id	sid	tid	token	lemma	pos
ejpam-7	1	1	european	european	PROPN
ejpam-7	1	2	journal	journal	PROPN
ejpam-7	1	3	of	of	ADP
ejpam-7	1	4	pure	pure	ADJ
ejpam-7	1	5	and	and	CCONJ
ejpam-7	1	6	applied	apply	VERB
ejpam-7	1	7	mathematics	mathematic	NOUN
ejpam-7	1	8	vol	vol	NOUN
ejpam-7	1	9	.	.	PROPN
ejpam-7	2	1	1	1	NUM
ejpam-7	2	2	,	,	PUNCT
ejpam-7	2	3	no	no	INTJ
ejpam-7	2	4	.	.	NOUN
ejpam-7	2	5	2	2	NUM
ejpam-7	2	6	,	,	PUNCT
ejpam-7	2	7	2008	2008	NUM
ejpam-7	2	8	,	,	PUNCT
ejpam-7	2	9	(	(	PUNCT
ejpam-7	2	10	21	21	NUM
ejpam-7	2	11	-	-	SYM
ejpam-7	2	12	31	31	NUM
ejpam-7	2	13	)	)	PUNCT
ejpam-7	2	14	issn	issn	PROPN
ejpam-7	2	15	1307	1307	NUM
ejpam-7	2	16	-	-	SYM
ejpam-7	2	17	5543	5543	NUM
ejpam-7	2	18	–	–	PUNCT
ejpam-7	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-7	2	20	some	some	DET
ejpam-7	2	21	results	result	VERB
ejpam-7	2	22	on	on	ADP
ejpam-7	2	23	k	k	NOUN
ejpam-7	2	24	-	-	NOUN
ejpam-7	2	25	contact	contact	NOUN
ejpam-7	2	26	and	and	CCONJ
ejpam-7	2	27	trans	tran	NOUN
ejpam-7	2	28	-	-	ADJ
ejpam-7	2	29	sasakian	sasakian	ADJ
ejpam-7	2	30	manifolds	manifolds	PROPN
ejpam-7	2	31	bagewadi	bagewadi	PROPN
ejpam-7	2	32	channabasappa1,∗	channabasappa1,∗	NOUN
ejpam-7	2	33	,	,	PUNCT
ejpam-7	2	34	basavarajappa	basavarajappa	ADJ
ejpam-7	2	35	n.s2	n.s2	NOUN
ejpam-7	2	36	,	,	PUNCT
ejpam-7	2	37	prakasha	prakasha	VERB
ejpam-7	2	38	d.g	d.g	PROPN
ejpam-7	2	39	1	1	NUM
ejpam-7	2	40	,	,	PUNCT
ejpam-7	2	41	and	and	CCONJ
ejpam-7	2	42	venkatesha1	venkatesha1	NOUN
ejpam-7	2	43	1	1	NUM
ejpam-7	2	44	department	department	NOUN
ejpam-7	2	45	of	of	ADP
ejpam-7	2	46	mathematics	mathematic	NOUN
ejpam-7	2	47	and	and	CCONJ
ejpam-7	2	48	computer	computer	NOUN
ejpam-7	2	49	science	science	NOUN
ejpam-7	2	50	,	,	PUNCT
ejpam-7	2	51	kuvempu	kuvempu	PROPN
ejpam-7	2	52	university	university	PROPN
ejpam-7	2	53	,	,	PUNCT
ejpam-7	2	54	jnana	jnana	PROPN
ejpam-7	2	55	sahyadri-577	sahyadri-577	PROPN
ejpam-7	2	56	451	451	NUM
ejpam-7	2	57	,	,	PUNCT
ejpam-7	2	58	shimoga	shimoga	PROPN
ejpam-7	2	59	,	,	PUNCT
ejpam-7	2	60	karnataka	karnataka	PROPN
ejpam-7	2	61	,	,	PUNCT
ejpam-7	2	62	india	india	PROPN
ejpam-7	2	63	.	.	PROPN
ejpam-7	2	64	2	2	NUM
ejpam-7	2	65	department	department	NOUN
ejpam-7	2	66	of	of	ADP
ejpam-7	2	67	mathematics	mathematics	PROPN
ejpam-7	2	68	,	,	PUNCT
ejpam-7	2	69	sbm	sbm	PROPN
ejpam-7	2	70	jain	jain	PROPN
ejpam-7	2	71	college	college	PROPN
ejpam-7	2	72	of	of	ADP
ejpam-7	2	73	engineering	engineering	NOUN
ejpam-7	2	74	,	,	PUNCT
ejpam-7	2	75	562	562	NUM
ejpam-7	2	76	112	112	NUM
ejpam-7	2	77	,	,	PUNCT
ejpam-7	2	78	jakkasandra	jakkasandra	PROPN
ejpam-7	2	79	bangalore	bangalore	PROPN
ejpam-7	2	80	.	.	PUNCT
ejpam-7	3	1	abstract	abstract	ADJ
ejpam-7	3	2	.	.	PUNCT
ejpam-7	4	1	we	we	PRON
ejpam-7	4	2	obtain	obtain	VERB
ejpam-7	4	3	results	result	NOUN
ejpam-7	4	4	on	on	ADP
ejpam-7	4	5	the	the	DET
ejpam-7	4	6	vanishing	vanishing	NOUN
ejpam-7	4	7	of	of	ADP
ejpam-7	4	8	divergence	divergence	NOUN
ejpam-7	4	9	of	of	ADP
ejpam-7	4	10	pseudo	pseudo	NOUN
ejpam-7	4	11	projective	projective	NOUN
ejpam-7	4	12	curvature	curvature	NOUN
ejpam-7	4	13	tensor	tensor	NOUN
ejpam-7	4	14	p̃	p̃	PROPN
ejpam-7	4	15	with	with	ADP
ejpam-7	4	16	respect	respect	NOUN
ejpam-7	4	17	to	to	ADP
ejpam-7	4	18	semi	semi	ADJ
ejpam-7	4	19	-	-	ADJ
ejpam-7	4	20	symmetric	symmetric	ADJ
ejpam-7	4	21	metric	metric	ADJ
ejpam-7	4	22	connection	connection	NOUN
ejpam-7	4	23	on	on	ADP
ejpam-7	4	24	k	k	NOUN
ejpam-7	4	25	-	-	NOUN
ejpam-7	4	26	contact	contact	NOUN
ejpam-7	4	27	and	and	CCONJ
ejpam-7	4	28	trans	trans	ADJ
ejpam-7	4	29	-	-	ADJ
ejpam-7	4	30	sasakian	sasakian	ADJ
ejpam-7	4	31	manifolds	manifold	NOUN
ejpam-7	4	32	.	.	PUNCT
ejpam-7	5	1	ams	am	NOUN
ejpam-7	5	2	subject	subject	ADJ
ejpam-7	5	3	classifications	classification	NOUN
ejpam-7	5	4	:	:	PUNCT
ejpam-7	5	5	53d15,53b15	53d15,53b15	NUM
ejpam-7	5	6	.	.	PUNCT
ejpam-7	6	1	key	key	ADJ
ejpam-7	6	2	words	word	NOUN
ejpam-7	6	3	:	:	PUNCT
ejpam-7	6	4	k	k	ADJ
ejpam-7	6	5	-	-	NOUN
ejpam-7	6	6	contact	contact	NOUN
ejpam-7	6	7	manifold	manifold	NOUN
ejpam-7	6	8	,	,	PUNCT
ejpam-7	6	9	trans	trans	ADJ
ejpam-7	6	10	-	-	ADJ
ejpam-7	6	11	sasakian	sasakian	ADJ
ejpam-7	6	12	manifold	manifold	NOUN
ejpam-7	6	13	,	,	PUNCT
ejpam-7	6	14	pseudo	pseudo	NOUN
ejpam-7	6	15	projective	projective	NOUN
ejpam-7	6	16	curvature	curvature	NOUN
ejpam-7	6	17	tensor	tensor	NOUN
ejpam-7	6	18	,	,	PUNCT
ejpam-7	6	19	η	η	PROPN
ejpam-7	6	20	-	-	PROPN
ejpam-7	6	21	einstein	einstein	PROPN
ejpam-7	6	22	manifold	manifold	NOUN
ejpam-7	6	23	.	.	PUNCT
ejpam-7	7	1	1	1	X
ejpam-7	7	2	.	.	X
ejpam-7	7	3	introduction	introduction	NOUN
ejpam-7	7	4	in	in	ADP
ejpam-7	7	5	1924	1924	NUM
ejpam-7	7	6	,	,	PUNCT
ejpam-7	7	7	friedman	friedman	NOUN
ejpam-7	7	8	and	and	CCONJ
ejpam-7	7	9	schouten	schouten	VERB
ejpam-7	8	1	[	[	X
ejpam-7	8	2	11	11	NUM
ejpam-7	8	3	]	]	PUNCT
ejpam-7	8	4	introduced	introduce	VERB
ejpam-7	8	5	the	the	DET
ejpam-7	8	6	notion	notion	NOUN
ejpam-7	8	7	of	of	ADP
ejpam-7	8	8	semi	semi	ADJ
ejpam-7	8	9	-	-	ADJ
ejpam-7	8	10	symmetric	symmetric	ADJ
ejpam-7	8	11	linear	linear	ADJ
ejpam-7	8	12	connection	connection	NOUN
ejpam-7	8	13	on	on	ADP
ejpam-7	8	14	a	a	DET
ejpam-7	8	15	differentiable	differentiable	ADJ
ejpam-7	8	16	manifold	manifold	NOUN
ejpam-7	8	17	.	.	PUNCT
ejpam-7	9	1	then	then	ADV
ejpam-7	9	2	in	in	ADP
ejpam-7	9	3	1932	1932	NUM
ejpam-7	9	4	,	,	PUNCT
ejpam-7	9	5	hayden	hayden	X
ejpam-7	10	1	[	[	X
ejpam-7	10	2	14	14	NUM
ejpam-7	10	3	]	]	PUNCT
ejpam-7	10	4	introduced	introduce	VERB
ejpam-7	10	5	the	the	DET
ejpam-7	10	6	idea	idea	NOUN
ejpam-7	10	7	of	of	ADP
ejpam-7	10	8	metric	metric	ADJ
ejpam-7	10	9	connection	connection	NOUN
ejpam-7	10	10	with	with	ADP
ejpam-7	10	11	a	a	DET
ejpam-7	10	12	torsion	torsion	NOUN
ejpam-7	10	13	on	on	ADP
ejpam-7	10	14	a	a	DET
ejpam-7	10	15	riemannain	riemannain	NOUN
ejpam-7	10	16	manifold	manifold	NOUN
ejpam-7	10	17	.	.	PUNCT
ejpam-7	11	1	a	a	DET
ejpam-7	11	2	systematic	systematic	ADJ
ejpam-7	11	3	study	study	NOUN
ejpam-7	11	4	of	of	ADP
ejpam-7	11	5	semi	semi	ADJ
ejpam-7	11	6	-	-	ADJ
ejpam-7	11	7	symmetric	symmetric	ADJ
ejpam-7	11	8	metric	metric	ADJ
ejpam-7	11	9	connection	connection	NOUN
ejpam-7	11	10	on	on	ADP
ejpam-7	11	11	a	a	DET
ejpam-7	11	12	riemannain	riemannain	NOUN
ejpam-7	11	13	manifold	manifold	NOUN
ejpam-7	11	14	has	have	AUX
ejpam-7	11	15	been	be	AUX
ejpam-7	11	16	given	give	VERB
ejpam-7	11	17	by	by	ADP
ejpam-7	11	18	yano	yano	PROPN
ejpam-7	12	1	[	[	X
ejpam-7	12	2	18	18	NUM
ejpam-7	12	3	]	]	PUNCT
ejpam-7	12	4	in	in	ADP
ejpam-7	12	5	1970	1970	NUM
ejpam-7	12	6	and	and	CCONJ
ejpam-7	12	7	later	later	ADV
ejpam-7	12	8	studied	study	VERB
ejpam-7	12	9	by	by	ADP
ejpam-7	12	10	k.s.amur	k.s.amur	NOUN
ejpam-7	12	11	and	and	CCONJ
ejpam-7	12	12	s.s.pujar	s.s.pujar	VERB
ejpam-7	13	1	[	[	X
ejpam-7	13	2	1	1	NUM
ejpam-7	13	3	]	]	PUNCT
ejpam-7	13	4	,	,	PUNCT
ejpam-7	13	5	c.s.bagewadi	c.s.bagewadi	NOUN
ejpam-7	14	1	[	[	X
ejpam-7	14	2	2	2	NUM
ejpam-7	14	3	]	]	PUNCT
ejpam-7	14	4	,	,	PUNCT
ejpam-7	14	5	u.c.de	u.c.de	PROPN
ejpam-7	14	6	et	et	PROPN
ejpam-7	14	7	al	al	PROPN
ejpam-7	15	1	[	[	X
ejpam-7	15	2	10	10	NUM
ejpam-7	15	3	]	]	PUNCT
ejpam-7	15	4	,	,	PUNCT
ejpam-7	15	5	sharafuddin	sharafuddin	VERB
ejpam-7	15	6	and	and	CCONJ
ejpam-7	15	7	hussain	hussain	VERB
ejpam-7	15	8	[	[	X
ejpam-7	15	9	16	16	NUM
ejpam-7	15	10	]	]	PUNCT
ejpam-7	15	11	and	and	CCONJ
ejpam-7	15	12	others	other	NOUN
ejpam-7	15	13	.	.	PUNCT
ejpam-7	16	1	the	the	DET
ejpam-7	16	2	authors	author	NOUN
ejpam-7	16	3	u.c.de	u.c.de	VERB
ejpam-7	17	1	[	[	X
ejpam-7	17	2	10	10	NUM
ejpam-7	17	3	]	]	PUNCT
ejpam-7	17	4	and	and	CCONJ
ejpam-7	17	5	c.s.bagewadi	c.s.bagewadi	NOUN
ejpam-7	17	6	et	et	PROPN
ejpam-7	17	7	al	al	PROPN
ejpam-7	17	8	[	[	PUNCT
ejpam-7	17	9	[	[	X
ejpam-7	17	10	3	3	NUM
ejpam-7	17	11	,	,	PUNCT
ejpam-7	17	12	12	12	NUM
ejpam-7	17	13	]	]	PUNCT
ejpam-7	17	14	]	]	PUNCT
ejpam-7	17	15	have	have	AUX
ejpam-7	17	16	obtained	obtain	VERB
ejpam-7	17	17	results	result	NOUN
ejpam-7	17	18	on	on	ADP
ejpam-7	17	19	the	the	DET
ejpam-7	17	20	conservativeness	conservativeness	NOUN
ejpam-7	17	21	of	of	ADP
ejpam-7	17	22	projective	projective	NOUN
ejpam-7	17	23	,	,	PUNCT
ejpam-7	17	24	pseudo	pseudo	NOUN
ejpam-7	17	25	projective	projective	NOUN
ejpam-7	17	26	,	,	PUNCT
ejpam-7	17	27	conformal	conformal	ADJ
ejpam-7	17	28	,	,	PUNCT
ejpam-7	17	29	concircular	concircular	ADJ
ejpam-7	17	30	,	,	PUNCT
ejpam-7	17	31	quasi	quasi	ADJ
ejpam-7	17	32	conformal	conformal	NOUN
ejpam-7	17	33	curvature	curvature	NOUN
ejpam-7	17	34	tensors	tensor	NOUN
ejpam-7	17	35	on	on	ADP
ejpam-7	17	36	k	k	NOUN
ejpam-7	17	37	-	-	NOUN
ejpam-7	17	38	contact	contact	NOUN
ejpam-7	17	39	,	,	PUNCT
ejpam-7	17	40	kenmotsu	kenmotsu	NOUN
ejpam-7	17	41	and	and	CCONJ
ejpam-7	17	42	trans	trans	PROPN
ejpam-7	17	43	-	-	ADJ
ejpam-7	17	44	sasakian	sasakian	ADJ
ejpam-7	17	45	manifolds	manifold	NOUN
ejpam-7	17	46	.	.	PUNCT
ejpam-7	18	1	in	in	ADP
ejpam-7	18	2	this	this	DET
ejpam-7	18	3	paper	paper	NOUN
ejpam-7	18	4	we	we	PRON
ejpam-7	18	5	extend	extend	VERB
ejpam-7	18	6	the	the	DET
ejpam-7	18	7	conservativeness	conservativeness	NOUN
ejpam-7	18	8	of	of	ADP
ejpam-7	18	9	pseudo	pseudo	NOUN
ejpam-7	18	10	projective	projective	NOUN
ejpam-7	18	11	curvature	curvature	NOUN
ejpam-7	18	12	tensor	tensor	NOUN
ejpam-7	18	13	to	to	ADP
ejpam-7	18	14	k	k	NOUN
ejpam-7	18	15	-	-	NOUN
ejpam-7	18	16	contact	contact	NOUN
ejpam-7	18	17	and	and	CCONJ
