP
ejpam-1048	126	11	b	b	PROPN
ejpam-1048	126	12	j	j	PROPN
ejpam-1048	126	13	+	+	PROPN
ejpam-1048	126	14	ak	ak	PROPN
ejpam-1048	126	15	b	b	PROPN
ejpam-1048	126	16	j	j	PROPN
ejpam-1048	126	17	+	+	CCONJ
ejpam-1048	126	18	bka	bka	PROPN
ejpam-1048	126	19	j	j	PROPN
ejpam-1048	126	20	�	�	PROPN
ejpam-1048	126	21	(	(	PUNCT
ejpam-1048	126	22	37	37	NUM
ejpam-1048	126	23	)	)	PUNCT
ejpam-1048	126	24	where	where	SCONJ
ejpam-1048	126	25	µ	µ	X
ejpam-1048	126	26	=	=	SYM
ejpam-1048	126	27	(	(	PUNCT
ejpam-1048	126	28	1−	1−	NUM
ejpam-1048	126	29	n)w	n)w	X
ejpam-1048	126	30	+	+	CCONJ
ejpam-1048	126	31	θa+	θa+	PROPN
ejpam-1048	126	32	b	b	PROPN
ejpam-1048	126	33	n−	n−	PROPN
ejpam-1048	126	34	1	1	NUM
ejpam-1048	126	35	(	(	PUNCT
ejpam-1048	126	36	38	38	NUM
ejpam-1048	126	37	)	)	PUNCT
ejpam-1048	126	38	suppose	suppose	VERB
ejpam-1048	126	39	that	that	SCONJ
ejpam-1048	126	40	µ	µ	PROPN
ejpam-1048	126	41	6=	6=	NUM
ejpam-1048	126	42	0	0	NUM
ejpam-1048	126	43	.	.	PUNCT
ejpam-1048	127	1	conversely	conversely	ADV
ejpam-1048	127	2	,	,	PUNCT
ejpam-1048	127	3	suppose	suppose	VERB
ejpam-1048	127	4	that	that	SCONJ
ejpam-1048	127	5	this	this	DET
ejpam-1048	127	6	manifold	manifold	NOUN
ejpam-1048	127	7	is	be	AUX
ejpam-1048	127	8	of	of	ADP
ejpam-1048	127	9	a	a	DET
ejpam-1048	127	10	mixed	mixed	ADJ
ejpam-1048	127	11	generalized	generalize	VERB
ejpam-1048	127	12	quasi	quasi	ADJ
ejpam-1048	127	13	constant	constant	ADJ
ejpam-1048	127	14	curvature	curvature	NOUN
ejpam-1048	127	15	.	.	PUNCT
ejpam-1048	128	1	multiplying	multiplying	NOUN
ejpam-1048	128	2	(	(	PUNCT
ejpam-1048	128	3	2	2	NUM
ejpam-1048	128	4	)	)	PUNCT
ejpam-1048	128	5	by	by	ADP
ejpam-1048	128	6	g	g	PROPN
ejpam-1048	128	7	i	i	PRON
ejpam-1048	128	8	m	m	PROPN
ejpam-1048	128	9	,	,	PUNCT
ejpam-1048	128	10	we	we	PRON
ejpam-1048	128	11	obtain	obtain	VERB
ejpam-1048	128	12	rk	rk	PRON
ejpam-1048	128	13	j	j	PROPN
ejpam-1048	128	14	=	=	SYM
ejpam-1048	128	15	�	�	PROPN
ejpam-1048	128	16	p(n−	p(n−	PROPN
ejpam-1048	128	17	1	1	NUM
ejpam-1048	128	18	)	)	PUNCT
ejpam-1048	128	19	+	+	CCONJ
ejpam-1048	128	20	qa+	qa+	ADJ
ejpam-1048	128	21	bs	bs	PROPN
ejpam-1048	128	22	�	�	PROPN
ejpam-1048	128	23	gk	gk	PROPN
ejpam-1048	128	24	j	j	PROPN
ejpam-1048	128	25	+	+	CCONJ
ejpam-1048	128	26	q(n−	q(n−	PROPN
ejpam-1048	128	27	2)aka	2)aka	NUM
ejpam-1048	128	28	j	j	PROPN
ejpam-1048	128	29	(	(	PUNCT
ejpam-1048	128	30	39	39	NUM
ejpam-1048	128	31	)	)	PUNCT
ejpam-1048	129	1	+	+	CCONJ
ejpam-1048	129	2	s(n−	s(n−	X
ejpam-1048	129	3	2)bk	2)bk	PROPN
ejpam-1048	129	4	b	b	PROPN
ejpam-1048	130	1	j	j	PROPN
ejpam-1048	130	2	+	+	CCONJ
ejpam-1048	130	3	t(n−	t(n−	PROPN
ejpam-1048	130	4	2	2	NUM
ejpam-1048	130	5	)	)	PUNCT
ejpam-1048	130	6	�	�	PROPN
ejpam-1048	130	7	ak	ak	PROPN
ejpam-1048	130	8	b	b	PROPN
ejpam-1048	130	9	j	j	PROPN
ejpam-1048	130	10	+	+	PROPN
ejpam-1048	130	11	bka	bka	PROPN
ejpam-1048	130	12	j	j	PROPN
ejpam-1048	130	13	�	�	PROPN
ejpam-1048	130	14	transvecting	transvecting	PROPN
ejpam-1048	130	15	(	(	PUNCT
ejpam-1048	130	16	39	39	NUM
ejpam-1048	130	17	)	)	PUNCT
ejpam-1048	130	18	with	with	ADP
ejpam-1048	130	19	gk	gk	PROPN
ejpam-1048	130	20	j	j	PROPN
ejpam-1048	130	21	,	,	PUNCT
ejpam-1048	130	22	we	we	PRON
ejpam-1048	130	23	find	find	VERB
ejpam-1048	130	24	r=	r=	ADJ
ejpam-1048	130	25	(	(	PUNCT
ejpam-1048	130	26	n−	n−	NOUN
ejpam-1048	130	27	1	1	NUM
ejpam-1048	130	28	)	)	PUNCT
ejpam-1048	130	29	�	�	PROPN
ejpam-1048	130	30	np+	np+	PROPN
ejpam-1048	130	31	2qa+	2qa+	PROPN
ejpam-1048	130	32	2sb	2sb	PROPN
ejpam-1048	130	33	�	�	PROPN