ejpam-7	18	18	trans	tran	NOUN
ejpam-7	18	19	-	-	ADJ
ejpam-7	18	20	sasakian	sasakian	ADJ
ejpam-7	18	21	manifolds	manifold	NOUN
ejpam-7	18	22	admitting	admit	VERB
ejpam-7	18	23	semi	semi	ADJ
ejpam-7	18	24	-	-	ADJ
ejpam-7	18	25	symmetric	symmetric	ADJ
ejpam-7	18	26	metric	metric	ADJ
ejpam-7	18	27	connection	connection	NOUN
ejpam-7	18	28	.	.	PUNCT
ejpam-7	19	1	after	after	ADP
ejpam-7	19	2	preliminaries	preliminary	NOUN
ejpam-7	19	3	in	in	ADP
ejpam-7	19	4	section	section	NOUN
ejpam-7	19	5	2	2	NUM
ejpam-7	19	6	,	,	PUNCT
ejpam-7	19	7	we	we	PRON
ejpam-7	19	8	study	study	VERB
ejpam-7	19	9	in	in	ADP
ejpam-7	19	10	section	section	NOUN
ejpam-7	19	11	3	3	NUM
ejpam-7	19	12	the	the	DET
ejpam-7	19	13	pseudo	pseudo	NOUN
ejpam-7	19	14	projective	projective	NOUN
ejpam-7	19	15	curvature	curvature	NOUN
ejpam-7	19	16	tensor	tensor	NOUN
ejpam-7	19	17	with	with	ADP
ejpam-7	19	18	respect	respect	NOUN
ejpam-7	19	19	to	to	ADP
ejpam-7	19	20	semi	semi	ADJ
ejpam-7	19	21	-	-	ADJ
ejpam-7	19	22	symmetric	symmetric	ADJ
ejpam-7	19	23	metric	metric	ADJ
ejpam-7	19	24	connection	connection	NOUN
ejpam-7	19	25	on	on	ADP
ejpam-7	19	26	k	k	ADJ
ejpam-7	19	27	-	-	NOUN
ejpam-7	19	28	contact	contact	NOUN
ejpam-7	19	29	manifold	manifold	NOUN
ejpam-7	19	30	.	.	PUNCT
ejpam-7	20	1	in	in	ADP
ejpam-7	20	2	the	the	DET
ejpam-7	20	3	section	section	NOUN
ejpam-7	20	4	4	4	NUM
ejpam-7	20	5	we	we	PRON
ejpam-7	20	6	study	study	VERB
ejpam-7	20	7	some	some	DET
ejpam-7	20	8	properties	property	NOUN
ejpam-7	20	9	regarding	regard	VERB
ejpam-7	20	10	pseudo	pseudo	NOUN
ejpam-7	20	11	projective	projective	NOUN
ejpam-7	20	12	curvature	curvature	NOUN
ejpam-7	20	13	tensor	tensor	NOUN
ejpam-7	20	14	with	with	ADP
ejpam-7	20	15	respect	respect	NOUN
ejpam-7	20	16	to	to	ADP
ejpam-7	20	17	this	this	DET
ejpam-7	20	18	connection	connection	NOUN
ejpam-7	20	19	on	on	ADP
ejpam-7	20	20	trans	trans	PROPN
ejpam-7	20	21	-	-	ADJ
ejpam-7	20	22	sasakian	sasakian	ADJ
ejpam-7	20	23	manifold	manifold	NOUN
ejpam-7	20	24	under	under	ADP
ejpam-7	20	25	the	the	DET
ejpam-7	20	26	condition	condition	NOUN
ejpam-7	20	27	φ(gradα	φ(gradα	NOUN
ejpam-7	20	28	)	)	PUNCT
ejpam-7	21	1	=	=	SYM
ejpam-7	22	1	(	(	PUNCT
ejpam-7	22	2	n−	n−	NOUN
ejpam-7	22	3	2)gradβ	2)gradβ	NUM
ejpam-7	22	4	and	and	CCONJ
ejpam-7	22	5	obtained	obtain	VERB
ejpam-7	22	6	some	some	DET
ejpam-7	22	7	interesting	interesting	ADJ
ejpam-7	22	8	results	result	NOUN
ejpam-7	22	9	.	.	PUNCT
ejpam-7	23	1	∗corresponding	∗corresponde	VERB
ejpam-7	23	2	author	author	NOUN
ejpam-7	23	3	.	.	PUNCT
ejpam-7	24	1	email	email	NOUN
ejpam-7	24	2	addresses	address	NOUN
ejpam-7	24	3	:	:	PUNCT
ejpam-7	24	4	prof	prof	NOUN
ejpam-7	24	5	bagewadi@yahoo.co.in	bagewadi@yahoo.co.in	PROPN
ejpam-7	24	6	(	(	PUNCT
ejpam-7	24	7	bagewadi	bagewadi	PROPN
ejpam-7	24	8	channabasappa	channabasappa	PROPN
ejpam-7	24	9	)	)	PUNCT
ejpam-7	24	10	,	,	PUNCT
ejpam-7	24	11	nsb	nsb	PROPN
ejpam-7	24	12	sbmjce@yahoo.co.in	sbmjce@yahoo.co.in	ADV
ejpam-7	24	13	(	(	PUNCT
ejpam-7	24	14	basavarajappa	basavarajappa	PROPN
ejpam-7	24	15	n.s	n.s	PROPN
ejpam-7	24	16	)	)	PUNCT
ejpam-7	24	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-7	25	1	21	21	NUM
ejpam-7	25	2	c	c	X
ejpam-7	25	3	©	©	PROPN
ejpam-7	25	4	2007	2007	NUM
ejpam-7	25	5	ejpam	ejpam	NOUN
ejpam-7	25	6	all	all	DET
ejpam-7	25	7	rights	right	NOUN
ejpam-7	25	8	reserved	reserve	VERB
ejpam-7	25	9	.	.	PUNCT
ejpam-7	26	1	bagewadi	bagewadi	PROPN
ejpam-7	26	2	c.s	c.s	PROPN
ejpam-7	26	3	.	.	PROPN
ejpam-7	26	4	et	et	PROPN
ejpam-7	26	5	al	al	PROPN
ejpam-7	26	6	.	.	PUNCT
ejpam-7	26	7	/	/	SYM
ejpam-7	26	8	eur	eur	PROPN
ejpam-7	26	9	.	.	PUNCT
ejpam-7	27	1	j.	j.	PROPN
ejpam-7	27	2	pure	pure	PROPN
ejpam-7	27	3	appl	appl	PROPN
ejpam-7	27	4	.	.	PROPN
ejpam-7	27	5	math	math	PROPN
ejpam-7	27	6	,	,	PUNCT
ejpam-7	27	7	1	1	NUM
ejpam-7	27	8	(	(	PUNCT
ejpam-7	27	9	2008	2008	NUM
ejpam-7	27	10	)	)	PUNCT
ejpam-7	27	11	,	,	PUNCT
ejpam-7	27	12	(	(	PUNCT
ejpam-7	27	13	21	21	NUM
ejpam-7	27	14	-	-	SYM
ejpam-7	27	15	31	31	NUM
ejpam-7	27	16	)	)	PUNCT
ejpam-7	27	17	22	22	NUM
ejpam-7	27	18	2	2	NUM
ejpam-7	27	19	.	.	PUNCT
ejpam-7	28	1	preliminaries	preliminary	NOUN
ejpam-7	28	2	let	let	VERB
ejpam-7	28	3	mn	mn	PROPN
ejpam-7	28	4	be	be	AUX
ejpam-7	28	5	an	an	DET
ejpam-7	28	6	almost	almost	ADV
ejpam-7	28	7	contact	contact	NOUN
ejpam-7	28	8	metric	metric	ADJ
ejpam-7	28	9	manifold	manifold	ADJ
ejpam-7	29	1	[	[	X
ejpam-7	29	2	9	9	NUM
ejpam-7	29	3	]	]	PUNCT
ejpam-7	29	4	with	with	ADP
ejpam-7	29	5	an	an	DET
ejpam-7	29	6	almost	almost	ADV
ejpam-7	29	7	contact	contact	NOUN
ejpam-7	29	8	metric	metric	ADJ
ejpam-7	29	9	structure	structure	NOUN
ejpam-7	29	10	(	(	PUNCT
ejpam-7	29	11	φ	φ	PROPN
ejpam-7	29	12	,	,	PUNCT
ejpam-7	29	13	ξ	ξ	PROPN
ejpam-7	29	14	,	,	PUNCT
ejpam-7	29	15	η	η	NOUN
ejpam-7	29	16	,	,	PUNCT
ejpam-7	29	17	g	g	NOUN
ejpam-7	29	18	)	)	PUNCT
ejpam-7	29	19	,	,	PUNCT
ejpam-7	29	20	that	that	ADV
ejpam-7	29	21	is	is	ADV
ejpam-7	29	22	,	,	PUNCT
ejpam-7	29	23	φ	φ	PROPN
ejpam-7	29	24	is	be	AUX
ejpam-7	29	25	a	a	DET
ejpam-7	29	26	(	(	PUNCT
ejpam-7	29	27	1	1	NUM
ejpam-7	29	28	,	,	PUNCT
ejpam-7	29	29	1	1	NUM
ejpam-7	29	30	)	)	PUNCT
ejpam-7	29	31	tensor	tensor	NOUN
ejpam-7	29	32	field	field	NOUN
ejpam-7	29	33	,	,	PUNCT
ejpam-7	29	34	ξ	ξ	PROPN
ejpam-7	29	35	is	be	AUX
ejpam-7	29	36	a	a	DET
ejpam-7	29	37	vector	vector	NOUN
ejpam-7	29	38	field	field	NOUN
ejpam-7	29	39	;	;	PUNCT
ejpam-7	29	40	η	η	PROPN
ejpam-7	29	41	is	be	AUX
ejpam-7	29	42	a	a	DET
ejpam-7	29	43	1	1	NUM
ejpam-7	29	44	-	-	PUNCT
ejpam-7	29	45	form	form	NOUN
ejpam-7	29	46	and	and	CCONJ
ejpam-7	29	47	g	g	NOUN
ejpam-7	29	48	is	be	AUX
ejpam-7	29	49	a	a	DET
ejpam-7	29	50	compatible	compatible	ADJ
ejpam-7	29	51	riemannian	riemannian	NOUN
ejpam-7	29	52	metric	metric	NOUN
ejpam-7	29	53	such	such	ADJ
ejpam-7	29	54	that	that	DET
ejpam-7	29	55	φ2	φ2	PROPN
ejpam-7	30	1	=	=	PUNCT
ejpam-7	30	2	−i	−i	PROPN
ejpam-7	31	1	+	+	CCONJ
ejpam-7	31	2	η	η	PROPN
ejpam-7	31	3	⊗	⊗	PROPN
ejpam-7	31	4	ξ	ξ	PROPN
ejpam-7	31	5	,	,	PUNCT
ejpam-7	31	6	η(ξ	η(ξ	PROPN
ejpam-7	31	7	)	)	PUNCT
ejpam-7	31	8	=	=	SYM
ejpam-7	31	9	1	1	NUM
ejpam-7	31	10	,	,	PUNCT
ejpam-7	31	11	φ(ξ	φ(ξ	NOUN
ejpam-7	31	12	)	)	PUNCT
ejpam-7	31	13	=	=	SYM
ejpam-7	31	14	0	0	NUM
ejpam-7	31	15	,	,	PUNCT
ejpam-7	31	16	η.φ	η.φ	NOUN
ejpam-7	31	17	=	=	SYM
ejpam-7	31	18	0	0	NUM
ejpam-7	31	19	,	,	PUNCT
ejpam-7	31	20	(	(	PUNCT
ejpam-7	31	21	2.1	2.1	NUM
ejpam-7	31	22	)	)	PUNCT
ejpam-7	31	23	g(φx	g(φx	NOUN
ejpam-7	31	24	,	,	PUNCT
ejpam-7	31	25	φy	φy	NOUN
ejpam-7	31	26	)	)	PUNCT
ejpam-7	32	1	=	=	SYM
ejpam-7	32	2	g(x	g(x	NOUN
ejpam-7	32	3	,	,	PUNCT
ejpam-7	32	4	y	y	PROPN
ejpam-7	32	5	)	)	PUNCT
ejpam-7	32	6	−	−	PROPN
ejpam-7	32	7	η(x)η(y	η(x)η(y	PROPN
ejpam-7	32	8	)	)	PUNCT
ejpam-7	32	9	,	,	PUNCT
ejpam-7	32	10	(	(	PUNCT
ejpam-7	32	11	2.2	2.2	NUM
ejpam-7	32	12	)	)	PUNCT
ejpam-7	32	13	g(x	g(x	NOUN
ejpam-7	32	14	,	,	PUNCT
ejpam-7	32	15	φy	φy	NOUN
ejpam-7	32	16	)	)	PUNCT
ejpam-7	32	17	=	=	SYM
ejpam-7	32	18	−g(φx	−g(φx	NOUN
ejpam-7	32	19	,	,	PUNCT
ejpam-7	32	20	y	y	PROPN
ejpam-7	32	21	)	)	PUNCT
ejpam-7	32	22	,	,	PUNCT
ejpam-7	32	23	g(x	g(x	PROPN
ejpam-7	32	24	,	,	PUNCT
ejpam-7	32	25	ξ	ξ	NOUN
ejpam-7	32	26	)	)	PUNCT
ejpam-7	32	27	=	=	SYM
ejpam-7	32	28	η(x	η(x	NOUN
ejpam-7	32	29	)	)	PUNCT
ejpam-7	32	30	,	,	PUNCT
ejpam-7	32	31	(	(	PUNCT
ejpam-7	32	32	2.3	2.3	NUM
ejpam-7	32	33	)	)	PUNCT
ejpam-7	32	34	for	for	ADP
ejpam-7	32	35	all	all	DET
ejpam-7	32	36	x	x	NOUN
ejpam-7	32	37	,	,	PUNCT
ejpam-7	32	38	y	y	PROPN
ejpam-7	32	39	∈	∈	PROPN
ejpam-7	32	40	tm	tm	NOUN
ejpam-7	32	41	.	.	PUNCT
ejpam-7	33	1	if	if	SCONJ
ejpam-7	33	2	mn	mn	PROPN
ejpam-7	33	3	is	be	AUX
ejpam-7	33	4	a	a	DET
ejpam-7	33	5	k	k	ADJ
ejpam-7	33	6	-	-	NOUN
ejpam-7	33	7	contact	contact	NOUN
ejpam-7	33	8	riemannian	riemannian	NOUN
ejpam-7	33	9	manifold	manifold	NOUN
ejpam-7	33	10	,	,	PUNCT
ejpam-7	33	11	then	then	ADV
ejpam-7	33	12	besides	besides	SCONJ
ejpam-7	33	13	(	(	PUNCT
ejpam-7	33	14	2.1	2.1	NUM
ejpam-7	33	15	)	)	PUNCT
ejpam-7	33	16	,	,	PUNCT
ejpam-7	33	17	(	(	PUNCT
ejpam-7	33	18	2.2	2.2	NUM
ejpam-7	33	19	)	)	PUNCT
ejpam-7	33	20	and	and	CCONJ
ejpam-7	33	21	(	(	PUNCT
ejpam-7	33	22	2.9	2.9	NUM
ejpam-7	33	23	)	)	PUNCT
ejpam-7	33	24	the	the	DET
ejpam-7	33	25	following	follow	VERB
ejpam-7	33	26	relations	relation	NOUN
ejpam-7	33	27	hold	hold	VERB
ejpam-7	33	28	[	[	X
ejpam-7	33	29	15	15	NUM
ejpam-7	33	30	]	]	X
ejpam-7	33	31	:	:	PUNCT
ejpam-7	33	32	∇xξ	∇xξ	NOUN
ejpam-7	33	33	=	=	SYM
ejpam-7	33	34	−φx	−φx	PROPN
ejpam-7	33	35	,	,	PUNCT
ejpam-7	33	36	(	(	PUNCT
ejpam-7	33	37	2.4	2.4	NUM
ejpam-7	33	38	)	)	PUNCT
ejpam-7	33	39	(	(	PUNCT
ejpam-7	33	40	∇xη)(y	∇xη)(y	NOUN
ejpam-7	33	41	)	)	PUNCT
ejpam-7	34	1	=	=	SYM
ejpam-7	34	2	−g(φx	−g(φx	NOUN
ejpam-7	34	3	,	,	PUNCT
ejpam-7	34	4	y	y	PROPN
ejpam-7	34	5	)	)	PUNCT
ejpam-7	34	6	,	,	PUNCT
ejpam-7	34	7	(	(	PUNCT
ejpam-7	34	8	2.5	2.5	NUM
ejpam-7	34	9	)	)	PUNCT
ejpam-7	34	10	s(x	s(x	PROPN
ejpam-7	34	11	,	,	PUNCT
ejpam-7	34	12	ξ	ξ	X
ejpam-7	34	13	)	)	PUNCT
ejpam-7	34	14	=	=	SYM
ejpam-7	34	15	(	(	PUNCT
ejpam-7	34	16	n−	n−	NOUN
ejpam-7	34	17	1)η(x	1)η(x	NUM
ejpam-7	34	18	)	)	PUNCT
ejpam-7	34	19	,	,	PUNCT
ejpam-7	34	20	(	(	PUNCT
ejpam-7	34	21	2.6	2.6	NUM
ejpam-7	34	22	)	)	PUNCT
ejpam-7	34	23	η(r(x	η(r(x	PROPN
ejpam-7	34	24	,	,	PUNCT
ejpam-7	34	25	y	y	PROPN
ejpam-7	34	26	)	)	PUNCT
ejpam-7	35	1	z	z	X
ejpam-7	35	2	)	)	PUNCT
ejpam-7	35	3	=	=	SYM
ejpam-7	36	1	g(y	g(y	NOUN
ejpam-7	36	2	,	,	PUNCT
ejpam-7	36	3	z)η(x)−	z)η(x)−	PROPN
ejpam-7	36	4	g(x	g(x	NOUN
ejpam-7	36	5	,	,	PUNCT
ejpam-7	36	6	z)η(y	z)η(y	NOUN
ejpam-7	36	7	)	)	PUNCT
ejpam-7	36	8	,	,	PUNCT
ejpam-7	36	9	(	(	PUNCT
ejpam-7	36	10	2.7	2.7	NUM
ejpam-7	36	11	)	)	PUNCT
ejpam-7	36	12	for	for	ADP
ejpam-7	36	13	any	any	DET
ejpam-7	36	14	vector	vector	NOUN
ejpam-7	36	15	fields	field	NOUN
ejpam-7	36	16	x	x	X
ejpam-7	36	17	,	,	PUNCT
ejpam-7	36	18	y	y	PROPN
ejpam-7	36	19	,	,	PUNCT
ejpam-7	36	20	where	where	SCONJ
ejpam-7	36	21	r	r	NOUN
ejpam-7	36	22	and	and	CCONJ
ejpam-7	36	23	s	s	NOUN
ejpam-7	36	24	denote	denote	NOUN
ejpam-7	36	25	respectively	respectively	ADV
ejpam-7	36	26	the	the	DET
ejpam-7	36	27	curvature	curvature	NOUN
ejpam-7	36	28	tensor	tensor	NOUN
ejpam-7	36	29	of	of	ADP
ejpam-7	36	30	type	type	NOUN
ejpam-7	36	31	(	(	PUNCT
ejpam-7	36	32	1	1	NUM
ejpam-7	36	33	,	,	PUNCT
ejpam-7	36	34	3	3	NUM
ejpam-7	36	35	)	)	PUNCT
ejpam-7	36	36	and	and	CCONJ
ejpam-7	36	37	the	the	DET
ejpam-7	36	38	ricci	ricci	PROPN
ejpam-7	36	39	tensor	tensor	NOUN
ejpam-7	36	40	of	of	ADP
ejpam-7	36	41	type	type	NOUN
ejpam-7	36	42	(	(	PUNCT
ejpam-7	36	43	0	0	NUM
ejpam-7	36	44	,	,	PUNCT
ejpam-7	36	45	2	2	NUM
ejpam-7	36	46	)	)	PUNCT
ejpam-7	36	47	.	.	PUNCT
ejpam-7	37	1	an	an	DET
ejpam-7	37	2	almost	almost	ADV
ejpam-7	37	3	contact	contact	NOUN
ejpam-7	37	4	metric	metric	ADJ
ejpam-7	37	5	structure	structure	NOUN
ejpam-7	37	6	(	(	PUNCT
ejpam-7	37	7	φ	φ	PROPN
ejpam-7	37	8	,	,	PUNCT
ejpam-7	37	9	ξ	ξ	PROPN
ejpam-7	37	10	,	,	PUNCT
ejpam-7	37	11	η	η	NOUN
ejpam-7	37	12	,	,	PUNCT
ejpam-7	37	13	g	g	NOUN
ejpam-7	37	14	)	)	PUNCT
ejpam-7	37	15	in	in	ADP
ejpam-7	37	16	m	m	PROPN
ejpam-7	37	17	is	be	AUX
ejpam-7	37	18	called	call	VERB
ejpam-7	37	19	trans	trans	ADJ
ejpam-7	37	20	-	-	ADJ
ejpam-7	37	21	sasakian	sasakian	ADJ
ejpam-7	37	22	structure	structure	NOUN
ejpam-7	37	23	[	[	X
ejpam-7	37	24	14	14	NUM
ejpam-7	37	25	]	]	X
ejpam-7	37	26	if	if	SCONJ
ejpam-7	37	27	(	(	PUNCT
ejpam-7	37	28	m	m	NOUN
ejpam-7	37	29	×	×	NOUN
ejpam-7	37	30	r	r	NOUN
ejpam-7	37	31	,	,	PUNCT
ejpam-7	37	32	j	j	PROPN
ejpam-7	37	33	,	,	PUNCT
ejpam-7	37	34	g	g	NOUN
ejpam-7	37	35	)	)	PUNCT
ejpam-7	37	36	belongs	belong	VERB
ejpam-7	37	37	to	to	ADP
ejpam-7	37	38	the	the	DET
ejpam-7	37	39	class	class	NOUN
ejpam-7	37	40	w4	w4	NOUN
ejpam-7	37	41	[	[	PUNCT
ejpam-7	37	42	[	[	X
ejpam-7	37	43	8	8	NUM
ejpam-7	37	44	]	]	PUNCT
ejpam-7	37	45	,	,	PUNCT
ejpam-7	37	46	[	[	X
ejpam-7	37	47	13	13	NUM
ejpam-7	37	48	]	]	X
ejpam-7	37	49	]	]	PUNCT
ejpam-7	37	50	where	where	SCONJ
ejpam-7	37	51	j	j	PROPN
ejpam-7	37	52	is	be	AUX
ejpam-7	37	53	the	the	DET
ejpam-7	37	54	almost	almost	ADV
ejpam-7	37	55	complex	complex	ADJ
ejpam-7	37	56	structure	structure	NOUN
ejpam-7	37	57	on	on	ADP
ejpam-7	37	58	m	m	PROPN
ejpam-7	37	59	×r	×r	PRON
ejpam-7	37	60	defined	define	VERB
ejpam-7	37	61	by	by	ADP
ejpam-7	37	62	j(x	j(x	PROPN
ejpam-7	37	63	,	,	PUNCT
ejpam-7	37	64	λd	λd	NOUN
ejpam-7	37	65	/	/	SYM
ejpam-7	37	66	dt	dt	NOUN
ejpam-7	37	67	)	)	PUNCT
ejpam-7	37	68	=	=	SYM
ejpam-7	38	1	(	(	PUNCT
ejpam-7	38	2	φx	φx	PROPN
ejpam-7	38	3	−	−	PROPN
ejpam-7	38	4	λξ	λξ	NOUN
ejpam-7	38	5	,	,	PUNCT
ejpam-7	38	6	η(x)d	η(x)d	PROPN
ejpam-7	38	7	/	/	SYM
ejpam-7	38	8	dt	dt	NOUN
ejpam-7	38	9	)	)	PUNCT
ejpam-7	38	10	for	for	ADP
ejpam-7	38	11	all	all	DET
ejpam-7	38	12	vector	vector	NOUN
ejpam-7	38	13	fields	field	NOUN
ejpam-7	38	14	x	x	PUNCT
ejpam-7	38	15	on	on	ADP
ejpam-7	38	16	m	m	PROPN
ejpam-7	38	17	and	and	CCONJ
ejpam-7	38	18	smooth	smooth	ADJ
ejpam-7	38	19	functions	function	NOUN
ejpam-7	38	20	λ	λ	X
ejpam-7	38	21	on	on	ADP
ejpam-7	38	22	m	m	NOUN
ejpam-7	38	23	×r	×r	NOUN
ejpam-7	38	24	and	and	CCONJ
ejpam-7	38	25	g	g	PROPN
ejpam-7	38	26	is	be	AUX
ejpam-7	38	27	the	the	DET
ejpam-7	38	28	product	product	NOUN
ejpam-7	38	29	metric	metric	ADJ
ejpam-7	38	30	on	on	ADP
ejpam-7	38	31	m	m	PROPN
ejpam-7	38	32	×r	×r	ADJ
ejpam-7	38	33	.	.	PUNCT
ejpam-7	39	1	this	this	PRON
ejpam-7	39	2	may	may	AUX
ejpam-7	39	3	be	be	AUX
ejpam-7	39	4	expressed	express	VERB
ejpam-7	39	5	by	by	ADP
ejpam-7	39	6	the	the	DET
ejpam-7	39	7	condition	condition	NOUN
ejpam-7	39	8	[	[	X
ejpam-7	39	9	8	8	NUM
ejpam-7	39	10	]	]	X
ejpam-7	39	11	(	(	PUNCT
ejpam-7	39	12	∇xφ)y	∇xφ)y	PROPN
ejpam-7	39	13	=	=	SYM
ejpam-7	39	14	α(g(x	α(g(x	NUM
ejpam-7	39	15	,	,	PUNCT
ejpam-7	39	16	y	y	NOUN
ejpam-7	39	17	)	)	PUNCT
ejpam-7	40	1	ξ	ξ	PROPN
ejpam-7	40	2	−	−	PROPN
ejpam-7	40	3	η(y	η(y	NOUN
ejpam-7	40	4	)	)	PUNCT
ejpam-7	40	5	x	x	X
ejpam-7	40	6	)	)	PUNCT
ejpam-7	41	1	+	+	CCONJ
ejpam-7	41	2	β(g(φx	β(g(φx	X
ejpam-7	41	3	,	,	PUNCT
ejpam-7	41	4	y	y	PROPN
ejpam-7	41	5	)	)	PUNCT
ejpam-7	41	6	ξ	ξ	PROPN
ejpam-7	41	7	−	−	PROPN
ejpam-7	41	8	η(y	η(y	PROPN
ejpam-7	41	9	)	)	PUNCT
ejpam-7	41	10	φx	φx	X
ejpam-7	41	11	)	)	PUNCT
ejpam-7	41	12	(	(	PUNCT
ejpam-7	41	13	2.8	2.8	NUM
ejpam-7	41	14	)	)	PUNCT
ejpam-7	41	15	for	for	ADP
ejpam-7	41	16	some	some	DET
ejpam-7	41	17	smooth	smooth	ADJ
ejpam-7	41	18	functions	function	NOUN
ejpam-7	41	19	functions	function	NOUN
ejpam-7	41	20	α	α	NOUN
ejpam-7	41	21	and	and	CCONJ
ejpam-7	41	22	β	β	X
ejpam-7	41	23	on	on	ADP
ejpam-7	41	24	m	m	PROPN
ejpam-7	41	25	,	,	PUNCT
ejpam-7	41	26	and	and	CCONJ
ejpam-7	41	27	we	we	PRON
ejpam-7	41	28	say	say	VERB
ejpam-7	41	29	that	that	SCONJ
ejpam-7	41	30	the	the	DET
ejpam-7	41	31	trans	trans	ADJ
ejpam-7	41	32	-	-	ADJ
ejpam-7	41	33	sasakian	sasakian	ADJ
ejpam-7	41	34	structure	structure	NOUN
ejpam-7	41	35	is	be	AUX
ejpam-7	41	36	of	of	ADP
ejpam-7	41	37	type	type	NOUN
ejpam-7	41	38	(	(	PUNCT
ejpam-7	41	39	α	α	NOUN
ejpam-7	41	40	,	,	PUNCT
ejpam-7	41	41	β	β	NOUN
ejpam-7	41	42	)	)	PUNCT
ejpam-7	41	43	.	.	PUNCT
ejpam-7	42	1	let	let	VERB
ejpam-7	42	2	m	m	PRON
ejpam-7	42	3	be	be	AUX
ejpam-7	42	4	a	a	DET
ejpam-7	42	5	n	n	CCONJ
ejpam-7	42	6	-	-	PUNCT
ejpam-7	42	7	dimensional	dimensional	ADJ
ejpam-7	42	8	trans	trans	ADJ
ejpam-7	42	9	-	-	ADJ
ejpam-7	42	10	sasakian	sasakian	ADJ
ejpam-7	42	11	manifold	manifold	NOUN
ejpam-7	42	12	.	.	PUNCT
ejpam-7	43	1	from	from	ADP
ejpam-7	43	2	(	(	PUNCT
ejpam-7	43	3	2.8)it	2.8)it	NUM
ejpam-7	43	4	is	be	AUX
ejpam-7	43	5	easy	easy	ADJ
ejpam-7	43	6	to	to	PART
ejpam-7	43	7	see	see	VERB
ejpam-7	43	8	that	that	DET
ejpam-7	43	9	∇xξ	∇xξ	PROPN
ejpam-7	43	10	=	=	PUNCT
ejpam-7	43	11	−αφx	−αφx	NOUN
ejpam-7	43	12	+	+	PUNCT
ejpam-7	43	13	β(x	β(x	NOUN
ejpam-7	43	14	−	−	PROPN
ejpam-7	43	15	η(x)ξ	η(x)ξ	PROPN
ejpam-7	43	16	)	)	PUNCT
ejpam-7	43	17	,	,	PUNCT
ejpam-7	43	18	(	(	PUNCT
ejpam-7	43	19	2.9	2.9	NUM
ejpam-7	43	20	)	)	PUNCT
ejpam-7	43	21	(	(	PUNCT
ejpam-7	43	22	∇xη)y	∇xη)y	NOUN
ejpam-7	43	23	=	=	SYM
ejpam-7	43	24	−αg(φx	−αg(φx	NOUN
ejpam-7	43	25	,	,	PUNCT
ejpam-7	43	26	y	y	PROPN
ejpam-7	43	27	)	)	PUNCT
ejpam-7	44	1	+	+	CCONJ
ejpam-7	44	2	βg(φx	βg(φx	NOUN
ejpam-7	44	3	,	,	PUNCT
ejpam-7	44	4	φy	φy	NOUN
ejpam-7	44	5	)	)	PUNCT
ejpam-7	44	6	.	.	PUNCT
ejpam-7	45	1	(	(	PUNCT
ejpam-7	45	2	2.10	2.10	NUM
ejpam-7	45	3	)	)	PUNCT
ejpam-7	45	4	in	in	ADP
ejpam-7	45	5	a	a	DET
ejpam-7	45	6	n	n	ADV
ejpam-7	45	7	-	-	PUNCT
ejpam-7	45	8	dimensional	dimensional	ADJ
ejpam-7	45	9	trans	trans	ADJ
ejpam-7	45	10	-	-	ADJ
ejpam-7	45	11	sasakian	sasakian	ADJ
ejpam-7	45	12	manifold	manifold	NOUN
ejpam-7	45	13	,	,	PUNCT
ejpam-7	45	14	we	we	PRON
ejpam-7	45	15	have	have	VERB
ejpam-7	45	16	r(ξ	r(ξ	NOUN
ejpam-7	45	17	,	,	PUNCT
ejpam-7	45	18	x)ξ	x)ξ	PUNCT
ejpam-7	46	1	=	=	SYM
ejpam-7	46	2	(	(	PUNCT
ejpam-7	46	3	α2	α2	ADJ
ejpam-7	46	4	−	−	PROPN
ejpam-7	46	5	β2	β2	PROPN
ejpam-7	46	6	−	−	PROPN
ejpam-7	46	7	ξβ)(η(x)ξ	ξβ)(η(x)ξ	NOUN
ejpam-7	46	8	−x	−x	NOUN
ejpam-7	46	9	)	)	PUNCT
ejpam-7	46	10	,	,	PUNCT
ejpam-7	46	11	(	(	PUNCT
ejpam-7	46	12	2.11	2.11	NUM
ejpam-7	46	13	)	)	PUNCT
ejpam-7	46	14	2αβ	2αβ	NOUN
ejpam-7	46	15	+	+	CCONJ
ejpam-7	46	16	ξα	ξα	ADJ
ejpam-7	46	17	=	=	NUM
ejpam-7	46	18	0	0	NUM
ejpam-7	46	19	,	,	PUNCT
ejpam-7	46	20	(	(	PUNCT
ejpam-7	46	21	2.12	2.12	NUM
ejpam-7	46	22	)	)	PUNCT
ejpam-7	46	23	s(x	s(x	PROPN
ejpam-7	46	24	,	,	PUNCT
ejpam-7	46	25	ξ	ξ	X
ejpam-7	46	26	)	)	PUNCT
ejpam-7	46	27	=	=	SYM
ejpam-7	46	28	(	(	PUNCT
ejpam-7	46	29	(	(	PUNCT
ejpam-7	46	30	n−	n−	NOUN
ejpam-7	46	31	1)(α2	1)(α2	NUM
ejpam-7	46	32	−	−	NOUN
ejpam-7	46	33	β2)−	β2)−	PROPN
ejpam-7	46	34	ξβ)η(x)−	ξβ)η(x)−	PROPN
ejpam-7	46	35	(	(	PUNCT
ejpam-7	46	36	n−	n−	NOUN
ejpam-7	46	37	2)xβ	2)xβ	NUM
ejpam-7	46	38	−	−	NOUN
ejpam-7	46	39	(	(	PUNCT
ejpam-7	46	40	φx)α	φx)α	PROPN
ejpam-7	46	41	.	.	PUNCT
ejpam-7	47	1	(	(	PUNCT
ejpam-7	47	2	2.13	2.13	NUM
ejpam-7	47	3	)	)	PUNCT
ejpam-7	47	4	if	if	SCONJ
ejpam-7	47	5	in	in	ADP
ejpam-7	47	6	a	a	DET
ejpam-7	47	7	n	n	ADV
ejpam-7	47	8	-	-	PUNCT
ejpam-7	47	9	dimensional	dimensional	ADJ
ejpam-7	47	10	trans	tran	NOUN
ejpam-7	47	11	sasakian	sasakian	NOUN
ejpam-7	47	12	manifold	manifold	NOUN
ejpam-7	47	13	of	of	ADP
ejpam-7	47	14	type(α	type(α	PROPN
ejpam-7	47	15	,	,	PUNCT
ejpam-7	47	16	β	β	NOUN
ejpam-7	47	17	)	)	PUNCT
ejpam-7	47	18	,	,	PUNCT
ejpam-7	47	19	we	we	PRON
ejpam-7	47	20	have	have	VERB
ejpam-7	47	21	[	[	X
ejpam-7	47	22	4	4	NUM
ejpam-7	47	23	]	]	X
ejpam-7	47	24	φ(gradα	φ(gradα	X
ejpam-7	47	25	)	)	PUNCT
ejpam-7	47	26	=	=	PUNCT
ejpam-7	48	1	(	(	PUNCT
ejpam-7	48	2	n−	n−	NOUN
ejpam-7	48	3	2)gradβ	2)gradβ	NUM
ejpam-7	48	4	,	,	PUNCT
ejpam-7	48	5	(	(	PUNCT
ejpam-7	48	6	2.14	2.14	NUM
ejpam-7	48	7	)	)	PUNCT
ejpam-7	48	8	bagewadi	bagewadi	PROPN
ejpam-7	48	9	c.s	c.s	PROPN
ejpam-7	48	10	.	.	PROPN
ejpam-7	48	11	et	et	PROPN
ejpam-7	48	12	al	al	PROPN
ejpam-7	48	13	.	.	PUNCT