ejpam-1048	130	34	(	(	PUNCT
ejpam-1048	130	35	40	40	NUM
ejpam-1048	130	36	)	)	PUNCT
ejpam-1048	130	37	let	let	VERB
ejpam-1048	130	38	us	we	PRON
ejpam-1048	130	39	substitute	substitute	VERB
ejpam-1048	130	40	(	(	PUNCT
ejpam-1048	130	41	2	2	NUM
ejpam-1048	130	42	)	)	PUNCT
ejpam-1048	130	43	,	,	PUNCT
ejpam-1048	130	44	(	(	PUNCT
ejpam-1048	130	45	39	39	NUM
ejpam-1048	130	46	)	)	PUNCT
ejpam-1048	130	47	and	and	CCONJ
ejpam-1048	130	48	(	(	PUNCT
ejpam-1048	130	49	40	40	NUM
ejpam-1048	130	50	)	)	PUNCT
ejpam-1048	130	51	in	in	ADP
ejpam-1048	130	52	(	(	PUNCT
ejpam-1048	130	53	28).then	28).then	ADV
ejpam-1048	130	54	,	,	PUNCT
ejpam-1048	130	55	if	if	SCONJ
ejpam-1048	130	56	w	w	NOUN
ejpam-1048	130	57	=	=	SYM
ejpam-1048	130	58	−p	−p	NOUN
ejpam-1048	130	59	,	,	PUNCT
ejpam-1048	130	60	θ	θ	PROPN
ejpam-1048	130	61	=	=	PUNCT
ejpam-1048	130	62	q	q	PROPN
ejpam-1048	130	63	and	and	CCONJ
ejpam-1048	130	64	t	t	NOUN
ejpam-1048	131	1	=	=	SYM
ejpam-1048	131	2	s	s	PART
ejpam-1048	131	3	=	=	SYM
ejpam-1048	131	4	1	1	NUM
ejpam-1048	131	5	n−1	n−1	PROPN
ejpam-1048	131	6	,	,	PUNCT
ejpam-1048	131	7	we	we	PRON
ejpam-1048	131	8	get	get	VERB
ejpam-1048	131	9	cik	cik	PROPN
ejpam-1048	131	10	jm	jm	PROPN
ejpam-1048	131	11	=	=	PROPN
ejpam-1048	131	12	0	0	PROPN
ejpam-1048	132	1	we	we	PRON
ejpam-1048	132	2	may	may	AUX
ejpam-1048	132	3	now	now	ADV
ejpam-1048	132	4	establish	establish	VERB
ejpam-1048	132	5	the	the	DET
ejpam-1048	132	6	following	follow	VERB
ejpam-1048	132	7	theorem	theorem	NOUN
ejpam-1048	132	8	:	:	PUNCT
ejpam-1048	132	9	theorem	theorem	NOUN
ejpam-1048	132	10	7	7	NUM
ejpam-1048	132	11	.	.	PUNCT
ejpam-1048	132	12	in	in	ADP
ejpam-1048	132	13	a	a	DET
ejpam-1048	132	14	riemannian	riemannian	NOUN
ejpam-1048	132	15	manifold	manifold	NOUN
ejpam-1048	132	16	with	with	ADP
ejpam-1048	132	17	a	a	DET
ejpam-1048	132	18	semi	semi	ADJ
ejpam-1048	132	19	symmetric	symmetric	ADJ
ejpam-1048	132	20	metric	metric	ADJ
ejpam-1048	132	21	connection	connection	NOUN
ejpam-1048	132	22	whose	whose	DET
ejpam-1048	132	23	the	the	DET
ejpam-1048	132	24	torsion	torsion	NOUN
ejpam-1048	132	25	tensor	tensor	NOUN
ejpam-1048	132	26	satisfies	satisfy	VERB
ejpam-1048	132	27	the	the	DET
ejpam-1048	132	28	condition	condition	NOUN
ejpam-1048	132	29	(	(	PUNCT
ejpam-1048	132	30	27	27	NUM
ejpam-1048	132	31	)	)	PUNCT
ejpam-1048	132	32	,	,	PUNCT
ejpam-1048	132	33	a	a	DET
ejpam-1048	132	34	necessary	necessary	ADJ
ejpam-1048	132	35	and	and	CCONJ
ejpam-1048	132	36	sufficient	sufficient	ADJ
ejpam-1048	132	37	condition	condition	NOUN
ejpam-1048	132	38	that	that	SCONJ
ejpam-1048	132	39	this	this	DET
ejpam-1048	132	40	manifold	manifold	NOUN
ejpam-1048	132	41	to	to	PART
ejpam-1048	132	42	be	be	AUX
ejpam-1048	132	43	of	of	ADP
ejpam-1048	132	44	a	a	DET
ejpam-1048	132	45	mixed	mixed	ADJ
ejpam-1048	132	46	generalized	generalize	VERB
ejpam-1048	132	47	quasi	quasi	ADJ
ejpam-1048	132	48	constant	constant	ADJ
ejpam-1048	132	49	curvature	curvature	NOUN
ejpam-1048	132	50	is	be	AUX
ejpam-1048	132	51	that	that	SCONJ
ejpam-1048	132	52	it	it	PRON
ejpam-1048	132	53	is	be	AUX
ejpam-1048	132	54	conformally	conformally	ADV
ejpam-1048	132	55	flat	flat	ADJ
ejpam-1048	132	56	.	.	PUNCT
ejpam-1048	133	1	when	when	SCONJ
ejpam-1048	133	2	we	we	PRON
ejpam-1048	133	3	compare	compare	VERB
ejpam-1048	133	4	(	(	PUNCT
ejpam-1048	133	5	37	37	NUM
ejpam-1048	133	6	)	)	PUNCT
ejpam-1048	133	7	with	with	ADP
ejpam-1048	133	8	(	(	PUNCT
ejpam-1048	133	9	1	1	NUM
ejpam-1048	133	10	)	)	PUNCT
ejpam-1048	133	11	,	,	PUNCT
ejpam-1048	133	12	if	if	SCONJ