ejpam-7	48	14	/	/	SYM
ejpam-7	48	15	eur	eur	PROPN
ejpam-7	48	16	.	.	PUNCT
ejpam-7	49	1	j.	j.	PROPN
ejpam-7	49	2	pure	pure	PROPN
ejpam-7	49	3	appl	appl	PROPN
ejpam-7	49	4	.	.	PROPN
ejpam-7	49	5	math	math	PROPN
ejpam-7	49	6	,	,	PUNCT
ejpam-7	49	7	1	1	NUM
ejpam-7	49	8	(	(	PUNCT
ejpam-7	49	9	2008	2008	NUM
ejpam-7	49	10	)	)	PUNCT
ejpam-7	49	11	,	,	PUNCT
ejpam-7	49	12	(	(	PUNCT
ejpam-7	49	13	21	21	NUM
ejpam-7	49	14	-	-	SYM
ejpam-7	49	15	31	31	NUM
ejpam-7	49	16	)	)	PUNCT
ejpam-7	49	17	23	23	NUM
ejpam-7	49	18	then	then	ADV
ejpam-7	49	19	(	(	PUNCT
ejpam-7	49	20	2.11	2.11	NUM
ejpam-7	49	21	)	)	PUNCT
ejpam-7	49	22	and	and	CCONJ
ejpam-7	49	23	(	(	PUNCT
ejpam-7	49	24	2.13	2.13	NUM
ejpam-7	49	25	)	)	PUNCT
ejpam-7	49	26	reduces	reduce	VERB
ejpam-7	49	27	to	to	ADP
ejpam-7	49	28	r(ξ	r(ξ	NOUN
ejpam-7	49	29	,	,	PUNCT
ejpam-7	49	30	x)ξ	x)ξ	PUNCT
ejpam-7	49	31	=	=	SYM
ejpam-7	49	32	(	(	PUNCT
ejpam-7	49	33	α2	α2	PROPN
ejpam-7	49	34	−	−	PROPN
ejpam-7	49	35	β2)(η(x)ξ	β2)(η(x)ξ	NOUN
ejpam-7	49	36	−x	−x	NOUN
ejpam-7	49	37	)	)	PUNCT
ejpam-7	49	38	,	,	PUNCT
ejpam-7	49	39	(	(	PUNCT
ejpam-7	49	40	2.15	2.15	NUM
ejpam-7	49	41	)	)	PUNCT
ejpam-7	49	42	s(x	s(x	PROPN
ejpam-7	49	43	,	,	PUNCT
ejpam-7	49	44	ξ	ξ	X
ejpam-7	49	45	)	)	PUNCT
ejpam-7	49	46	=	=	SYM
ejpam-7	50	1	(	(	PUNCT
ejpam-7	50	2	n−	n−	NOUN
ejpam-7	50	3	1)(α2	1)(α2	NUM
ejpam-7	50	4	−	−	NOUN
ejpam-7	50	5	β2)η(x	β2)η(x	NOUN
ejpam-7	50	6	)	)	PUNCT
ejpam-7	50	7	.	.	PUNCT
ejpam-7	51	1	(	(	PUNCT
ejpam-7	51	2	2.16	2.16	NUM
ejpam-7	51	3	)	)	PUNCT
ejpam-7	51	4	in	in	ADP
ejpam-7	51	5	this	this	DET
ejpam-7	51	6	paper	paper	NOUN
ejpam-7	51	7	we	we	PRON
ejpam-7	51	8	study	study	VERB
ejpam-7	51	9	trans	trans	PROPN
ejpam-7	51	10	sasakian	sasakian	PROPN
ejpam-7	51	11	manifold	manifold	ADJ
ejpam-7	51	12	under	under	ADP
ejpam-7	51	13	the	the	DET
ejpam-7	51	14	condition	condition	NOUN
ejpam-7	51	15	(	(	PUNCT
ejpam-7	51	16	2.14	2.14	NUM
ejpam-7	51	17	)	)	PUNCT
ejpam-7	51	18	.	.	PUNCT
ejpam-7	52	1	let	let	AUX
ejpam-7	52	2	(	(	PUNCT
ejpam-7	52	3	mn	mn	NOUN
ejpam-7	52	4	,	,	PUNCT
ejpam-7	52	5	g	g	NOUN
ejpam-7	52	6	)	)	PUNCT
ejpam-7	52	7	be	be	VERB
ejpam-7	52	8	an	an	DET
ejpam-7	52	9	n	n	ADV
ejpam-7	52	10	-	-	PUNCT
ejpam-7	52	11	dimensional	dimensional	ADJ
ejpam-7	52	12	riemannian	riemannian	ADJ
ejpam-7	52	13	manifold	manifold	NOUN
ejpam-7	52	14	of	of	ADP
ejpam-7	52	15	class	class	NOUN
ejpam-7	52	16	c∞	c∞	PROPN
ejpam-7	52	17	with	with	ADP
ejpam-7	52	18	metric	metric	ADJ
ejpam-7	52	19	tensor	tensor	NOUN
ejpam-7	52	20	g	g	NOUN
ejpam-7	52	21	and	and	CCONJ
ejpam-7	52	22	let	let	VERB
ejpam-7	52	23	∇	∇	PROPN
ejpam-7	52	24	be	be	AUX
ejpam-7	52	25	the	the	DET
ejpam-7	52	26	levi	levi	PROPN
ejpam-7	52	27	-	-	PUNCT
ejpam-7	52	28	civita	civita	PROPN
ejpam-7	52	29	connection	connection	NOUN
ejpam-7	52	30	on	on	ADP
ejpam-7	52	31	mn	mn	PROPN
ejpam-7	52	32	.	.	PUNCT
ejpam-7	53	1	a	a	DET
ejpam-7	53	2	linear	linear	ADJ
ejpam-7	53	3	connection	connection	NOUN
ejpam-7	53	4	∇̃	∇̃	X
ejpam-7	54	1	on	on	ADP
ejpam-7	54	2	(	(	PUNCT
ejpam-7	54	3	mn	mn	PROPN
ejpam-7	54	4	,	,	PUNCT
ejpam-7	54	5	g	g	NOUN
ejpam-7	54	6	)	)	PUNCT
ejpam-7	54	7	is	be	AUX
ejpam-7	54	8	said	say	VERB
ejpam-7	54	9	to	to	PART
ejpam-7	54	10	be	be	AUX
ejpam-7	54	11	semi	semi	ADV
ejpam-7	54	12	symmetric	symmetric	ADJ
ejpam-7	54	13	[	[	X
ejpam-7	54	14	16	16	NUM
ejpam-7	54	15	]	]	PUNCT
ejpam-7	54	16	if	if	SCONJ
ejpam-7	54	17	the	the	DET
ejpam-7	54	18	torsion	torsion	NOUN
ejpam-7	54	19	tensor	tensor	NOUN
ejpam-7	54	20	t	t	NOUN
ejpam-7	54	21	of	of	ADP
ejpam-7	54	22	the	the	DET
ejpam-7	54	23	connection	connection	NOUN
ejpam-7	54	24	∇̃	∇̃	NUM
ejpam-7	54	25	satisfies	satisfy	VERB
ejpam-7	54	26	t	t	PROPN
ejpam-7	54	27	(	(	PUNCT
ejpam-7	54	28	x	x	X
ejpam-7	54	29	,	,	PUNCT
ejpam-7	54	30	y	y	PROPN
ejpam-7	54	31	)	)	PUNCT
ejpam-7	54	32	=	=	PUNCT
ejpam-7	55	1	π(y	π(y	PROPN
ejpam-7	55	2	)	)	PUNCT
ejpam-7	55	3	x	x	SYM
ejpam-7	56	1	−	−	PROPN
ejpam-7	56	2	π(x)y	π(x)y	PROPN
ejpam-7	56	3	,	,	PUNCT
ejpam-7	56	4	(	(	PUNCT
ejpam-7	56	5	2.17	2.17	NUM
ejpam-7	56	6	)	)	PUNCT
ejpam-7	56	7	where	where	SCONJ
ejpam-7	56	8	π	π	PROPN
ejpam-7	56	9	is	be	AUX
ejpam-7	56	10	a	a	DET
ejpam-7	56	11	1	1	NUM
ejpam-7	56	12	-	-	PUNCT
ejpam-7	56	13	form	form	NOUN
ejpam-7	56	14	on	on	ADP
ejpam-7	56	15	mn	mn	PROPN
ejpam-7	56	16	with	with	ADP
ejpam-7	56	17	ρ	ρ	PROPN
ejpam-7	56	18	as	as	ADP
ejpam-7	56	19	associated	associate	VERB
ejpam-7	56	20	vector	vector	NOUN
ejpam-7	56	21	field	field	NOUN
ejpam-7	56	22	,	,	PUNCT
ejpam-7	56	23	i.e.	i.e.	X
ejpam-7	56	24	,	,	PUNCT
ejpam-7	56	25	π(x	π(x	NOUN
ejpam-7	56	26	)	)	PUNCT
ejpam-7	56	27	=	=	SYM
ejpam-7	57	1	g(x	g(x	NOUN
ejpam-7	57	2	,	,	PUNCT
ejpam-7	57	3	ρ	ρ	NOUN
ejpam-7	57	4	)	)	PUNCT
ejpam-7	57	5	for	for	ADP
ejpam-7	57	6	any	any	DET
ejpam-7	57	7	differentiable	differentiable	ADJ
ejpam-7	57	8	vector	vector	NOUN
ejpam-7	57	9	field	field	NOUN
ejpam-7	57	10	x	x	PUNCT
ejpam-7	57	11	on	on	ADP
ejpam-7	57	12	mn	mn	PROPN
ejpam-7	57	13	.	.	PUNCT
ejpam-7	58	1	a	a	DET
ejpam-7	58	2	semi	semi	ADJ
ejpam-7	58	3	-	-	ADJ
ejpam-7	58	4	symmetric	symmetric	ADJ
ejpam-7	58	5	connection	connection	NOUN
ejpam-7	58	6	∇̃	∇̃	PRON
ejpam-7	58	7	is	be	AUX
ejpam-7	58	8	called	call	VERB
ejpam-7	58	9	semi	semi	ADJ
ejpam-7	58	10	-	-	ADJ
ejpam-7	58	11	symmetric	symmetric	ADJ
ejpam-7	58	12	metric	metric	ADJ
ejpam-7	58	13	connection	connection	NOUN
ejpam-7	58	14	[	[	X
ejpam-7	58	15	5	5	X
ejpam-7	58	16	]	]	PUNCT
ejpam-7	58	17	if	if	SCONJ
ejpam-7	58	18	it	it	PRON
ejpam-7	58	19	further	far	ADV
ejpam-7	58	20	satisfies	satisfy	VERB
ejpam-7	58	21	∇̃g	∇̃g	X
ejpam-7	58	22	=	=	PUNCT
ejpam-7	59	1	0	0	X
ejpam-7	59	2	.	.	PUNCT
ejpam-7	60	1	in	in	ADP
ejpam-7	60	2	an	an	DET
ejpam-7	60	3	almost	almost	ADV
ejpam-7	60	4	contact	contact	NOUN
ejpam-7	60	5	manifold	manifold	ADJ
ejpam-7	60	6	semi	semi	ADJ
ejpam-7	60	7	-	-	ADJ
ejpam-7	60	8	symmetric	symmetric	ADJ
ejpam-7	60	9	metric	metric	ADJ
ejpam-7	60	10	connection	connection	NOUN
ejpam-7	60	11	is	be	AUX
ejpam-7	60	12	defined	define	VERB
ejpam-7	60	13	by	by	ADP
ejpam-7	60	14	identifying	identify	VERB
ejpam-7	60	15	the	the	DET
ejpam-7	60	16	1	1	NUM
ejpam-7	60	17	-	-	PUNCT
ejpam-7	60	18	form	form	NOUN
ejpam-7	60	19	π	π	PROPN
ejpam-7	60	20	of	of	ADP
ejpam-7	60	21	(	(	PUNCT
ejpam-7	60	22	2.17	2.17	NUM
ejpam-7	60	23	)	)	PUNCT
ejpam-7	60	24	with	with	ADP
ejpam-7	60	25	the	the	DET
ejpam-7	60	26	contact	contact	NOUN
ejpam-7	60	27	-	-	PUNCT
ejpam-7	60	28	form	form	NOUN
ejpam-7	60	29	η	η	NOUN
ejpam-7	60	30	,	,	PUNCT
ejpam-7	60	31	i.e.	i.e.	X
ejpam-7	60	32	,	,	PUNCT
ejpam-7	60	33	by	by	ADP
ejpam-7	60	34	setting	set	VERB
ejpam-7	60	35	[	[	X
ejpam-7	60	36	16	16	NUM
ejpam-7	60	37	]	]	X
ejpam-7	60	38	t	t	PROPN
ejpam-7	60	39	(	(	PUNCT
ejpam-7	60	40	x	x	X
ejpam-7	60	41	,	,	PUNCT
ejpam-7	60	42	y	y	PROPN
ejpam-7	60	43	)	)	PUNCT
ejpam-7	60	44	=	=	SYM
ejpam-7	60	45	η(y	η(y	NOUN
ejpam-7	60	46	)	)	PUNCT
ejpam-7	60	47	x	x	PUNCT
ejpam-7	61	1	−	−	PROPN
ejpam-7	61	2	η(x)y	η(x)y	PROPN
ejpam-7	61	3	(	(	PUNCT
ejpam-7	61	4	2.18	2.18	NUM
ejpam-7	61	5	)	)	PUNCT
ejpam-7	61	6	with	with	ADP
ejpam-7	61	7	ξ	ξ	PROPN
ejpam-7	61	8	as	as	ADP
ejpam-7	61	9	associated	associate	VERB
ejpam-7	61	10	vector	vector	NOUN
ejpam-7	61	11	field	field	NOUN
ejpam-7	61	12	.	.	PUNCT
ejpam-7	62	1	i.e.	i.e.	X
ejpam-7	62	2	,	,	PUNCT
ejpam-7	62	3	g(x	g(x	NOUN
ejpam-7	62	4	,	,	PUNCT
ejpam-7	62	5	ξ	ξ	NOUN
ejpam-7	62	6	)	)	PUNCT
ejpam-7	62	7	=	=	SYM
ejpam-7	62	8	η(x	η(x	NOUN
ejpam-7	62	9	)	)	PUNCT
ejpam-7	62	10	.	.	PUNCT
ejpam-7	63	1	the	the	DET
ejpam-7	63	2	relation	relation	NOUN
ejpam-7	63	3	between	between	ADP
ejpam-7	63	4	the	the	DET
ejpam-7	63	5	semi	semi	ADJ
ejpam-7	63	6	-	-	ADJ
ejpam-7	63	7	symmetric	symmetric	ADJ
ejpam-7	63	8	metric	metric	ADJ
ejpam-7	63	9	connection	connection	NOUN
ejpam-7	63	10	∇̃	∇̃	PRON
ejpam-7	63	11	and	and	CCONJ
ejpam-7	63	12	the	the	DET
ejpam-7	63	13	levi	levi	PROPN
ejpam-7	63	14	-	-	PUNCT
ejpam-7	63	15	civita	civita	PROPN
ejpam-7	63	16	connection	connection	NOUN
ejpam-7	63	17	∇	∇	X
ejpam-7	63	18	of	of	ADP
ejpam-7	63	19	(	(	PUNCT
ejpam-7	63	20	mn	mn	PROPN
ejpam-7	63	21	,	,	PUNCT
ejpam-7	63	22	g	g	NOUN
ejpam-7	63	23	)	)	PUNCT
ejpam-7	63	24	has	have	AUX
ejpam-7	63	25	been	be	AUX
ejpam-7	63	26	obtained	obtain	VERB
ejpam-7	63	27	by	by	ADP
ejpam-7	63	28	k.yano	k.yano	NOUN
ejpam-7	64	1	[	[	X
ejpam-7	64	2	18	18	NUM
ejpam-7	64	3	]	]	PUNCT
ejpam-7	64	4	,	,	PUNCT
ejpam-7	64	5	which	which	PRON
ejpam-7	64	6	is	be	AUX
ejpam-7	64	7	given	give	VERB
ejpam-7	64	8	by	by	ADP
ejpam-7	64	9	∇̃xy	∇̃xy	PRON
ejpam-7	64	10	=	=	SYM
ejpam-7	64	11	∇xy	∇xy	PROPN
ejpam-7	64	12	+	+	NUM
ejpam-7	64	13	η(y	η(y	NOUN
ejpam-7	64	14	)	)	PUNCT
ejpam-7	64	15	x	x	SYM
ejpam-7	64	16	−	−	PROPN
ejpam-7	64	17	g(x	g(x	NOUN
ejpam-7	64	18	,	,	PUNCT
ejpam-7	64	19	y	y	PROPN
ejpam-7	64	20	)	)	PUNCT
ejpam-7	64	21	ξ	ξ	PROPN
ejpam-7	64	22	,	,	PUNCT
ejpam-7	64	23	(	(	PUNCT
ejpam-7	64	24	2.19	2.19	NUM
ejpam-7	64	25	)	)	PUNCT
ejpam-7	64	26	where	where	SCONJ
ejpam-7	64	27	η(y	η(y	NOUN
ejpam-7	64	28	)	)	PUNCT
ejpam-7	65	1	=	=	PUNCT
ejpam-7	65	2	g(y	g(y	PROPN
ejpam-7	65	3	,	,	PUNCT
ejpam-7	65	4	ξ	ξ	NOUN
ejpam-7	65	5	)	)	PUNCT
ejpam-7	65	6	.	.	PUNCT
ejpam-7	66	1	further	far	ADV
ejpam-7	66	2	,	,	PUNCT
ejpam-7	66	3	a	a	DET
ejpam-7	66	4	relation	relation	NOUN
ejpam-7	66	5	between	between	ADP
ejpam-7	66	6	the	the	DET
ejpam-7	66	7	curvature	curvature	NOUN
ejpam-7	66	8	tensor	tensor	NOUN
ejpam-7	66	9	r	r	NOUN