ejpam-1048	133	13	p(n−	p(n−	PROPN
ejpam-1048	133	14	1	1	NUM
ejpam-1048	133	15	)	)	PUNCT
ejpam-1048	133	16	+	+	NUM
ejpam-1048	133	17	qa+	qa+	ADJ
ejpam-1048	133	18	bs	bs	PROPN
ejpam-1048	133	19	6=	6=	PROPN
ejpam-1048	133	20	0	0	NUM
ejpam-1048	133	21	,	,	PUNCT
ejpam-1048	133	22	we	we	PRON
ejpam-1048	133	23	can	can	AUX
ejpam-1048	133	24	say	say	VERB
ejpam-1048	133	25	that	that	SCONJ
ejpam-1048	133	26	this	this	DET
ejpam-1048	133	27	manifold	manifold	NOUN
ejpam-1048	133	28	is	be	AUX
ejpam-1048	133	29	a	a	DET
ejpam-1048	133	30	mixed	mixed	ADJ
ejpam-1048	133	31	generalized	generalize	VERB
ejpam-1048	133	32	quasi	quasi	NOUN
ejpam-1048	133	33	einstein	einstein	PROPN
ejpam-1048	133	34	manifold	manifold	PROPN
ejpam-1048	133	35	.	.	PUNCT
ejpam-1048	134	1	thus	thus	ADV
ejpam-1048	134	2	,	,	PUNCT
ejpam-1048	134	3	we	we	PRON
ejpam-1048	134	4	can	can	AUX
ejpam-1048	134	5	state	state	VERB
ejpam-1048	134	6	the	the	DET
ejpam-1048	134	7	following	following	NOUN
ejpam-1048	134	8	theorem	theorem	NOUN
ejpam-1048	134	9	:	:	PUNCT
ejpam-1048	134	10	references	reference	NOUN
ejpam-1048	134	11	160	160	NUM
ejpam-1048	134	12	theorem	theorem	NOUN
ejpam-1048	134	13	8	8	NUM
ejpam-1048	134	14	.	.	PUNCT
ejpam-1048	135	1	a	a	DET
ejpam-1048	135	2	conformal	conformal	ADJ
ejpam-1048	135	3	flat	flat	ADJ
ejpam-1048	135	4	riemannian	riemannian	NOUN
ejpam-1048	135	5	manifold	manifold	NOUN
ejpam-1048	135	6	with	with	ADP
ejpam-1048	135	7	a	a	DET
ejpam-1048	135	8	semi	semi	ADJ
ejpam-1048	135	9	symmetric	symmetric	ADJ
ejpam-1048	135	10	metric	metric	ADJ
ejpam-1048	135	11	connection	connection	NOUN
ejpam-1048	135	12	whose	whose	DET
ejpam-1048	135	13	the	the	DET
ejpam-1048	135	14	torsion	torsion	NOUN
ejpam-1048	135	15	tensor	tensor	NOUN
ejpam-1048	135	16	satisfies	satisfy	VERB
ejpam-1048	135	17	the	the	DET
ejpam-1048	135	18	condition	condition	NOUN
ejpam-1048	135	19	(	(	PUNCT
ejpam-1048	135	20	27	27	NUM
ejpam-1048	135	21	)	)	PUNCT
ejpam-1048	135	22	is	be	AUX
ejpam-1048	135	23	a	a	DET
ejpam-1048	135	24	mixed	mixed	ADJ
ejpam-1048	135	25	generalized	generalize	VERB
ejpam-1048	135	26	quasi	quasi	NOUN
ejpam-1048	135	27	einstein	einstein	PROPN
ejpam-1048	135	28	manifold	manifold	PROPN
ejpam-1048	135	29	.	.	PUNCT
ejpam-1048	136	1	theorem	theorem	VERB
ejpam-1048	136	2	9	9	NUM
ejpam-1048	136	3	.	.	PUNCT
ejpam-1048	137	1	[	[	X
ejpam-1048	137	2	13	13	NUM
ejpam-1048	137	3	]	]	X
ejpam-1048	137	4	if	if	SCONJ
ejpam-1048	137	5	a	a	DET
ejpam-1048	137	6	riemannian	riemannian	ADJ
ejpam-1048	137	7	manifold	manifold	NOUN
ejpam-1048	137	8	admits	admit	VERB
ejpam-1048	137	9	a	a	DET
ejpam-1048	137	10	semi	semi	ADJ
ejpam-1048	137	11	symmetric	symmetric	ADJ
ejpam-1048	137	12	metric	metric	ADJ
ejpam-1048	137	13	connection	connection	NOUN
ejpam-1048	137	14	with	with	ADP
ejpam-1048	137	15	constant	constant	ADJ
ejpam-1048	137	16	sectional	sectional	ADJ
ejpam-1048	137	17	curvature	curvature	NOUN
ejpam-1048	137	18	,	,	PUNCT
ejpam-1048	137	19	then	then	ADV
ejpam-1048	137	20	this	this	DET
ejpam-1048	137	21	manifold	manifold	NOUN
ejpam-1048	137	22	is	be	AUX
ejpam-1048	137	23	conformally	conformally	ADV
ejpam-1048	137	24	flat	flat	ADJ
ejpam-1048	137	25	.	.	PUNCT
ejpam-1048	138	1	thus	thus	ADV
ejpam-1048	138	2	,	,	PUNCT
ejpam-1048	138	3	in	in	ADP
ejpam-1048	138	4	virtue	virtue	NOUN
ejpam-1048	138	5	of	of	ADP
ejpam-1048	138	6	theorem	theorem	ADJ
ejpam-1048	138	7	7	7	NUM
ejpam-1048	138	8	,	,	PUNCT
ejpam-1048	138	9	theorem	theorem	VERB
ejpam-1048	138	10	8	8	NUM
ejpam-1048	138	11	and	and	CCONJ