ejpam-7	66	10	and	and	CCONJ
ejpam-7	66	11	r̃	r̃	NOUN
ejpam-7	66	12	of	of	ADP
ejpam-7	66	13	type	type	NOUN
ejpam-7	66	14	(	(	PUNCT
ejpam-7	66	15	1	1	NUM
ejpam-7	66	16	,	,	PUNCT
ejpam-7	66	17	3	3	NUM
ejpam-7	66	18	)	)	PUNCT
ejpam-7	66	19	of	of	ADP
ejpam-7	66	20	the	the	DET
ejpam-7	66	21	connections	connection	NOUN
ejpam-7	66	22	∇	∇	X
ejpam-7	66	23	and	and	CCONJ
ejpam-7	66	24	∇̃	∇̃	PRON
ejpam-7	66	25	respectively	respectively	ADV
ejpam-7	66	26	is	be	AUX
ejpam-7	66	27	given	give	VERB
ejpam-7	66	28	by	by	ADP
ejpam-7	66	29	[	[	X
ejpam-7	66	30	18	18	NUM
ejpam-7	66	31	]	]	PUNCT
ejpam-7	66	32	.	.	PUNCT
ejpam-7	67	1	r̃(x	r̃(x	PROPN
ejpam-7	67	2	,	,	PUNCT
ejpam-7	67	3	y	y	PROPN
ejpam-7	67	4	)	)	PUNCT
ejpam-7	67	5	z	z	PROPN
ejpam-7	67	6	=	=	SYM
ejpam-7	67	7	r(x	r(x	PROPN
ejpam-7	67	8	,	,	PUNCT
ejpam-7	67	9	y	y	NOUN
ejpam-7	67	10	)	)	PUNCT
ejpam-7	67	11	z	z	NOUN
ejpam-7	67	12	−k(y	−k(y	NOUN
ejpam-7	67	13	,	,	PUNCT
ejpam-7	67	14	z)x	z)x	X
ejpam-7	67	15	+	+	SYM
ejpam-7	67	16	k(x	k(x	NOUN
ejpam-7	67	17	,	,	PUNCT
ejpam-7	67	18	z)y	z)y	NOUN
ejpam-7	67	19	−	−	PROPN
ejpam-7	67	20	g(y	g(y	PROPN
ejpam-7	67	21	,	,	PUNCT
ejpam-7	67	22	z)fx	z)fx	PROPN
ejpam-7	67	23	+	+	CCONJ
ejpam-7	67	24	g(x	g(x	PROPN
ejpam-7	67	25	,	,	PUNCT
ejpam-7	67	26	z)fy	z)fy	PROPN
ejpam-7	67	27	.	.	PUNCT
ejpam-7	67	28	(	(	PUNCT
ejpam-7	67	29	2.20	2.20	NUM
ejpam-7	67	30	)	)	PUNCT
ejpam-7	67	31	where	where	SCONJ
ejpam-7	67	32	k	k	PROPN
ejpam-7	67	33	is	be	AUX
ejpam-7	67	34	a	a	DET
ejpam-7	67	35	tensor	tensor	NOUN
ejpam-7	67	36	field	field	NOUN
ejpam-7	67	37	of	of	ADP
ejpam-7	67	38	type	type	NOUN
ejpam-7	67	39	(	(	PUNCT
ejpam-7	67	40	0	0	NUM
ejpam-7	67	41	,	,	PUNCT
ejpam-7	67	42	2	2	NUM
ejpam-7	67	43	)	)	PUNCT
ejpam-7	67	44	defined	define	VERB
ejpam-7	67	45	by	by	ADP
ejpam-7	67	46	k(y	k(y	PROPN
ejpam-7	67	47	,	,	PUNCT
ejpam-7	67	48	z	z	NOUN
ejpam-7	67	49	)	)	PUNCT
ejpam-7	67	50	=	=	SYM
ejpam-7	67	51	g(fy	g(fy	PROPN
ejpam-7	67	52	,	,	PUNCT
ejpam-7	67	53	z	z	NOUN
ejpam-7	67	54	)	)	PUNCT
ejpam-7	67	55	=	=	SYM
ejpam-7	67	56	(	(	PUNCT
ejpam-7	67	57	∇y	∇y	PROPN
ejpam-7	67	58	η)(z)−	η)(z)−	PROPN
ejpam-7	67	59	η(y	η(y	PROPN
ejpam-7	67	60	)	)	PUNCT
ejpam-7	67	61	η(z	η(z	PROPN
ejpam-7	67	62	)	)	PUNCT
ejpam-7	68	1	+	+	CCONJ
ejpam-7	68	2	1	1	NUM
ejpam-7	68	3	2	2	NUM
ejpam-7	68	4	η(ξ)g(y	η(ξ)g(y	NOUN
ejpam-7	68	5	,	,	PUNCT
ejpam-7	68	6	z	z	NOUN
ejpam-7	68	7	)	)	PUNCT
ejpam-7	68	8	,	,	PUNCT
ejpam-7	68	9	(	(	PUNCT
ejpam-7	68	10	2.21	2.21	NUM
ejpam-7	68	11	)	)	PUNCT
ejpam-7	68	12	for	for	ADP
ejpam-7	68	13	any	any	DET
ejpam-7	68	14	vector	vector	NOUN
ejpam-7	68	15	fields	field	NOUN
ejpam-7	68	16	x	x	PUNCT
ejpam-7	68	17	and	and	CCONJ
ejpam-7	68	18	y	y	PROPN
ejpam-7	68	19	.	.	PUNCT
ejpam-7	69	1	from	from	ADP
ejpam-7	69	2	(	(	PUNCT
ejpam-7	69	3	2.20	2.20	NUM
ejpam-7	69	4	)	)	PUNCT
ejpam-7	69	5	,	,	PUNCT
ejpam-7	69	6	it	it	PRON
ejpam-7	69	7	follows	follow	VERB
ejpam-7	69	8	that	that	SCONJ
ejpam-7	69	9	s̃(y	s̃(y	PROPN
ejpam-7	69	10	,	,	PUNCT
ejpam-7	69	11	z	z	NOUN
ejpam-7	69	12	)	)	PUNCT
ejpam-7	69	13	=	=	SYM
ejpam-7	69	14	s(y	s(y	PROPN
ejpam-7	69	15	,	,	PUNCT
ejpam-7	69	16	z)−	z)−	PROPN
ejpam-7	69	17	(	(	PUNCT
ejpam-7	69	18	n−	n−	NOUN
ejpam-7	69	19	2)k(y	2)k(y	NUM
ejpam-7	69	20	,	,	PUNCT
ejpam-7	69	21	z)−	z)−	NUM
ejpam-7	69	22	a.g(y	a.g(y	NOUN
ejpam-7	69	23	,	,	PUNCT
ejpam-7	69	24	z	z	NOUN
ejpam-7	69	25	)	)	PUNCT
ejpam-7	69	26	(	(	PUNCT
ejpam-7	69	27	2.22	2.22	NUM
ejpam-7	69	28	)	)	PUNCT
ejpam-7	69	29	where	where	SCONJ
ejpam-7	69	30	s̃	s̃	PROPN
ejpam-7	69	31	denotes	denote	VERB
ejpam-7	69	32	the	the	DET
ejpam-7	69	33	ricci	ricci	PROPN
ejpam-7	69	34	tensor	tensor	NOUN
ejpam-7	69	35	with	with	ADP
ejpam-7	69	36	respect	respect	NOUN
ejpam-7	69	37	to	to	ADP
ejpam-7	69	38	∇̃	∇̃	PRON
ejpam-7	69	39	and	and	CCONJ
ejpam-7	69	40	a	a	DET
ejpam-7	69	41	=	=	PUNCT
ejpam-7	69	42	tr.k	tr.k	NOUN
ejpam-7	69	43	.	.	PUNCT
ejpam-7	70	1	differentiating	differentiate	VERB
ejpam-7	70	2	(	(	PUNCT
ejpam-7	70	3	2.22	2.22	NUM
ejpam-7	70	4	)	)	PUNCT
ejpam-7	70	5	covariantly	covariantly	ADV
ejpam-7	70	6	with	with	ADP
ejpam-7	70	7	respect	respect	NOUN
ejpam-7	70	8	to	to	ADP
ejpam-7	70	9	x	x	SYM
ejpam-7	70	10	,	,	PUNCT
ejpam-7	70	11	we	we	PRON
ejpam-7	70	12	obtain	obtain	VERB
ejpam-7	70	13	[	[	X
ejpam-7	70	14	6	6	NUM
ejpam-7	70	15	]	]	PUNCT
ejpam-7	70	16	(	(	PUNCT
ejpam-7	70	17	∇̃x	∇̃x	NOUN
ejpam-7	70	18	s̃)(y	s̃)(y	ADJ
ejpam-7	70	19	,	,	PUNCT
ejpam-7	70	20	z	z	NOUN
ejpam-7	70	21	)	)	PUNCT
ejpam-7	70	22	=	=	SYM
ejpam-7	70	23	(	(	PUNCT
ejpam-7	70	24	∇xs)(y	∇xs)(y	PROPN
ejpam-7	70	25	,	,	PUNCT
ejpam-7	70	26	z)−	z)−	PROPN
ejpam-7	70	27	(	(	PUNCT
ejpam-7	70	28	n−	n−	NOUN
ejpam-7	70	29	2)(∇xk)(y	2)(∇xk)(y	NUM
ejpam-7	70	30	,	,	PUNCT
ejpam-7	70	31	z)−	z)−	PROPN
ejpam-7	70	32	η(y	η(y	PROPN
ejpam-7	70	33	)	)	PUNCT
ejpam-7	71	1	s(x	s(x	PROPN
ejpam-7	71	2	,	,	PUNCT
ejpam-7	71	3	z)−	z)−	PROPN
ejpam-7	71	4	η(z)s(x	η(z)s(x	PROPN
ejpam-7	71	5	,	,	PUNCT
ejpam-7	71	6	y	y	PROPN
ejpam-7	71	7	)	)	PUNCT
ejpam-7	72	1	+	+	PROPN
ejpam-7	72	2	(	(	PUNCT
ejpam-7	72	3	n−	n−	NOUN
ejpam-7	72	4	2)η(y	2)η(y	NUM
ejpam-7	72	5	)	)	PUNCT
ejpam-7	73	1	k(x	k(x	PROPN
ejpam-7	73	2	,	,	PUNCT
ejpam-7	73	3	z	z	NOUN
ejpam-7	73	4	)	)	PUNCT
ejpam-7	74	1	+	+	CCONJ
ejpam-7	74	2	(	(	PUNCT
ejpam-7	74	3	n−	n−	NOUN
ejpam-7	74	4	2)η(z)k(y	2)η(z)k(y	NUM
ejpam-7	74	5	,	,	PUNCT
ejpam-7	74	6	x	x	X
ejpam-7	74	7	)	)	PUNCT
ejpam-7	75	1	+	+	CCONJ
ejpam-7	75	2	g(x	g(x	PROPN
ejpam-7	75	3	,	,	PUNCT
ejpam-7	75	4	y	y	NOUN
ejpam-7	75	5	)	)	PUNCT
ejpam-7	75	6	s(ξ	s(ξ	PROPN
ejpam-7	75	7	,	,	PUNCT
ejpam-7	75	8	z	z	NOUN
ejpam-7	75	9	)	)	PUNCT
ejpam-7	76	1	+	+	ADV
ejpam-7	76	2	g(x	g(x	NOUN
ejpam-7	76	3	,	,	PUNCT
ejpam-7	76	4	z)s(y	z)s(y	NUM
ejpam-7	76	5	,	,	PUNCT
ejpam-7	76	6	ξ)−	ξ)−	PROPN
ejpam-7	76	7	(	(	PUNCT
ejpam-7	76	8	n−	n−	NOUN
ejpam-7	76	9	2)g(x	2)g(x	NUM
ejpam-7	76	10	,	,	PUNCT
ejpam-7	76	11	z)k(y	z)k(y	NOUN
ejpam-7	76	12	,	,	PUNCT
ejpam-7	76	13	ξ)−	ξ)−	PROPN
ejpam-7	76	14	(	(	PUNCT
ejpam-7	76	15	n−	n−	NOUN
ejpam-7	76	16	2)g(x	2)g(x	NUM
ejpam-7	76	17	,	,	PUNCT
ejpam-7	76	18	y	y	PROPN
ejpam-7	76	19	)	)	PUNCT
ejpam-7	76	20	k(z	k(z	PROPN
ejpam-7	76	21	,	,	PUNCT
ejpam-7	76	22	ξ)(2.23	ξ)(2.23	PROPN
ejpam-7	76	23	)	)	PUNCT
ejpam-7	76	24	bagewadi	bagewadi	PROPN
ejpam-7	76	25	c.s	c.s	PROPN
ejpam-7	76	26	.	.	PROPN
ejpam-7	76	27	et	et	PROPN
ejpam-7	76	28	al	al	PROPN
ejpam-7	76	29	.	.	PUNCT
ejpam-7	76	30	/	/	SYM
ejpam-7	76	31	eur	eur	PROPN
ejpam-7	76	32	.	.	PUNCT
ejpam-7	77	1	j.	j.	PROPN
ejpam-7	77	2	pure	pure	PROPN
ejpam-7	77	3	appl	appl	PROPN
ejpam-7	77	4	.	.	PROPN
ejpam-7	77	5	math	math	PROPN
ejpam-7	77	6	,	,	PUNCT
ejpam-7	77	7	1	1	NUM
ejpam-7	77	8	(	(	PUNCT
ejpam-7	77	9	2008	2008	NUM
ejpam-7	77	10	)	)	PUNCT
ejpam-7	77	11	,	,	PUNCT
ejpam-7	77	12	(	(	PUNCT
ejpam-7	77	13	21	21	NUM
ejpam-7	77	14	-	-	SYM
ejpam-7	77	15	31	31	NUM
ejpam-7	77	16	)	)	PUNCT
ejpam-7	77	17	24	24	NUM
ejpam-7	77	18	now	now	ADV
ejpam-7	77	19	let	let	VERB
ejpam-7	77	20	ei	ei	PART
ejpam-7	77	21	be	be	AUX
ejpam-7	77	22	an	an	DET
ejpam-7	77	23	orthogonal	orthogonal	ADJ
ejpam-7	77	24	basis	basis	NOUN
ejpam-7	77	25	of	of	ADP
ejpam-7	77	26	the	the	DET
ejpam-7	77	27	tangent	tangent	ADJ
ejpam-7	77	28	space	space	NOUN
ejpam-7	77	29	at	at	ADP
ejpam-7	77	30	each	each	DET
ejpam-7	77	31	point	point	NOUN
ejpam-7	77	32	of	of	ADP
ejpam-7	77	33	the	the	DET
ejpam-7	77	34	manifold	manifold	ADJ
ejpam-7	77	35	mn	mn	PROPN
ejpam-7	77	36	for	for	ADP
ejpam-7	77	37	i	i	PROPN
ejpam-7	77	38	=	=	NOUN
ejpam-7	77	39	1	1	NUM
ejpam-7	77	40	,	,	PUNCT
ejpam-7	77	41	2	2	NUM
ejpam-7	77	42	,	,	PUNCT
ejpam-7	77	43	....	....	PUNCT
ejpam-7	77	44	,	,	PUNCT
ejpam-7	77	45	n.	n.	PROPN
ejpam-7	77	46	putting	put	VERB
ejpam-7	77	47	y	y	NOUN
ejpam-7	77	48	=	=	PUNCT
ejpam-7	77	49	z	z	NOUN
ejpam-7	77	50	=	=	PUNCT
ejpam-7	77	51	ei	ei	NOUN
ejpam-7	77	52	in	in	ADP
ejpam-7	77	53	(	(	PUNCT
ejpam-7	77	54	2.23	2.23	NUM
ejpam-7	77	55	)	)	PUNCT
ejpam-7	77	56	and	and	CCONJ
ejpam-7	77	57	then	then	ADV
ejpam-7	77	58	taking	take	VERB
ejpam-7	77	59	summation	summation	NOUN
ejpam-7	77	60	over	over	ADP
ejpam-7	77	61	the	the	DET
ejpam-7	77	62	index	index	NOUN
ejpam-7	77	63	i	i	PRON
ejpam-7	77	64	,	,	PUNCT
ejpam-7	77	65	we	we	PRON
ejpam-7	77	66	get	get	VERB
ejpam-7	77	67	∇̃x	∇̃x	PRON
ejpam-7	77	68	r̃	r̃	NOUN
ejpam-7	77	69	=	=	SYM
ejpam-7	77	70	∇xr	∇xr	NOUN
ejpam-7	77	71	−	−	PROPN
ejpam-7	77	72	(	(	PUNCT
ejpam-7	77	73	n−	n−	NOUN
ejpam-7	77	74	2)(∇xa	2)(∇xa	NUM
ejpam-7	77	75	)	)	PUNCT
ejpam-7	77	76	(	(	PUNCT
ejpam-7	77	77	2.24	2.24	NUM
ejpam-7	77	78	)	)	PUNCT
ejpam-7	77	79	further	far	ADV
ejpam-7	77	80	,	,	PUNCT
ejpam-7	77	81	since	since	SCONJ
ejpam-7	77	82	ξ	ξ	PROPN
ejpam-7	77	83	is	be	AUX
ejpam-7	77	84	a	a	DET
ejpam-7	77	85	killing	kill	VERB
ejpam-7	77	86	vector	vector	NOUN
ejpam-7	77	87	in	in	ADP
ejpam-7	77	88	k	k	ADJ
ejpam-7	77	89	-	-	NOUN
ejpam-7	77	90	contact	contact	NOUN
ejpam-7	77	91	manifold	manifold	NOUN
ejpam-7	77	92	.	.	PUNCT
ejpam-7	78	1	s	s	X
ejpam-7	78	2	,	,	PUNCT
ejpam-7	78	3	α	α	NOUN
ejpam-7	78	4	,	,	PUNCT
ejpam-7	78	5	r	r	NOUN
ejpam-7	78	6	,	,	PUNCT
ejpam-7	78	7	and	and	CCONJ
ejpam-7	78	8	a	a	PRON
ejpam-7	78	9	are	be	AUX
ejpam-7	78	10	invariant	invariant	ADJ
ejpam-7	78	11	under	under	ADP
ejpam-7	78	12	it	it	PRON
ejpam-7	78	13	,	,	PUNCT
ejpam-7	78	14	i.e.	i.e.	X
ejpam-7	78	15	,	,	PUNCT
ejpam-7	78	16	lξs	lξs	NOUN
ejpam-7	78	17	=	=	SYM
ejpam-7	78	18	0	0	NUM
ejpam-7	78	19	,	,	PUNCT
ejpam-7	78	20	lξr	lξr	VERB
ejpam-7	78	21	=	=	SYM
ejpam-7	78	22	0	0	PUNCT
ejpam-7	78	23	(	(	PUNCT
ejpam-7	78	24	2.25	2.25	NUM
ejpam-7	78	25	)	)	PUNCT
ejpam-7	78	26	lξk	lξk	NOUN
ejpam-7	78	27	=	=	SYM
ejpam-7	78	28	0	0	PROPN
ejpam-7	78	29	,	,	PUNCT
ejpam-7	78	30	lξa	lξa	NOUN
ejpam-7	78	31	=	=	SYM
ejpam-7	78	32	0	0	NUM
ejpam-7	78	33	(	(	PUNCT
ejpam-7	78	34	2.26	2.26	NUM
ejpam-7	78	35	)	)	PUNCT
ejpam-7	78	36	we	we	PRON
ejpam-7	78	37	recall	recall	VERB
ejpam-7	78	38	some	some	DET
ejpam-7	78	39	definitions	definition	NOUN
ejpam-7	78	40	which	which	PRON
ejpam-7	78	41	are	be	AUX
ejpam-7	78	42	used	use	VERB
ejpam-7	78	43	in	in	ADP
ejpam-7	78	44	later	later	ADJ
ejpam-7	78	45	section	section	NOUN
ejpam-7	78	46	,	,	PUNCT
ejpam-7	78	47	a	a	DET
ejpam-7	78	48	riemannian	riemannian	ADJ
ejpam-7	78	49	manifold	manifold	NOUN
ejpam-7	78	50	is	be	AUX
ejpam-7	78	51	said	say	VERB
ejpam-7	78	52	to	to	PART
ejpam-7	78	53	be	be	AUX
ejpam-7	78	54	η	η	PROPN
ejpam-7	78	55	-	-	ADJ
ejpam-7	78	56	einstein	einstein	ADJ
ejpam-7	78	57	manifold	manifold	NOUN
ejpam-7	78	58	if	if	SCONJ
ejpam-7	78	59	the	the	DET
ejpam-7	78	60	ricci	ricci	PROPN
ejpam-7	78	61	tensor	tensor	NOUN
ejpam-7	78	62	s	s	PART
ejpam-7	78	63	is	be	AUX
ejpam-7	78	64	of	of	ADP
ejpam-7	78	65	the	the	DET
ejpam-7	78	66	form	form	NOUN
ejpam-7	78	67	s(x	s(x	PROPN
ejpam-7	78	68	,	,	PUNCT
ejpam-7	78	69	y	y	PROPN
ejpam-7	78	70	)	)	PUNCT
ejpam-7	78	71	=	=	PUNCT
ejpam-7	79	1	λg(x	λg(x	X
ejpam-7	79	2	,	,	PUNCT
ejpam-7	79	3	y	y	PROPN
ejpam-7	79	4	)	)	PUNCT
ejpam-7	79	5	+	+	CCONJ
ejpam-7	79	6	µη(x)η(y	µη(x)η(y	NOUN
ejpam-7	79	7	)	)	PUNCT
ejpam-7	79	8	where	where	SCONJ
ejpam-7	79	9	λ	λ	NOUN
ejpam-7	79	10	,	,	PUNCT
ejpam-7	79	11	µ	µ	X
ejpam-7	79	12	are	be	AUX
ejpam-7	79	13	the	the	DET
ejpam-7	79	14	associated	associate	VERB
ejpam-7	79	15	functions	function	NOUN
ejpam-7	79	16	on	on	ADP
ejpam-7	79	17	the	the	DET
ejpam-7	79	18	manifold	manifold	NOUN
ejpam-7	79	19	.	.	PUNCT
ejpam-7	80	1	a	a	DET
ejpam-7	80	2	riemannian	riemannian	ADJ
ejpam-7	80	3	manifold	manifold	NOUN
ejpam-7	80	4	is	be	AUX
ejpam-7	80	5	said	say	VERB
ejpam-7	80	6	to	to	PART
ejpam-7	80	7	be	be	AUX
ejpam-7	80	8	cyclic	cyclic	ADJ
ejpam-7	80	9	-	-	PUNCT
ejpam-7	80	10	ricci	ricci	NOUN
ejpam-7	80	11	tensor	tensor	NOUN
ejpam-7	80	12	,	,	PUNCT
ejpam-7	80	13	if	if	SCONJ
ejpam-7	80	14	the	the	DET
ejpam-7	80	15	ricci	ricci	PROPN
ejpam-7	80	16	tensor	tensor	NOUN
ejpam-7	80	17	s	s	PART
ejpam-7	80	18	satisfies	satisfie	NOUN
ejpam-7	80	19	the	the	DET
ejpam-7	80	20	condition	condition	NOUN
ejpam-7	80	21	(	(	PUNCT
ejpam-7	80	22	∇xs)(y	∇xs)(y	PROPN
ejpam-7	80	23	,	,	PUNCT
ejpam-7	80	24	z	z	NOUN
ejpam-7	80	25	)	)	PUNCT
ejpam-7	81	1	+	+	CCONJ
ejpam-7	81	2	(	(	PUNCT
ejpam-7	81	3	∇y	∇y	PROPN
ejpam-7	81	4	s)(z	s)(z	PROPN
ejpam-7	81	5	,	,	PUNCT
ejpam-7	81	6	x	x	X
ejpam-7	81	7	)	)	PUNCT
ejpam-7	81	8	+	+	CCONJ
ejpam-7	81	9	(	(	PUNCT
ejpam-7	81	10	∇zs)(x	∇zs)(x	PROPN
ejpam-7	81	11	,	,	PUNCT
ejpam-7	81	12	y	y	PROPN
ejpam-7	81	13	)	)	PUNCT
ejpam-7	82	1	=	=	SYM
ejpam-7	82	2	0	0	NUM
ejpam-7	82	3	3	3	X
ejpam-7	82	4	.	.	PUNCT
ejpam-7	83	1	k	k	X
ejpam-7	83	2	-	-	PUNCT
ejpam-7	83	3	contact	contact	NOUN
ejpam-7	83	4	manifold	manifold	NOUN
ejpam-7	83	5	admitting	admit	VERB
ejpam-7	83	6	a	a	DET
ejpam-7	83	7	semi	semi	ADJ
ejpam-7	83	8	-	-	ADJ
ejpam-7	83	9	symmetric	symmetric	ADJ
ejpam-7	83	10	metric	metric	ADJ
ejpam-7	83	11	connection	connection	NOUN
ejpam-7	83	12	with	with	ADP
ejpam-7	83	13	div.p̃	div.p̃	PROPN
ejpam-7	83	14	=	=	PUNCT
ejpam-7	83	15	0	0	PROPN
ejpam-7	83	16	the	the	DET
ejpam-7	83	17	pseudo	pseudo	NOUN
ejpam-7	83	18	projective	projective	NOUN
ejpam-7	83	19	curvature	curvature	NOUN
ejpam-7	83	20	tensor	tensor	NOUN
ejpam-7	83	21	on	on	ADP
ejpam-7	83	22	a	a	DET
ejpam-7	83	23	riemannian	riemannian	ADJ
ejpam-7	83	24	manifold	manifold	NOUN
ejpam-7	83	25	is	be	AUX
ejpam-7	83	26	given	give	VERB
ejpam-7	83	27	by	by	ADP
ejpam-7	83	28	(	(	PUNCT
ejpam-7	83	29	[	[	X
ejpam-7	83	30	7	7	NUM
ejpam-7	83	31	]	]	PUNCT
ejpam-7	83	32	,	,	PUNCT
ejpam-7	83	33	[	[	X
ejpam-7	83	34	17	17	NUM
ejpam-7	83	35	]	]	SYM
ejpam-7	83	36	)	)	PUNCT
ejpam-7	84	1	p̃	p̃	PROPN
ejpam-7	84	2	(	(	PUNCT
ejpam-7	84	3	x	x	PROPN
ejpam-7	84	4	,	,	PUNCT
ejpam-7	84	5	y	y	NOUN
ejpam-7	84	6	)	)	PUNCT
ejpam-7	84	7	z	z	NOUN
ejpam-7	84	8	=	=	SYM
ejpam-7	84	9	ar(x	ar(x	X
ejpam-7	84	10	,	,	PUNCT
ejpam-7	84	11	y	y	NOUN
ejpam-7	84	12	)	)	PUNCT
ejpam-7	84	13	z	z	PROPN
ejpam-7	85	1	+	+	NUM
ejpam-7	85	2	b(s(y	b(s(y	NUM
ejpam-7	85	3	,	,	PUNCT
ejpam-7	85	4	z)x	z)x	PUNCT
ejpam-7	85	5	−	−	ADP
ejpam-7	85	6	s(x	s(x	NOUN
ejpam-7	85	7	,	,	PUNCT
ejpam-7	85	8	z)y	z)y	NUM
ejpam-7	85	9	]	]	PUNCT
ejpam-7	85	10	r	r	NOUN
ejpam-7	85	11	n	n	CCONJ
ejpam-7	85	12	[	[	PUNCT
ejpam-7	85	13	a	a	DET
ejpam-7	85	14	n−	n−	NOUN
ejpam-7	85	15	1	1	NUM
ejpam-7	85	16	+	+	SYM
ejpam-7	85	17	b	b	NOUN
ejpam-7	85	18	]	]	X
ejpam-7	86	1	[	[	X
ejpam-7	86	2	g(y	g(y	NOUN
ejpam-7	86	3	,	,	PUNCT
ejpam-7	86	4	z)x	z)x	PUNCT
ejpam-7	86	5	−	−	ADP
ejpam-7	86	6	g(x	g(x	NOUN
ejpam-7	86	7	,	,	PUNCT
ejpam-7	86	8	z)y	z)y	NUM
ejpam-7	86	9	]	]	PUNCT
ejpam-7	86	10	.	.	PUNCT
ejpam-7	87	1	(	(	PUNCT
ejpam-7	87	2	3.1	3.1	NUM
ejpam-7	87	3	)	)	PUNCT
ejpam-7	87	4	in	in	ADP
ejpam-7	87	5	this	this	DET
ejpam-7	87	6	section	section	NOUN
ejpam-7	87	7	we	we	PRON
ejpam-7	87	8	prove	prove	VERB
ejpam-7	87	9	the	the	DET
ejpam-7	87	10	following	following	NOUN
ejpam-7	87	11	:	:	PUNCT
ejpam-7	87	12	if	if	SCONJ
ejpam-7	87	13	a	a	DET
ejpam-7	87	14	k	k	NOUN
ejpam-7	87	15	-	-	NOUN
ejpam-7	87	16	contact	contact	PROPN
ejpam-7	87	17	manifold	manifold	PROPN
ejpam-7	87	18	mn	mn	PROPN
ejpam-7	87	19	(	(	PUNCT
ejpam-7	87	20	n	n	CCONJ
ejpam-7	87	21	>	>	SYM
ejpam-7	87	22	2	2	NUM
ejpam-7	87	23	)	)	PUNCT
ejpam-7	87	24	admits	admit	VERB
ejpam-7	87	25	a	a	DET
ejpam-7	87	26	semisymmetric	semisymmetric	ADJ
ejpam-7	87	27	metric	metric	ADJ
ejpam-7	87	28	connection	connection	NOUN
ejpam-7	87	29	and	and	CCONJ
ejpam-7	87	30	if	if	SCONJ
ejpam-7	87	31	the	the	DET
ejpam-7	87	32	pseudo	pseudo	NOUN
ejpam-7	87	33	projective	projective	NOUN
ejpam-7	87	34	curvature	curvature	NOUN
ejpam-7	87	35	tensor	tensor	NOUN
ejpam-7	87	36	with	with	ADP
ejpam-7	87	37	respect	respect	NOUN
ejpam-7	87	38	to	to	ADP
ejpam-7	87	39	this	this	DET
ejpam-7	87	40	connection	connection	NOUN
ejpam-7	87	41	is	be	AUX
ejpam-7	87	42	conservative	conservative	ADJ
ejpam-7	87	43	,	,	PUNCT
ejpam-7	87	44	then	then	ADV
ejpam-7	87	45	the	the	DET
ejpam-7	87	46	manifold	manifold	NOUN
ejpam-7	87	47	is	be	AUX
ejpam-7	87	48	η	η	NOUN
ejpam-7	87	49	-	-	NOUN
ejpam-7	87	50	einstein	einstein	NOUN
ejpam-7	87	51	;	;	PUNCT
ejpam-7	87	52	the	the	DET
ejpam-7	87	53	scalar	scalar	ADJ
ejpam-7	87	54	curvature	curvature	NOUN
ejpam-7	87	55	of	of	ADP
ejpam-7	87	56	such	such	DET
ejpam-7	87	57	a	a	DET
ejpam-7	87	58	manifold	manifold	NOUN
ejpam-7	87	59	is	be	AUX
ejpam-7	87	60	given	give	VERB
ejpam-7	87	61	by	by	ADP
ejpam-7	87	62	(	(	PUNCT
ejpam-7	87	63	3.14	3.14	NUM
ejpam-7	87	64	)	)	PUNCT
ejpam-7	87	65	.	.	PUNCT
ejpam-7	88	1	proof	proof	NOUN
ejpam-7	88	2	.	.	PUNCT
ejpam-7	89	1	:	:	PUNCT
ejpam-7	89	2	let	let	VERB
ejpam-7	89	3	us	we	PRON
ejpam-7	89	4	suppose	suppose	VERB
ejpam-7	89	5	that	that	SCONJ
ejpam-7	89	6	in	in	ADP
ejpam-7	89	7	a	a	DET
ejpam-7	89	8	k	k	NOUN
ejpam-7	89	9	-	-	NOUN
ejpam-7	89	10	contact	contact	NOUN
ejpam-7	89	11	manifoldmn	manifoldmn	NOUN
ejpam-7	89	12	with	with	ADP
ejpam-7	89	13	respect	respect	NOUN
ejpam-7	89	14	to	to	ADP
ejpam-7	89	15	semi	semi	ADJ
ejpam-7	89	16	-	-	ADJ
ejpam-7	89	17	symmetric	symmetric	ADJ
ejpam-7	89	18	metric	metric	ADJ
ejpam-7	89	19	connection	connection	NOUN
ejpam-7	89	20	div.c	div.c	PROPN
ejpam-7	89	21	=	=	SYM
ejpam-7	89	22	0	0	NUM
ejpam-7	89	23	where	where	SCONJ
ejpam-7	89	24	div	div	PROPN
ejpam-7	89	25	denotes	denote	VERB
ejpam-7	89	26	the	the	DET
ejpam-7	89	27	divergence	divergence	NOUN
ejpam-7	89	28	.	.	PUNCT
ejpam-7	90	1	differentiate	differentiate	NOUN
ejpam-7	90	2	(	(	PUNCT
ejpam-7	90	3	3.1	3.1	NUM
ejpam-7	90	4	)	)	PUNCT
ejpam-7	90	5	covariantly	covariantly	ADV
ejpam-7	90	6	and	and	CCONJ
ejpam-7	90	7	then	then	ADV
ejpam-7	90	8	contracting	contract	VERB
ejpam-7	90	9	we	we	PRON
ejpam-7	90	10	get	get	VERB
ejpam-7	90	11	div.p̃	div.p̃	PROPN
ejpam-7	90	12	.	.	PUNCT
ejpam-7	91	1	by	by	ADP
ejpam-7	91	2	virtue	virtue	NOUN
ejpam-7	91	3	of	of	ADP
ejpam-7	91	4	conservabagewadi	conservabagewadi	PROPN
ejpam-7	91	5	c.s	c.s	PROPN
ejpam-7	91	6	.	.	PROPN
ejpam-7	91	7	et	et	PROPN
ejpam-7	91	8	al	al	PROPN
ejpam-7	91	9	.	.	PUNCT
ejpam-7	91	10	/	/	SYM
ejpam-7	91	11	eur	eur	PROPN
ejpam-7	91	12	.	.	PUNCT
ejpam-7	92	1	j.	j.	PROPN
ejpam-7	92	2	pure	pure	PROPN
ejpam-7	92	3	appl	appl	PROPN
ejpam-7	92	4	.	.	PROPN
ejpam-7	92	5	math	math	PROPN
ejpam-7	92	6	,	,	PUNCT
ejpam-7	92	7	1	1	NUM
ejpam-7	92	8	(	(	PUNCT
ejpam-7	92	9	2008	2008	NUM
ejpam-7	92	10	)	)	PUNCT
ejpam-7	92	11	,	,	PUNCT
ejpam-7	92	12	(	(	PUNCT
ejpam-7	92	13	21	21	NUM
ejpam-7	92	14	-	-	SYM
ejpam-7	92	15	31	31	NUM
ejpam-7	92	16	)	)	PUNCT
ejpam-7	92	17	25	25	NUM
ejpam-7	92	18	tiveness	tiveness	NOUN
ejpam-7	92	19	of	of	ADP
ejpam-7	92	20	p̃	p̃	PROPN
ejpam-7	92	21	i.e.	i.e.	X
ejpam-7	92	22	,div.p̃	,div.p̃	PUNCT
ejpam-7	92	23	=	=	NOUN
ejpam-7	92	24	0	0	NUM
ejpam-7	92	25	,	,	PUNCT
ejpam-7	92	26	we	we	PRON
ejpam-7	92	27	obtain	obtain	VERB
ejpam-7	92	28	(	(	PUNCT
ejpam-7	92	29	a+	a+	PUNCT
ejpam-7	92	30	b)[(∇xs)(y	b)[(∇xs)(y	NOUN
ejpam-7	92	31	,	,	PUNCT
ejpam-7	92	32	z)−	z)−	PROPN
ejpam-7	92	33	(	(	PUNCT