ejpam-1048	138	12	theorem	theorem	VERB
ejpam-1048	138	13	9	9	NUM
ejpam-1048	138	14	,	,	PUNCT
ejpam-1048	138	15	we	we	PRON
ejpam-1048	138	16	can	can	AUX
ejpam-1048	138	17	establish	establish	VERB
ejpam-1048	138	18	the	the	DET
ejpam-1048	138	19	following	follow	VERB
ejpam-1048	138	20	theorems	theorem	NOUN
ejpam-1048	138	21	:	:	PUNCT
ejpam-1048	138	22	theorem	theorem	NOUN
ejpam-1048	138	23	10	10	NUM
ejpam-1048	138	24	.	.	PUNCT
ejpam-1048	139	1	if	if	SCONJ
ejpam-1048	139	2	the	the	DET
ejpam-1048	139	3	sectional	sectional	ADJ
ejpam-1048	139	4	curvature	curvature	NOUN
ejpam-1048	139	5	of	of	ADP
ejpam-1048	139	6	a	a	DET
ejpam-1048	139	7	riemannian	riemannian	NOUN
ejpam-1048	139	8	manifold	manifold	NOUN
ejpam-1048	139	9	with	with	ADP
ejpam-1048	139	10	a	a	DET
ejpam-1048	139	11	semi	semi	ADJ
ejpam-1048	139	12	symmetric	symmetric	ADJ
ejpam-1048	139	13	metric	metric	ADJ
ejpam-1048	139	14	connection	connection	NOUN
ejpam-1048	139	15	whose	whose	DET
ejpam-1048	139	16	the	the	DET
ejpam-1048	139	17	torsion	torsion	NOUN
ejpam-1048	139	18	tensor	tensor	NOUN
ejpam-1048	139	19	satisfies	satisfy	VERB
ejpam-1048	139	20	the	the	DET
ejpam-1048	139	21	condition	condition	NOUN
ejpam-1048	139	22	(	(	PUNCT
ejpam-1048	139	23	27	27	NUM
ejpam-1048	139	24	)	)	PUNCT
ejpam-1048	139	25	is	be	AUX
ejpam-1048	139	26	independent	independent	ADJ
ejpam-1048	139	27	from	from	ADP
ejpam-1048	139	28	the	the	DET
ejpam-1048	139	29	orientation	orientation	NOUN
ejpam-1048	139	30	chosen	choose	VERB
ejpam-1048	139	31	,	,	PUNCT
ejpam-1048	139	32	then	then	ADV
ejpam-1048	139	33	i	i	PRON
ejpam-1048	139	34	it	it	PRON
ejpam-1048	139	35	is	be	AUX
ejpam-1048	139	36	of	of	ADP
ejpam-1048	139	37	a	a	DET
ejpam-1048	139	38	mixed	mixed	ADJ
ejpam-1048	139	39	generalized	generalize	VERB
ejpam-1048	139	40	quasi	quasi	ADJ
ejpam-1048	139	41	constant	constant	ADJ
ejpam-1048	139	42	curvature	curvature	NOUN
ejpam-1048	139	43	,	,	PUNCT
ejpam-1048	139	44	ii	ii	VERB
ejpam-1048	139	45	it	it	PRON
ejpam-1048	139	46	is	be	AUX
ejpam-1048	139	47	a	a	DET
ejpam-1048	139	48	mixed	mixed	ADJ
ejpam-1048	139	49	generalized	generalize	VERB
ejpam-1048	139	50	quasi	quasi	NOUN
ejpam-1048	139	51	einstein	einstein	PROPN
ejpam-1048	139	52	manifold	manifold	PROPN
ejpam-1048	139	53	.	.	PUNCT
ejpam-1048	140	1	theorem	theorem	VERB
ejpam-1048	140	2	11	11	NUM
ejpam-1048	140	3	.	.	PUNCT
ejpam-1048	141	1	if	if	SCONJ
ejpam-1048	141	2	the	the	DET
ejpam-1048	141	3	sectional	sectional	ADJ
ejpam-1048	141	4	curvature	curvature	NOUN
ejpam-1048	141	5	of	of	ADP
ejpam-1048	141	6	a	a	DET
ejpam-1048	141	7	riemannian	riemannian	NOUN
ejpam-1048	141	8	manifold	manifold	NOUN
ejpam-1048	141	9	with	with	ADP
ejpam-1048	141	10	a	a	DET
ejpam-1048	141	11	semi	semi	ADJ
ejpam-1048	141	12	symmetric	symmetric	ADJ
ejpam-1048	141	13	metric	metric	ADJ
ejpam-1048	141	14	connection	connection	NOUN
ejpam-1048	141	15	whose	whose	DET
ejpam-1048	141	16	the	the	DET
ejpam-1048	141	17	torsion	torsion	NOUN
ejpam-1048	141	18	tensor	tensor	NOUN
ejpam-1048	141	19	satisfies	satisfy	VERB
ejpam-1048	141	20	the	the	DET
ejpam-1048	141	21	condition	condition	NOUN
ejpam-1048	141	22	(	(	PUNCT
ejpam-1048	141	23	27	27	NUM
ejpam-1048	141	24	)	)	PUNCT
ejpam-1048	141	25	is	be	AUX
ejpam-1048	141	26	independent	independent	ADJ
ejpam-1048	141	27	from	from	ADP
ejpam-1048	141	28	the	the	DET
ejpam-1048	141	29	orientation	orientation	NOUN
ejpam-1048	141	30	chosen	choose	VERB
ejpam-1048	141	31	,	,	PUNCT
ejpam-1048	141	32	then	then	ADV
ejpam-1048	141	33	the	the	DET