ejpam-7	92	34	∇y	∇y	PROPN
ejpam-7	92	35	s)(x	s)(x	PROPN
ejpam-7	92	36	,	,	PUNCT
ejpam-7	92	37	z)]−	z)]−	X
ejpam-7	93	1	[	[	X
ejpam-7	93	2	a+	a+	PUNCT
ejpam-7	93	3	b(n−	b(n−	PROPN
ejpam-7	93	4	2)][(∇xk)(y	2)][(∇xk)(y	NUM
ejpam-7	93	5	,	,	PUNCT
ejpam-7	93	6	z)−	z)−	PROPN
ejpam-7	93	7	(	(	PUNCT
ejpam-7	93	8	∇yk)(x	∇yk)(x	PROPN
ejpam-7	93	9	,	,	PUNCT
ejpam-7	93	10	z	z	NOUN
ejpam-7	93	11	)	)	PUNCT
ejpam-7	93	12	]	]	PUNCT
ejpam-7	94	1	=	=	SYM
ejpam-7	94	2	(	(	PUNCT
ejpam-7	94	3	a−	a−	PROPN
ejpam-7	94	4	b)[s(y	b)[s(y	NOUN
ejpam-7	94	5	,	,	PUNCT
ejpam-7	94	6	z)η(x)−	z)η(x)−	NOUN
ejpam-7	94	7	s(x	s(x	PROPN
ejpam-7	94	8	,	,	PUNCT
ejpam-7	94	9	z)η(y	z)η(y	NOUN
ejpam-7	94	10	)	)	PUNCT
ejpam-7	95	1	]	]	PUNCT
ejpam-7	95	2	−	−	PROPN
ejpam-7	95	3	a(n−	a(n−	PROPN
ejpam-7	95	4	1)η(r(x	1)η(r(x	PROPN
ejpam-7	95	5	,	,	PUNCT
ejpam-7	95	6	y	y	PROPN
ejpam-7	95	7	)	)	PUNCT
ejpam-7	95	8	z	z	NOUN
ejpam-7	95	9	)	)	PUNCT
ejpam-7	96	1	+	+	NUM
ejpam-7	96	2	a.s(x	a.s(x	NOUN
ejpam-7	96	3	,	,	PUNCT
ejpam-7	96	4	y	y	PROPN
ejpam-7	96	5	)	)	PUNCT
ejpam-7	96	6	η(z	η(z	PROPN
ejpam-7	96	7	)	)	PUNCT
ejpam-7	97	1	+	+	ADJ
ejpam-7	97	2	a(n−a−	a(n−a−	NOUN
ejpam-7	97	3	1)[g(y	1)[g(y	NUM
ejpam-7	97	4	,	,	PUNCT
ejpam-7	97	5	z)η(x)−	z)η(x)−	PROPN
ejpam-7	97	6	g(x	g(x	NOUN
ejpam-7	97	7	,	,	PUNCT
ejpam-7	97	8	z)η(y	z)η(y	NOUN
ejpam-7	97	9	)	)	PUNCT
ejpam-7	97	10	]	]	PUNCT
ejpam-7	98	1	+	+	CCONJ
ejpam-7	98	2	b[g(y	b[g(y	NOUN
ejpam-7	98	3	,	,	PUNCT
ejpam-7	98	4	z)s(x	z)s(x	NUM
ejpam-7	98	5	,	,	PUNCT
ejpam-7	98	6	ξ)−	ξ)−	PROPN
ejpam-7	98	7	g(x	g(x	PROPN
ejpam-7	98	8	,	,	PUNCT
ejpam-7	98	9	z)s(y	z)s(y	NOUN
ejpam-7	98	10	,	,	PUNCT
ejpam-7	98	11	ξ)](3.2	ξ)](3.2	PROPN
ejpam-7	98	12	)	)	PUNCT
ejpam-7	98	13	+	+	NOUN
ejpam-7	98	14	(	(	PUNCT
ejpam-7	98	15	a+	a+	PUNCT
ejpam-7	98	16	b(n−	b(n−	PROPN
ejpam-7	98	17	2))[k(x	2))[k(x	NUM
ejpam-7	98	18	,	,	PUNCT
ejpam-7	98	19	y	y	PROPN
ejpam-7	98	20	)	)	PUNCT
ejpam-7	98	21	η(z)−k(x	η(z)−k(x	ADP
ejpam-7	98	22	,	,	PUNCT
ejpam-7	98	23	z)η(y	z)η(y	X
ejpam-7	98	24	)	)	PUNCT
ejpam-7	99	1	+	+	PUNCT
ejpam-7	99	2	k(y	k(y	PROPN
ejpam-7	99	3	,	,	PUNCT
ejpam-7	99	4	x)η(z)−k(y	x)η(z)−k(y	PROPN
ejpam-7	99	5	,	,	PUNCT
ejpam-7	99	6	z)η(x	z)η(x	NOUN
ejpam-7	99	7	)	)	PUNCT
ejpam-7	99	8	]	]	PUNCT
ejpam-7	99	9	−b(n−	−b(n−	NUM
ejpam-7	99	10	2)[g(y	2)[g(y	NUM
ejpam-7	99	11	,	,	PUNCT
ejpam-7	99	12	z)k(x	z)k(x	PROPN
ejpam-7	99	13	,	,	PUNCT
ejpam-7	99	14	ξ	ξ	X
ejpam-7	99	15	)	)	PUNCT
ejpam-7	99	16	+	+	CCONJ
ejpam-7	99	17	g(x	g(x	NOUN
ejpam-7	99	18	,	,	PUNCT
ejpam-7	99	19	z)k(y	z)k(y	NOUN
ejpam-7	99	20	,	,	PUNCT
ejpam-7	99	21	ξ	ξ	NOUN
ejpam-7	99	22	)	)	PUNCT
ejpam-7	99	23	]	]	PUNCT
ejpam-7	100	1	+	+	CCONJ
ejpam-7	100	2	1	1	NUM
ejpam-7	100	3	n	n	NOUN
ejpam-7	100	4	[	[	PUNCT
ejpam-7	100	5	a+	a+	PUNCT
ejpam-7	100	6	(	(	PUNCT
ejpam-7	100	7	n−	n−	NOUN
ejpam-7	100	8	1	1	NUM
ejpam-7	100	9	)	)	PUNCT
ejpam-7	100	10	(	(	PUNCT
ejpam-7	100	11	n−	n−	NOUN
ejpam-7	100	12	1	1	NUM
ejpam-7	100	13	)	)	PUNCT
ejpam-7	100	14	]	]	PUNCT
ejpam-7	101	1	[	[	X
ejpam-7	101	2	g(y	g(y	NOUN
ejpam-7	101	3	,	,	PUNCT
ejpam-7	101	4	z)∇xr	z)∇xr	NOUN
ejpam-7	101	5	−g(x	−g(x	ADJ
ejpam-7	101	6	,	,	PUNCT
ejpam-7	101	7	z)∇y	z)∇y	NOUN
ejpam-7	101	8	r	r	X
ejpam-7	101	9	]	]	X
ejpam-7	101	10	+	+	CCONJ
ejpam-7	101	11	[	[	PUNCT
ejpam-7	101	12	a+	a+	SYM
ejpam-7	101	13	1	1	NUM
ejpam-7	101	14	n	n	NOUN
ejpam-7	101	15	a+	a+	PUNCT
ejpam-7	101	16	(	(	PUNCT
ejpam-7	101	17	n−	n−	NOUN
ejpam-7	101	18	1	1	NUM
ejpam-7	101	19	)	)	PUNCT
ejpam-7	101	20	(	(	PUNCT
ejpam-7	101	21	n−	n−	NOUN
ejpam-7	101	22	1	1	NUM
ejpam-7	101	23	)	)	PUNCT
ejpam-7	101	24	]	]	PUNCT
ejpam-7	102	1	[	[	X
ejpam-7	102	2	g(y	g(y	X
ejpam-7	102	3	,	,	PUNCT
ejpam-7	102	4	z)∇xa−	z)∇xa−	ADJ
ejpam-7	102	5	g(x	g(x	NOUN
ejpam-7	102	6	,	,	PUNCT
ejpam-7	102	7	z)∇ya	z)∇ya	PROPN
ejpam-7	102	8	]	]	PUNCT
ejpam-7	102	9	.	.	PUNCT
ejpam-7	103	1	by	by	ADP
ejpam-7	103	2	virtue	virtue	NOUN
ejpam-7	103	3	of	of	ADP
ejpam-7	103	4	(	(	PUNCT
ejpam-7	103	5	2.1	2.1	NUM
ejpam-7	103	6	)	)	PUNCT
ejpam-7	103	7	and	and	CCONJ
ejpam-7	103	8	(	(	PUNCT
ejpam-7	103	9	2.4	2.4	NUM
ejpam-7	103	10	)	)	PUNCT
ejpam-7	103	11	we	we	PRON
ejpam-7	103	12	obtain	obtain	VERB
ejpam-7	103	13	from	from	ADP
ejpam-7	103	14	(	(	PUNCT
ejpam-7	103	15	2.21	2.21	NUM
ejpam-7	103	16	)	)	PUNCT
ejpam-7	104	1	that	that	SCONJ
ejpam-7	104	2	k(x	k(x	PROPN
ejpam-7	104	3	,	,	PUNCT
ejpam-7	104	4	y	y	PROPN
ejpam-7	104	5	)	)	PUNCT
ejpam-7	104	6	=	=	PUNCT
ejpam-7	104	7	g(x	g(x	NOUN
ejpam-7	104	8	,	,	PUNCT
ejpam-7	104	9	φy	φy	NOUN
ejpam-7	104	10	)	)	PUNCT
ejpam-7	104	11	−	−	PROPN
ejpam-7	104	12	η(x)η(y	η(x)η(y	NOUN
ejpam-7	104	13	)	)	PUNCT
ejpam-7	105	1	+	+	CCONJ
ejpam-7	105	2	1	1	NUM
ejpam-7	105	3	2	2	NUM
ejpam-7	105	4	g(x	g(x	NOUN
ejpam-7	105	5	,	,	PUNCT
ejpam-7	105	6	y	y	PROPN
ejpam-7	105	7	)	)	PUNCT
ejpam-7	105	8	.	.	PUNCT
ejpam-7	106	1	(	(	PUNCT
ejpam-7	106	2	3.3	3.3	NUM
ejpam-7	106	3	)	)	PUNCT
ejpam-7	106	4	k(x	k(x	PROPN
ejpam-7	106	5	,	,	PUNCT
ejpam-7	106	6	ξ	ξ	X
ejpam-7	106	7	)	)	PUNCT
ejpam-7	106	8	=	=	SYM
ejpam-7	106	9	−1	−1	NOUN
ejpam-7	106	10	2	2	NUM
ejpam-7	106	11	η(x	η(x	X
ejpam-7	106	12	)	)	PUNCT
ejpam-7	106	13	(	(	PUNCT
ejpam-7	106	14	3.4	3.4	NUM
ejpam-7	106	15	)	)	PUNCT
ejpam-7	106	16	lx	lx	NOUN
ejpam-7	106	17	=	=	SYM
ejpam-7	106	18	−φx	−φx	PROPN
ejpam-7	106	19	−	−	PROPN
ejpam-7	106	20	η(x)ξ	η(x)ξ	PROPN
ejpam-7	107	1	+	+	CCONJ
ejpam-7	107	2	1	1	NUM
ejpam-7	107	3	2	2	NUM
ejpam-7	107	4	x.	x.	NOUN
ejpam-7	107	5	(	(	PUNCT
ejpam-7	107	6	3.5	3.5	NUM
ejpam-7	107	7	)	)	PUNCT
ejpam-7	107	8	now	now	ADV
ejpam-7	107	9	putting	put	VERB
ejpam-7	107	10	x	x	X
ejpam-7	107	11	=	=	SYM
ejpam-7	107	12	ξ	ξ	X
ejpam-7	107	13	in	in	ADP
ejpam-7	107	14	(	(	PUNCT
ejpam-7	107	15	3.2	3.2	NUM
ejpam-7	107	16	)	)	PUNCT
ejpam-7	107	17	,	,	PUNCT
ejpam-7	107	18	then	then	ADV
ejpam-7	107	19	using	use	VERB
ejpam-7	107	20	(	(	PUNCT
ejpam-7	107	21	2.1	2.1	NUM
ejpam-7	107	22	)	)	PUNCT
ejpam-7	107	23	,	,	PUNCT
ejpam-7	107	24	(	(	PUNCT
ejpam-7	107	25	2.6),(2.7),(3.3	2.6),(2.7),(3.3	NUM
ejpam-7	107	26	)	)	PUNCT
ejpam-7	107	27	and	and	CCONJ
ejpam-7	107	28	(	(	PUNCT
ejpam-7	107	29	3.4	3.4	NUM
ejpam-7	107	30	)	)	PUNCT
ejpam-7	107	31	,	,	PUNCT
ejpam-7	107	32	we	we	PRON
ejpam-7	107	33	get	get	VERB
ejpam-7	107	34	(	(	PUNCT
ejpam-7	107	35	a+	a+	PUNCT
ejpam-7	107	36	b)[(∇ξs)(y	b)[(∇ξs)(y	NOUN
ejpam-7	107	37	,	,	PUNCT
ejpam-7	107	38	z)−	z)−	PROPN
ejpam-7	107	39	(	(	PUNCT
ejpam-7	107	40	∇y	∇y	PROPN
ejpam-7	107	41	s)(ξ	s)(ξ	NUM
ejpam-7	107	42	,	,	PUNCT
ejpam-7	107	43	z)]−	z)]−	X
ejpam-7	108	1	[	[	X
ejpam-7	108	2	a+	a+	X
ejpam-7	108	3	n(n−	n(n−	PROPN
ejpam-7	108	4	2)][(∇ξk)(y	2)][(∇ξk)(y	NUM
ejpam-7	108	5	,	,	PUNCT
ejpam-7	108	6	z)−	z)−	PROPN
ejpam-7	108	7	(	(	PUNCT
ejpam-7	108	8	∇yk)(ξ	∇yk)(ξ	PROPN
ejpam-7	108	9	,	,	PUNCT
ejpam-7	108	10	z	z	NOUN
ejpam-7	108	11	)	)	PUNCT
ejpam-7	108	12	]	]	PUNCT
ejpam-7	109	1	=	=	PUNCT
ejpam-7	110	1	[	[	X
ejpam-7	110	2	a+	a+	PUNCT
ejpam-7	110	3	n(n−	n(n−	PROPN
ejpam-7	110	4	2)])g(φy	2)])g(φy	NUM
ejpam-7	110	5	,	,	PUNCT
ejpam-7	110	6	z	z	NOUN
ejpam-7	110	7	)	)	PUNCT
ejpam-7	111	1	+	+	CCONJ
ejpam-7	111	2	(	(	PUNCT
ejpam-7	111	3	a−	a−	PROPN
ejpam-7	111	4	b)s(y	b)s(y	NOUN
ejpam-7	111	5	,	,	PUNCT
ejpam-7	111	6	z	z	NOUN
ejpam-7	111	7	)	)	PUNCT
ejpam-7	112	1	+	+	CCONJ
ejpam-7	112	2	[	[	PUNCT
ejpam-7	112	3	a	a	PRON
ejpam-7	112	4	(	(	PUNCT
ejpam-7	112	5	a+	a+	SYM
ejpam-7	112	6	1	1	NUM
ejpam-7	112	7	2	2	NUM
ejpam-7	112	8	)	)	PUNCT
ejpam-7	113	1	+	+	CCONJ
ejpam-7	113	2	b(2n−	b(2n−	PROPN
ejpam-7	113	3	3	3	NUM
ejpam-7	113	4	)	)	PUNCT
ejpam-7	113	5	]	]	PUNCT
ejpam-7	114	1	g(y	g(y	PROPN
ejpam-7	114	2	,	,	PUNCT
ejpam-7	114	3	z	z	NOUN
ejpam-7	114	4	)	)	PUNCT
ejpam-7	114	5	−	−	PROPN
ejpam-7	114	6	[	[	PUNCT
ejpam-7	114	7	a	a	X
ejpam-7	114	8	(	(	PUNCT
ejpam-7	114	9	a+	a+	SYM
ejpam-7	114	10	1	1	NUM
ejpam-7	114	11	2	2	NUM
ejpam-7	114	12	)	)	PUNCT
ejpam-7	114	13	+	+	CCONJ
ejpam-7	114	14	b(n−	b(n−	VERB
ejpam-7	114	15	2	2	NUM
ejpam-7	114	16	)	)	PUNCT
ejpam-7	114	17	]	]	PUNCT
ejpam-7	114	18	η(y	η(y	PROPN
ejpam-7	114	19	)	)	PUNCT
ejpam-7	114	20	η(z	η(z	PROPN
ejpam-7	114	21	)	)	PUNCT
ejpam-7	115	1	+	+	CCONJ
ejpam-7	115	2	1	1	NUM
ejpam-7	115	3	n	n	NOUN
ejpam-7	115	4	[	[	PUNCT
ejpam-7	115	5	a+	a+	PUNCT
ejpam-7	115	6	(	(	PUNCT
ejpam-7	115	7	n−	n−	NOUN
ejpam-7	115	8	1	1	NUM
ejpam-7	115	9	)	)	PUNCT
ejpam-7	115	10	(	(	PUNCT
ejpam-7	115	11	n−	n−	NOUN
ejpam-7	115	12	1	1	NUM
ejpam-7	115	13	)	)	PUNCT
ejpam-7	115	14	]	]	PUNCT
ejpam-7	116	1	[	[	X
ejpam-7	116	2	g(y	g(y	X
ejpam-7	116	3	,	,	PUNCT
ejpam-7	116	4	z)∇ξr	z)∇ξr	ADV
ejpam-7	116	5	−	−	PROPN
ejpam-7	116	6	η(z)∇y	η(z)∇y	PROPN
ejpam-7	116	7	r](3.6	r](3.6	PROPN
ejpam-7	116	8	)	)	PUNCT
ejpam-7	117	1	+	+	CCONJ
ejpam-7	117	2	[	[	PUNCT
ejpam-7	117	3	a+	a+	SYM
ejpam-7	117	4	1	1	NUM
ejpam-7	117	5	n	n	NOUN
ejpam-7	117	6	a+	a+	PUNCT
ejpam-7	117	7	(	(	PUNCT
ejpam-7	117	8	n−	n−	NOUN
ejpam-7	117	9	1	1	NUM
ejpam-7	117	10	)	)	PUNCT
ejpam-7	117	11	(	(	PUNCT
ejpam-7	117	12	n−	n−	NOUN
ejpam-7	117	13	1	1	NUM
ejpam-7	117	14	)	)	PUNCT
ejpam-7	117	15	]	]	PUNCT
ejpam-7	118	1	[	[	X
ejpam-7	118	2	g(y	g(y	X
ejpam-7	118	3	,	,	PUNCT
ejpam-7	118	4	z)∇ξa−	z)∇ξa−	NOUN
ejpam-7	118	5	η(z)∇ya	η(z)∇ya	NOUN
ejpam-7	118	6	]	]	PUNCT
ejpam-7	118	7	.	.	PUNCT
ejpam-7	119	1	from	from	ADP
ejpam-7	119	2	(	(	PUNCT
ejpam-7	119	3	2.25	2.25	NUM
ejpam-7	119	4	)	)	PUNCT
ejpam-7	119	5	and	and	CCONJ
ejpam-7	119	6	(	(	PUNCT
ejpam-7	119	7	2.26	2.26	NUM
ejpam-7	119	8	)	)	PUNCT
ejpam-7	119	9	,	,	PUNCT