ejpam-1048	141	34	condition	condition	NOUN
ejpam-1048	141	35	(	(	PUNCT
ejpam-1048	141	36	24	24	NUM
ejpam-1048	141	37	)	)	PUNCT
ejpam-1048	141	38	is	be	AUX
ejpam-1048	141	39	satisfied	satisfied	ADJ
ejpam-1048	141	40	.	.	PUNCT
ejpam-1048	142	1	references	reference	NOUN
ejpam-1048	142	2	[	[	X
ejpam-1048	142	3	1	1	X
ejpam-1048	142	4	]	]	PUNCT
ejpam-1048	142	5	a	a	DET
ejpam-1048	142	6	bhattacharyya	bhattacharyya	ADJ
ejpam-1048	142	7	and	and	CCONJ
ejpam-1048	142	8	t	t	X
ejpam-1048	142	9	de	de	PROPN
ejpam-1048	142	10	.	.	PROPN
ejpam-1048	142	11	on	on	ADP
ejpam-1048	142	12	mixed	mixed	ADJ
ejpam-1048	142	13	generalized	generalized	ADJ
ejpam-1048	142	14	quasi	quasi	ADJ
ejpam-1048	142	15	-	-	ADJ
ejpam-1048	142	16	einstein	einstein	ADJ
ejpam-1048	142	17	manifolds	manifolds	PROPN
ejpam-1048	142	18	.	.	PUNCT
ejpam-1048	143	1	diff	diff	NOUN
ejpam-1048	143	2	.	.	PUNCT
ejpam-1048	144	1	geo.dym	geo.dym	PROPN
ejpam-1048	144	2	systm	systm	PROPN
ejpam-1048	144	3	.	.	PUNCT
ejpam-1048	145	1	a.	a.	NOUN
ejpam-1048	145	2	,	,	PUNCT
ejpam-1048	145	3	40	40	NUM
ejpam-1048	145	4	-	-	SYM
ejpam-1048	145	5	46	46	NUM
ejpam-1048	145	6	,	,	PUNCT
ejpam-1048	145	7	9	9	NUM
ejpam-1048	145	8	,	,	PUNCT
ejpam-1048	145	9	2007	2007	NUM
ejpam-1048	145	10	.	.	PUNCT
ejpam-1048	146	1	[	[	X
ejpam-1048	146	2	2	2	NUM
ejpam-1048	146	3	]	]	X
ejpam-1048	146	4	u	u	X
ejpam-1048	146	5	c	c	PROPN
ejpam-1048	146	6	de	de	X
ejpam-1048	146	7	and	and	CCONJ
ejpam-1048	146	8	j	j	PROPN
ejpam-1048	146	9	sengupta	sengupta	NOUN
ejpam-1048	146	10	.	.	PUNCT
ejpam-1048	147	1	on	on	ADP
ejpam-1048	147	2	a	a	DET
ejpam-1048	147	3	type	type	NOUN
ejpam-1048	147	4	of	of	ADP
ejpam-1048	147	5	semi	semi	ADJ
ejpam-1048	147	6	symmetric	symmetric	ADJ
ejpam-1048	147	7	metric	metric	ADJ
ejpam-1048	147	8	connection	connection	NOUN
ejpam-1048	147	9	on	on	ADP
ejpam-1048	147	10	an	an	DET
ejpam-1048	147	11	almost	almost	ADV
ejpam-1048	147	12	contact	contact	NOUN
ejpam-1048	147	13	metric	metric	ADJ
ejpam-1048	147	14	manifold	manifold	ADJ
ejpam-1048	147	15	,	,	PUNCT
ejpam-1048	147	16	facta	facta	PROPN
ejpam-1048	147	17	universitatis	universitatis	PROPN
ejpam-1048	147	18	(	(	PUNCT
ejpam-1048	147	19	niš	niš	NOUN
ejpam-1048	147	20	)	)	PUNCT
ejpam-1048	147	21	,	,	PUNCT
ejpam-1048	147	22	ser	ser	PROPN
ejpam-1048	147	23	.	.	PROPN
ejpam-1048	147	24	math	math	PROPN
ejpam-1048	147	25	.	.	PUNCT
ejpam-1048	148	1	inform	inform	NOUN
ejpam-1048	148	2	.	.	PUNCT
ejpam-1048	149	1	,	,	PUNCT
ejpam-1048	149	2	87	87	NUM
ejpam-1048	149	3	-	-	SYM
ejpam-1048	149	4	96	96	NUM
ejpam-1048	149	5	,	,	PUNCT
ejpam-1048	149	6	16	16	NUM
ejpam-1048	149	7	,	,	PUNCT
ejpam-1048	149	8	2001	2001	NUM
ejpam-1048	149	9	.	.	PUNCT
ejpam-1048	150	1	[	[	X
ejpam-1048	150	2	3	3	X
ejpam-1048	150	3	]	]	X
ejpam-1048	150	4	u	u	X
ejpam-1048	150	5	c	c	PROPN
ejpam-1048	150	6	de	de	X
ejpam-1048	150	7	and	and	CCONJ
ejpam-1048	150	8	b	b	X
ejpam-1048	150	9	k	k	PROPN
ejpam-1048	150	10	de	de	PROPN
ejpam-1048	150	11	.	.	PUNCT
ejpam-1048	151	1	some	some	DET
ejpam-1048	151	2	properties	property	NOUN
ejpam-1048	151	3	of	of	ADP
ejpam-1048	151	4	a	a	DET
ejpam-1048	151	5	semi	semi	ADJ
ejpam-1048	151	6	symmetric	symmetric	ADJ
ejpam-1048	151	7	metric	metric	ADJ
ejpam-1048	151	8	connection	connection	NOUN
ejpam-1048	151	9	on	on	ADP
ejpam-1048	151	10	a	a	DET
ejpam-1048	151	11	riemannian	riemannian	ADJ
ejpam-1048	151	12	manifold	manifold	NOUN
ejpam-1048	151	13	.	.	PUNCT
ejpam-1048	152	1	istanbul	istanbul	PROPN
ejpam-1048	152	2	univ	univ	PROPN
ejpam-1048	152	3	.	.	PUNCT
ejpam-1048	153	1	fen	fen	PROPN
ejpam-1048	153	2	fak	fak	PROPN
ejpam-1048	153	3	.	.	PUNCT
ejpam-1048	154	1	mat	mat	PROPN
ejpam-1048	154	2	.	.	PUNCT
ejpam-1048	154	3	derg	derg	PROPN
ejpam-1048	154	4	.	.	PUNCT
ejpam-1048	154	5	,	,	PUNCT
ejpam-1048	155	1	pp	pp	PROPN
ejpam-1048	155	2	.	.	PUNCT
ejpam-1048	156	1	111	111	NUM
ejpam-1048	156	2	-	-	SYM
ejpam-1048	156	3	117	117	NUM
ejpam-1048	156	4	,	,	PUNCT
ejpam-1048	156	5	54	54	NUM
ejpam-1048	156	6	,	,	PUNCT
ejpam-1048	156	7	1995	1995	NUM
ejpam-1048	156	8	.	.	PUNCT
ejpam-1048	157	1	[	[	X
ejpam-1048	157	2	4	4	NUM
ejpam-1048	157	3	]	]	X
ejpam-1048	157	4	u	u	X
ejpam-1048	157	5	c	c	X
ejpam-1048	157	6	de	de	X
ejpam-1048	157	7	and	and	CCONJ
ejpam-1048	157	8	s	s	PROPN
ejpam-1048	157	9	c	c	PROPN
ejpam-1048	157	10	biswas	biswas	PROPN
ejpam-1048	157	11	.	.	PUNCT
ejpam-1048	158	1	on	on	ADP
ejpam-1048	158	2	a	a	DET
ejpam-1048	158	3	type	type	NOUN
ejpam-1048	158	4	of	of	ADP
ejpam-1048	158	5	semi	semi	ADJ
ejpam-1048	158	6	symmetric	symmetric	ADJ
ejpam-1048	158	7	metric	metric	ADJ
ejpam-1048	158	8	connection	connection	NOUN
ejpam-1048	158	9	on	on	ADP
ejpam-1048	158	10	a	a	DET
ejpam-1048	158	11	riemannian	riemannian	ADJ
ejpam-1048	158	12	manifold	manifold	NOUN
ejpam-1048	158	13	.	.	PUNCT
ejpam-1048	159	1	publ	publ	PROPN
ejpam-1048	159	2	.	.	PUNCT
ejpam-1048	160	1	inst	inst	PROPN
ejpam-1048	160	2	.	.	PUNCT
ejpam-1048	160	3	math	math	NOUN
ejpam-1048	160	4	.	.	PUNCT
ejpam-1048	161	1	(	(	PUNCT
ejpam-1048	161	2	beograd	beograd	PROPN
ejpam-1048	161	3	)	)	PUNCT
ejpam-1048	161	4	(	(	PUNCT
ejpam-1048	161	5	n.	n.	PROPN
ejpam-1048	161	6	s.	s.	PROPN
ejpam-1048	161	7	)	)	PUNCT
ejpam-1048	161	8	,	,	PUNCT
ejpam-1048	161	9	90	90	NUM
ejpam-1048	161	10	-	-	SYM
ejpam-1048	161	11	96	96	NUM
ejpam-1048	161	12	,	,	PUNCT
ejpam-1048	161	13	61	61	NUM
ejpam-1048	161	14	,	,	PUNCT
ejpam-1048	161	15	75	75	NUM
ejpam-1048	161	16	,	,	PUNCT
ejpam-1048	161	17	1997	1997	NUM
ejpam-1048	161	18	.	.	PUNCT
ejpam-1048	162	1	[	[	X
ejpam-1048	162	2	5	5	NUM
ejpam-1048	162	3	]	]	X
ejpam-1048	162	4	u	u	X
ejpam-1048	162	5	c	c	X
ejpam-1048	162	6	de	de	PROPN
ejpam-1048	162	7	and	and	CCONJ
ejpam-1048	162	8	g	g	PROPN
ejpam-1048	162	9	c	c	PROPN
ejpam-1048	162	10	ghosh	ghosh	PROPN
ejpam-1048	162	11	.	.	PUNCT
ejpam-1048	163	1	on	on	ADP
ejpam-1048	163	2	generalized	generalized	ADJ
ejpam-1048	163	3	quasi	quasi	ADJ
ejpam-1048	163	4	-	-	ADJ
ejpam-1048	163	5	einstein	einstein	ADJ
ejpam-1048	163	6	manifolds	manifolds	PROPN
ejpam-1048	163	7	.	.	PUNCT
ejpam-1048	164	1	kyungpook	kyungpook	PROPN
ejpam-1048	164	2	math	math	PROPN
ejpam-1048	164	3	.	.	PUNCT
ejpam-1048	165	1	j.	j.	PROPN
ejpam-1048	165	2	,	,	PUNCT
ejpam-1048	165	3	607	607	NUM
ejpam-1048	165	4	-	-	SYM
ejpam-1048	165	5	615	615	NUM
ejpam-1048	165	6	,	,	PUNCT
ejpam-1048	165	7	44	44	NUM
ejpam-1048	165	8	,	,	PUNCT
ejpam-1048	165	9	4	4	NUM
ejpam-1048	165	10	,	,	PUNCT
ejpam-1048	165	11	2004	2004	NUM
ejpam-1048	165	12	.	.	PUNCT
ejpam-1048	166	1	[	[	X
ejpam-1048	166	2	6	6	NUM
ejpam-1048	166	3	]	]	PUNCT
ejpam-1048	166	4	t	t	PROPN
ejpam-1048	166	5	imai	imai	PROPN
ejpam-1048	166	6	.	.	PUNCT
ejpam-1048	167	1	notes	note	NOUN
ejpam-1048	167	2	on	on	ADP
ejpam-1048	167	3	semi	semi	ADJ
ejpam-1048	167	4	symmetric	symmetric	ADJ
ejpam-1048	167	5	metric	metric	ADJ
ejpam-1048	167	6	connections	connection	NOUN
ejpam-1048	167	7	.	.	PUNCT
ejpam-1048	168	1	tensor	tensor	NOUN
ejpam-1048	168	2	(	(	PUNCT
ejpam-1048	168	3	n.s	n.s	PROPN
ejpam-1048	168	4	.	.	PROPN
ejpam-1048	168	5	)	)	PUNCT
ejpam-1048	168	6	,	,	PUNCT
ejpam-1048	168	7	293	293	NUM
ejpam-1048	168	8	-	-	SYM
ejpam-1048	168	9	296	296	NUM
ejpam-1048	168	10	,	,	PUNCT
ejpam-1048	168	11	24	24	NUM
ejpam-1048	168	12	,	,	PUNCT
ejpam-1048	168	13	1972	1972	NUM
ejpam-1048	168	14	.	.	PUNCT
ejpam-1048	169	1	[	[	X
ejpam-1048	169	2	7	7	NUM
ejpam-1048	169	3	]	]	X
ejpam-1048	169	4	s	s	X
ejpam-1048	169	5	kobayashi	kobayashi	PROPN
ejpam-1048	169	6	and	and	CCONJ
ejpam-1048	169	7	k	k	PROPN
ejpam-1048	169	8	nomizu	nomizu	PROPN
ejpam-1048	169	9	.	.	PUNCT
ejpam-1048	170	1	foundations	foundation	NOUN
ejpam-1048	170	2	of	of	ADP
ejpam-1048	170	3	differential	differential	ADJ
ejpam-1048	170	4	geometry	geometry	NOUN
ejpam-1048	170	5	.	.	PUNCT
ejpam-1048	171	1	w.	w.	PROPN
ejpam-1048	171	2	interscience	interscience	NOUN
ejpam-1048	171	3	publishers	publisher	NOUN
ejpam-1048	171	4	,	,	PUNCT
ejpam-1048	171	5	new	new	PROPN
ejpam-1048	171	6	york	york	PROPN
ejpam-1048	171	7	,	,	PUNCT
ejpam-1048	171	8	1963	1963	NUM
ejpam-1048	171	9	.	.	PUNCT
ejpam-1048	172	1	[	[	X
ejpam-1048	172	2	8	8	NUM
ejpam-1048	172	3	]	]	SYM
ejpam-1048	172	4	c	c	NOUN
ejpam-1048	172	5	murathan	murathan	NOUN
ejpam-1048	172	6	and	and	CCONJ
ejpam-1048	172	7	c	c	PROPN
ejpam-1048	172	8	özgür	özgür	NOUN
ejpam-1048	172	9	.	.	PUNCT
ejpam-1048	173	1	riemannian	riemannian	PROPN
ejpam-1048	173	2	manifolds	manifold	NOUN
ejpam-1048	173	3	with	with	ADP
ejpam-1048	173	4	semi	semi	ADJ
ejpam-1048	173	5	-	-	ADJ
ejpam-1048	173	6	symmmetric	symmmetric	ADJ
ejpam-1048	173	7	metric	metric	ADJ
ejpam-1048	173	8	connection	connection	NOUN
ejpam-1048	173	9	satisfying	satisfy	VERB
ejpam-1048	173	10	some	some	DET
ejpam-1048	173	11	semisymmetry	semisymmetry	NOUN
ejpam-1048	173	12	conditions	condition	NOUN
ejpam-1048	173	13	.	.	PUNCT
ejpam-1048	174	1	proceedings	proceeding	NOUN
ejpam-1048	174	2	of	of	ADP
ejpam-1048	174	3	the	the	DET
ejpam-1048	174	4	estonian	estonian	ADJ
ejpam-1048	174	5	academy	academy	PROPN
ejpam-1048	174	6	of	of	ADP
ejpam-1048	174	7	sciences	sciences	PROPN
ejpam-1048	174	8	,	,	PUNCT
ejpam-1048	174	9	210	210	NUM
ejpam-1048	174	10	-	-	SYM
ejpam-1048	174	11	216	216	NUM
ejpam-1048	174	12	,	,	PUNCT
ejpam-1048	174	13	57	57	NUM
ejpam-1048	174	14	,	,	PUNCT
ejpam-1048	174	15	4	4	NUM
ejpam-1048	174	16	,	,	PUNCT
ejpam-1048	174	17	2008	2008	NUM
ejpam-1048	174	18	.	.	PUNCT
ejpam-1048	175	1	references	reference	NOUN
ejpam-1048	175	2	161	161	NUM
ejpam-1048	175	3	[	[	X
ejpam-1048	175	4	9	9	NUM
ejpam-1048	175	5	]	]	PUNCT
ejpam-1048	175	6	e	e	X
ejpam-1048	175	7	pak	pak	PROPN
ejpam-1048	175	8	.	.	PUNCT
ejpam-1048	176	1	on	on	ADP
ejpam-1048	176	2	the	the	DET
ejpam-1048	176	3	pseudo	pseudo	NOUN
ejpam-1048	176	4	-	-	ADJ
ejpam-1048	176	5	riemannian	riemannian	ADJ
ejpam-1048	176	6	spaces	space	NOUN
ejpam-1048	176	7	.	.	PUNCT
ejpam-1048	177	1	j.	j.	PROPN
ejpam-1048	177	2	korean	korean	PROPN
ejpam-1048	177	3	math	math	PROPN
ejpam-1048	177	4	.	.	PUNCT
ejpam-1048	178	1	soc	soc	PROPN
ejpam-1048	178	2	.	.	PROPN
ejpam-1048	179	1	,	,	PUNCT
ejpam-1048	179	2	23	23	NUM
ejpam-1048	179	3	-	-	SYM
ejpam-1048	179	4	31	31	NUM
ejpam-1048	179	5	,	,	PUNCT
ejpam-1048	179	6	6,1969	6,1969	NOUN
ejpam-1048	179	7	.	.	PUNCT
ejpam-1048	180	1	[	[	X
ejpam-1048	180	2	10	10	NUM
ejpam-1048	180	3	]	]	PUNCT
ejpam-1048	180	4	l	l	NOUN
ejpam-1048	180	5	tamássy	tamássy	NOUN
ejpam-1048	180	6	and	and	CCONJ
ejpam-1048	180	7	t	t	NOUN
ejpam-1048	180	8	q	q	PROPN
ejpam-1048	180	9	binh	binh	PROPN
ejpam-1048	180	10	.	.	PUNCT
ejpam-1048	181	1	on	on	ADP
ejpam-1048	181	2	the	the	DET
ejpam-1048	181	3	non	non	NOUN
ejpam-1048	181	4	-	-	NOUN
ejpam-1048	181	5	existence	existence	NOUN
ejpam-1048	181	6	of	of	ADP
ejpam-1048	181	7	certain	certain	ADJ
ejpam-1048	181	8	connections	connection	NOUN
ejpam-1048	181	9	with	with	ADP
ejpam-1048	181	10	torsion	torsion	NOUN
ejpam-1048	181	11	and	and	CCONJ
ejpam-1048	181	12	of	of	ADP
ejpam-1048	181	13	constant	constant	ADJ
ejpam-1048	181	14	curvature	curvature	NOUN
ejpam-1048	181	15	.	.	PUNCT
ejpam-1048	182	1	publ	publ	PROPN
ejpam-1048	182	2	.	.	PUNCT
ejpam-1048	183	1	math	math	NOUN
ejpam-1048	183	2	.	.	PUNCT
ejpam-1048	184	1	debrecen	debrecen	PROPN
ejpam-1048	184	2	,	,	PUNCT
ejpam-1048	184	3	283	283	NUM
ejpam-1048	184	4	-	-	SYM
ejpam-1048	184	5	288	288	NUM
ejpam-1048	184	6	,	,	PUNCT
ejpam-1048	184	7	36	36	NUM
ejpam-1048	184	8	,	,	PUNCT
ejpam-1048	184	9	1989	1989	NUM
ejpam-1048	184	10	.	.	PUNCT
ejpam-1048	185	1	[	[	X
ejpam-1048	185	2	11	11	NUM
ejpam-1048	185	3	]	]	X
ejpam-1048	185	4	k	k	PROPN
ejpam-1048	185	5	yano	yano	PROPN
ejpam-1048	185	6	.	.	PUNCT
ejpam-1048	186	1	on	on	ADP
ejpam-1048	186	2	semi	semi	ADJ
ejpam-1048	186	3	symmetric	symmetric	ADJ
ejpam-1048	186	4	metric	metric	ADJ
ejpam-1048	186	5	connection	connection	NOUN
ejpam-1048	186	6	.	.	PUNCT
ejpam-1048	187	1	rev	rev	PROPN
ejpam-1048	187	2	.	.	PROPN
ejpam-1048	187	3	roumaine	roumaine	PROPN
ejpam-1048	187	4	,	,	PUNCT
ejpam-1048	187	5	math	math	NOUN
ejpam-1048	187	6	.	.	PUNCT
ejpam-1048	188	1	pures	pure	NOUN
ejpam-1048	188	2	appl	appl	PROPN
ejpam-1048	188	3	.	.	PROPN
ejpam-1048	188	4	,	,	PUNCT
ejpam-1048	188	5	15791586,15	15791586,15	NUM
ejpam-1048	188	6	,	,	PUNCT
ejpam-1048	188	7	1970	1970	NUM
ejpam-1048	188	8	.	.	PUNCT
ejpam-1048	189	1	[	[	X
ejpam-1048	189	2	12	12	NUM
ejpam-1048	189	3	]	]	X
ejpam-1048	189	4	k	k	PROPN
ejpam-1048	189	5	yano	yano	PROPN
ejpam-1048	189	6	and	and	CCONJ
ejpam-1048	189	7	m	m	PROPN
ejpam-1048	189	8	kon	kon	PROPN
ejpam-1048	189	9	.	.	PUNCT
ejpam-1048	190	1	structures	structure	NOUN
ejpam-1048	190	2	on	on	ADP
ejpam-1048	190	3	manifolds	manifold	NOUN
ejpam-1048	190	4	.	.	PUNCT
ejpam-1048	191	1	series	series	PROPN
ejpam-1048	191	2	in	in	ADP
ejpam-1048	191	3	pure	pure	ADJ
ejpam-1048	191	4	math	math	NOUN
ejpam-1048	191	5	.	.	PUNCT
ejpam-1048	191	6	,	,	PUNCT
ejpam-1048	191	7	world	world	NOUN
ejpam-1048	191	8	scientific	scientific	NOUN
ejpam-1048	191	9	,	,	PUNCT
ejpam-1048	191	10	1984	1984	NUM
ejpam-1048	191	11	.	.	PUNCT
ejpam-1048	192	1	[	[	X
ejpam-1048	192	2	13	13	NUM
ejpam-1048	192	3	]	]	SYM
ejpam-1048	192	4	f	f	PROPN
ejpam-1048	192	5	ö	ö	NOUN
ejpam-1048	192	6	zengin	zengin	NOUN
ejpam-1048	192	7	s	s	VERB
ejpam-1048	192	8	a	a	DET
ejpam-1048	192	9	uysal	uysal	NOUN
ejpam-1048	192	10	and	and	CCONJ
ejpam-1048	192	11	s	s	VERB
ejpam-1048	192	12	a	a	DET
ejpam-1048	192	13	demirbağ.	demirbağ.	PROPN
ejpam-1048	192	14	on	on	ADP
ejpam-1048	192	15	sectional	sectional	ADJ
ejpam-1048	192	16	curvature	curvature	NOUN
ejpam-1048	192	17	of	of	ADP
ejpam-1048	192	18	a	a	DET
ejpam-1048	192	19	riemannian	riemannian	NOUN
ejpam-1048	192	20	manifold	manifold	NOUN
ejpam-1048	192	21	with	with	ADP
ejpam-1048	192	22	semi	semi	ADJ
ejpam-1048	192	23	-	-	ADJ
ejpam-1048	192	24	symmetric	symmetric	ADJ
ejpam-1048	192	25	connection	connection	NOUN
ejpam-1048	192	26	.	.	PUNCT
ejpam-1048	193	1	annales	annale	VERB
ejpam-1048	193	2	polonici	polonici	PROPN
ejpam-1048	193	3	mathematici	mathematici	PROPN
ejpam-1048	193	4	,	,	PUNCT
ejpam-1048	193	5	(	(	PUNCT
ejpam-1048	193	6	in	in	ADP
ejpam-1048	193	7	print	print	NOUN
ejpam-1048	193	8	)	)	PUNCT
ejpam-1048	193	9	.	.	PUNCT