ejpam-7	119	10	we	we	PRON
ejpam-7	119	11	obtain	obtain	VERB
ejpam-7	119	12	(	(	PUNCT
ejpam-7	119	13	∇ξs)(y	∇ξs)(y	NUM
ejpam-7	119	14	,	,	PUNCT
ejpam-7	119	15	z	z	NOUN
ejpam-7	119	16	)	)	PUNCT
ejpam-7	119	17	=	=	PUNCT
ejpam-7	120	1	−s(∇y	−s(∇y	PROPN
ejpam-7	120	2	ξ	ξ	PROPN
ejpam-7	120	3	,	,	PUNCT
ejpam-7	120	4	z)−	z)−	PROPN
ejpam-7	120	5	s(y,∇zξ	s(y,∇zξ	PROPN
ejpam-7	120	6	)	)	PUNCT
ejpam-7	120	7	,	,	PUNCT
ejpam-7	120	8	(	(	PUNCT
ejpam-7	120	9	∇ξr	∇ξr	ADV
ejpam-7	120	10	)	)	PUNCT
ejpam-7	120	11	=	=	SYM
ejpam-7	120	12	0	0	NUM
ejpam-7	120	13	,	,	PUNCT
ejpam-7	120	14	(	(	PUNCT
ejpam-7	120	15	3.7	3.7	NUM
ejpam-7	120	16	)	)	PUNCT
ejpam-7	120	17	(	(	PUNCT
ejpam-7	120	18	∇ξk)(y	∇ξk)(y	PROPN
ejpam-7	120	19	,	,	PUNCT
ejpam-7	120	20	z	z	NOUN
ejpam-7	120	21	)	)	PUNCT
ejpam-7	120	22	=	=	PUNCT
ejpam-7	120	23	−k(∇y	−k(∇y	NOUN
ejpam-7	120	24	ξ	ξ	PROPN
ejpam-7	120	25	,	,	PUNCT
ejpam-7	120	26	z)−k(y,∇zξ	z)−k(y,∇zξ	NOUN
ejpam-7	120	27	)	)	PUNCT
ejpam-7	120	28	,	,	PUNCT
ejpam-7	120	29	(	(	PUNCT
ejpam-7	120	30	∇ξa	∇ξa	NOUN
ejpam-7	120	31	)	)	PUNCT
ejpam-7	120	32	=	=	SYM
ejpam-7	120	33	0	0	NUM
ejpam-7	120	34	,	,	PUNCT
ejpam-7	120	35	(	(	PUNCT
ejpam-7	120	36	3.8	3.8	NUM
ejpam-7	120	37	)	)	PUNCT
ejpam-7	120	38	respectively	respectively	ADV
ejpam-7	120	39	.	.	PUNCT
ejpam-7	121	1	by	by	ADP
ejpam-7	121	2	using(3.7)and(3.8	using(3.7)and(3.8	NOUN
ejpam-7	121	3	)	)	PUNCT
ejpam-7	121	4	in	in	ADP
ejpam-7	121	5	(	(	PUNCT
ejpam-7	121	6	3.6	3.6	NUM
ejpam-7	121	7	)	)	PUNCT
ejpam-7	121	8	,	,	PUNCT
ejpam-7	121	9	we	we	PRON
ejpam-7	121	10	have	have	VERB
ejpam-7	121	11	(	(	PUNCT
ejpam-7	121	12	a+	a+	X
ejpam-7	121	13	b)[−s(∇y	b)[−s(∇y	NOUN
ejpam-7	121	14	ξ	ξ	PROPN
ejpam-7	121	15	,	,	PUNCT
ejpam-7	121	16	z)−	z)−	PROPN
ejpam-7	121	17	s(y,∇zξ)−	s(y,∇zξ)−	X
ejpam-7	122	1	(	(	PUNCT
ejpam-7	122	2	∇y	∇y	PROPN
ejpam-7	122	3	s)(ξ	s)(ξ	NOUN
ejpam-7	122	4	,	,	PUNCT
ejpam-7	122	5	z	z	NOUN
ejpam-7	122	6	)	)	PUNCT
ejpam-7	122	7	]	]	PUNCT
ejpam-7	123	1	=	=	PUNCT
ejpam-7	124	1	[	[	X
ejpam-7	124	2	a+	a+	X
ejpam-7	124	3	n(n−	n(n−	PROPN
ejpam-7	124	4	2)][−k(∇y	2)][−k(∇y	PROPN
ejpam-7	124	5	ξ	ξ	PROPN
ejpam-7	124	6	,	,	PUNCT
ejpam-7	124	7	z)−k(y,∇zξ)−	z)−k(y,∇zξ)−	PROPN
ejpam-7	124	8	(	(	PUNCT
ejpam-7	124	9	∇yk)(ξ	∇yk)(ξ	PROPN
ejpam-7	124	10	,	,	PUNCT
ejpam-7	124	11	z	z	NOUN
ejpam-7	124	12	)	)	PUNCT
ejpam-7	124	13	]	]	PUNCT
ejpam-7	125	1	+	+	PUNCT
ejpam-7	125	2	[	[	X
ejpam-7	125	3	a+	a+	X
ejpam-7	125	4	n(n−	n(n−	PROPN
ejpam-7	125	5	2)])g(φy	2)])g(φy	NUM
ejpam-7	125	6	,	,	PUNCT
ejpam-7	125	7	z	z	NOUN
ejpam-7	125	8	)	)	PUNCT
ejpam-7	126	1	+	+	CCONJ
ejpam-7	126	2	(	(	PUNCT
ejpam-7	126	3	a−	a−	PROPN
ejpam-7	126	4	b)s(y	b)s(y	NOUN
ejpam-7	126	5	,	,	PUNCT
ejpam-7	126	6	z	z	NOUN
ejpam-7	126	7	)	)	PUNCT
ejpam-7	127	1	+	+	CCONJ
ejpam-7	127	2	[	[	PUNCT
ejpam-7	127	3	a	a	PRON
ejpam-7	127	4	(	(	PUNCT
ejpam-7	127	5	a+	a+	SYM
ejpam-7	127	6	1	1	NUM
ejpam-7	127	7	2	2	NUM
ejpam-7	127	8	)	)	PUNCT
ejpam-7	128	1	+	+	CCONJ
ejpam-7	128	2	b(2n−	b(2n−	PROPN
ejpam-7	128	3	3	3	NUM
ejpam-7	128	4	)	)	PUNCT
ejpam-7	128	5	]	]	PUNCT
ejpam-7	129	1	g(y	g(y	PROPN
ejpam-7	129	2	,	,	PUNCT
ejpam-7	129	3	z	z	NOUN
ejpam-7	129	4	)	)	PUNCT
ejpam-7	129	5	−	−	PROPN
ejpam-7	129	6	[	[	PUNCT
ejpam-7	129	7	a	a	X
ejpam-7	129	8	(	(	PUNCT
ejpam-7	129	9	a+	a+	SYM
ejpam-7	129	10	1	1	NUM
ejpam-7	129	11	2	2	NUM
ejpam-7	129	12	)	)	PUNCT
ejpam-7	129	13	+	+	CCONJ
ejpam-7	129	14	b(n−	b(n−	VERB
ejpam-7	129	15	2	2	NUM
ejpam-7	129	16	)	)	PUNCT
ejpam-7	129	17	]	]	PUNCT
ejpam-7	129	18	η(y	η(y	PROPN
ejpam-7	129	19	)	)	PUNCT
ejpam-7	129	20	η(z	η(z	PROPN
ejpam-7	129	21	)	)	PUNCT
ejpam-7	130	1	+	+	CCONJ
ejpam-7	130	2	1	1	NUM
ejpam-7	130	3	n	n	NOUN
ejpam-7	130	4	[	[	PUNCT
ejpam-7	130	5	a+	a+	PUNCT
ejpam-7	130	6	(	(	PUNCT
ejpam-7	130	7	n−	n−	NOUN
ejpam-7	130	8	1	1	NUM
ejpam-7	130	9	)	)	PUNCT
ejpam-7	130	10	(	(	PUNCT
ejpam-7	130	11	n−	n−	NOUN
ejpam-7	130	12	1	1	NUM
ejpam-7	130	13	)	)	PUNCT
ejpam-7	130	14	]	]	PUNCT
ejpam-7	131	1	[	[	X
ejpam-7	131	2	g(y	g(y	NOUN
ejpam-7	131	3	,	,	PUNCT
ejpam-7	131	4	z)∇ξr	z)∇ξr	PROPN
ejpam-7	131	5	−	−	PROPN
ejpam-7	131	6	η(z)∇y	η(z)∇y	PROPN
ejpam-7	131	7	r](3.9	r](3.9	PROPN
ejpam-7	131	8	)	)	PUNCT
ejpam-7	132	1	+	+	CCONJ
ejpam-7	132	2	[	[	PUNCT
ejpam-7	132	3	a+	a+	SYM
ejpam-7	132	4	1	1	NUM
ejpam-7	132	5	n	n	NOUN
ejpam-7	132	6	a+	a+	PUNCT
ejpam-7	132	7	(	(	PUNCT
ejpam-7	132	8	n−	n−	NOUN
ejpam-7	132	9	1	1	NUM
ejpam-7	132	10	)	)	PUNCT
ejpam-7	132	11	(	(	PUNCT
ejpam-7	132	12	n−	n−	NOUN
ejpam-7	132	13	1	1	NUM
ejpam-7	132	14	)	)	PUNCT
ejpam-7	132	15	]	]	PUNCT
ejpam-7	133	1	[	[	X
ejpam-7	133	2	g(y	g(y	X
ejpam-7	133	3	,	,	PUNCT
ejpam-7	133	4	z)∇ξa−	z)∇ξa−	NOUN
ejpam-7	133	5	η(z)∇ya	η(z)∇ya	NOUN
ejpam-7	133	6	]	]	PUNCT
ejpam-7	133	7	.	.	PUNCT
ejpam-7	134	1	bagewadi	bagewadi	PROPN
ejpam-7	134	2	c.s	c.s	PROPN
ejpam-7	134	3	.	.	PROPN
ejpam-7	134	4	et	et	PROPN
ejpam-7	134	5	al	al	PROPN
ejpam-7	134	6	.	.	PUNCT
ejpam-7	134	7	/	/	SYM
ejpam-7	134	8	eur	eur	PROPN
ejpam-7	134	9	.	.	PUNCT
ejpam-7	135	1	j.	j.	PROPN
ejpam-7	135	2	pure	pure	PROPN
ejpam-7	135	3	appl	appl	PROPN
ejpam-7	135	4	.	.	PROPN
ejpam-7	135	5	math	math	PROPN
ejpam-7	135	6	,	,	PUNCT
ejpam-7	135	7	1	1	NUM
ejpam-7	135	8	(	(	PUNCT
ejpam-7	135	9	2008	2008	NUM
ejpam-7	135	10	)	)	PUNCT
ejpam-7	135	11	,	,	PUNCT
ejpam-7	135	12	(	(	PUNCT
ejpam-7	135	13	21	21	NUM
ejpam-7	135	14	-	-	SYM
ejpam-7	135	15	31	31	NUM
ejpam-7	135	16	)	)	PUNCT
ejpam-7	135	17	26	26	NUM
ejpam-7	135	18	using	use	VERB
ejpam-7	135	19	(	(	PUNCT
ejpam-7	135	20	2.4	2.4	NUM
ejpam-7	135	21	)	)	PUNCT
ejpam-7	135	22	,	,	PUNCT
ejpam-7	135	23	(	(	PUNCT
ejpam-7	135	24	2.6	2.6	NUM
ejpam-7	135	25	)	)	PUNCT
ejpam-7	135	26	and	and	CCONJ
ejpam-7	135	27	(	(	PUNCT
ejpam-7	135	28	3.4	3.4	NUM
ejpam-7	135	29	)	)	PUNCT
ejpam-7	135	30	in	in	ADP
ejpam-7	135	31	(	(	PUNCT
ejpam-7	135	32	3.9	3.9	NUM
ejpam-7	135	33	)	)	PUNCT
ejpam-7	135	34	,	,	PUNCT
ejpam-7	135	35	we	we	PRON
ejpam-7	135	36	get	get	VERB
ejpam-7	135	37	−(a+	−(a+	NOUN
ejpam-7	135	38	b)s(φy	b)s(φy	X
ejpam-7	135	39	,	,	PUNCT
ejpam-7	135	40	z)−	z)−	PROPN
ejpam-7	135	41	(	(	PUNCT
ejpam-7	135	42	a−	a−	PROPN
ejpam-7	135	43	b)s(y	b)s(y	NOUN
ejpam-7	135	44	,	,	PUNCT
ejpam-7	135	45	z	z	NOUN
ejpam-7	135	46	)	)	PUNCT
ejpam-7	135	47	=	=	PUNCT
ejpam-7	136	1	[	[	PUNCT
ejpam-7	136	2	a	a	X
ejpam-7	136	3	(	(	PUNCT
ejpam-7	136	4	a+	a+	SYM
ejpam-7	136	5	3	3	NUM
ejpam-7	136	6	2	2	NUM
ejpam-7	136	7	)	)	PUNCT
ejpam-7	137	1	+	+	CCONJ
ejpam-7	137	2	b(3n−	b(3n−	PROPN
ejpam-7	137	3	5	5	NUM
ejpam-7	137	4	)	)	PUNCT
ejpam-7	137	5	]	]	PUNCT
ejpam-7	138	1	g(y	g(y	PROPN
ejpam-7	138	2	,	,	PUNCT
ejpam-7	138	3	z)−	z)−	PROPN
ejpam-7	138	4	[	[	PUNCT
ejpam-7	138	5	a	a	X
ejpam-7	138	6	(	(	PUNCT
ejpam-7	138	7	a+	a+	SYM
ejpam-7	138	8	3	3	NUM
ejpam-7	138	9	2	2	NUM
ejpam-7	138	10	)	)	PUNCT
ejpam-7	138	11	−	−	PROPN
ejpam-7	138	12	2b(n−	2b(n−	NUM
ejpam-7	138	13	2	2	NUM
ejpam-7	138	14	)	)	PUNCT
ejpam-7	138	15	]	]	PUNCT
ejpam-7	138	16	η(y	η(y	PROPN
ejpam-7	138	17	)	)	PUNCT
ejpam-7	138	18	η(z	η(z	PROPN
ejpam-7	138	19	)	)	PUNCT
ejpam-7	139	1	+	+	PUNCT
ejpam-7	140	1	[	[	X
ejpam-7	140	2	a(n+	a(n+	ADJ
ejpam-7	140	3	1	1	NUM
ejpam-7	140	4	)	)	PUNCT
ejpam-7	140	5	+	+	CCONJ
ejpam-7	140	6	b(3n−	b(3n−	PROPN
ejpam-7	140	7	5)]g(φy	5)]g(φy	NUM
ejpam-7	140	8	,	,	PUNCT
ejpam-7	140	9	z)−	z)−	PROPN
ejpam-7	140	10	1	1	NUM
ejpam-7	140	11	n	n	NOUN
ejpam-7	140	12	[	[	PUNCT
ejpam-7	140	13	a+	a+	PUNCT
ejpam-7	140	14	(	(	PUNCT
ejpam-7	140	15	n−	n−	NOUN
ejpam-7	140	16	1	1	NUM
ejpam-7	140	17	)	)	PUNCT
ejpam-7	140	18	(	(	PUNCT
ejpam-7	140	19	n−	n−	NOUN
ejpam-7	140	20	1	1	NUM
ejpam-7	140	21	)	)	PUNCT
ejpam-7	140	22	]	]	PUNCT
ejpam-7	141	1	η(z)∇y	η(z)∇y	PROPN
ejpam-7	141	2	r	r	NOUN
ejpam-7	141	3	−	−	PROPN
ejpam-7	142	1	[	[	PUNCT
ejpam-7	142	2	a+	a+	SYM
ejpam-7	142	3	1	1	NUM
ejpam-7	142	4	n	n	NOUN
ejpam-7	142	5	a+	a+	PUNCT
ejpam-7	142	6	(	(	PUNCT
ejpam-7	142	7	n−	n−	NOUN
ejpam-7	142	8	1	1	NUM
ejpam-7	142	9	)	)	PUNCT
ejpam-7	142	10	(	(	PUNCT
ejpam-7	142	11	n−	n−	NOUN
ejpam-7	142	12	1	1	NUM
ejpam-7	142	13	)	)	PUNCT
ejpam-7	142	14	]	]	PUNCT
ejpam-7	142	15	η(z)∇ya	η(z)∇ya	NOUN
ejpam-7	142	16	.	.	PUNCT
ejpam-7	143	1	(	(	PUNCT
ejpam-7	143	2	3.10	3.10	NUM
ejpam-7	143	3	)	)	PUNCT
ejpam-7	143	4	next	next	ADV
ejpam-7	143	5	,	,	PUNCT
ejpam-7	143	6	by	by	ADP
ejpam-7	143	7	replacing	replace	VERB
ejpam-7	143	8	z	z	NOUN
ejpam-7	143	9	by	by	ADP
ejpam-7	143	10	φz	φz	PRON
ejpam-7	143	11	in	in	ADP
ejpam-7	143	12	above	above	ADV
ejpam-7	143	13	and	and	CCONJ
ejpam-7	143	14	then	then	ADV
ejpam-7	143	15	using	use	VERB
ejpam-7	143	16	(	(	PUNCT
ejpam-7	143	17	2.1	2.1	NUM
ejpam-7	143	18	)	)	PUNCT
ejpam-7	143	19	,	,	PUNCT
ejpam-7	143	20	we	we	PRON
ejpam-7	143	21	obtain	obtain	VERB
ejpam-7	143	22	−(a+	−(a+	NOUN
ejpam-7	143	23	b)s(φy	b)s(φy	X
ejpam-7	143	24	,	,	PUNCT
ejpam-7	143	25	φz)−	φz)−	NUM
ejpam-7	143	26	(	(	PUNCT
ejpam-7	143	27	a−	a−	PROPN
ejpam-7	143	28	b)s(y	b)s(y	NOUN
ejpam-7	143	29	,	,	PUNCT
ejpam-7	143	30	φz	φz	NOUN
ejpam-7	143	31	)	)	PUNCT
ejpam-7	143	32	[	[	PUNCT
ejpam-7	143	33	a	a	DET
ejpam-7	143	34	(	(	PUNCT
ejpam-7	143	35	a+	a+	SYM
ejpam-7	143	36	3	3	NUM
ejpam-7	143	37	2	2	NUM
ejpam-7	143	38	)	)	PUNCT
ejpam-7	143	39	+	+	CCONJ
ejpam-7	143	40	b(3n−	b(3n−	PROPN
ejpam-7	143	41	5	5	NUM
ejpam-7	143	42	)	)	PUNCT
ejpam-7	143	43	]	]	PUNCT
ejpam-7	144	1	g(y	g(y	PROPN
ejpam-7	144	2	,	,	PUNCT
ejpam-7	144	3	φz	φz	NOUN
ejpam-7	144	4	)	)	PUNCT
ejpam-7	144	5	+	+	CCONJ
ejpam-7	145	1	[	[	X
ejpam-7	145	2	a(n+	a(n+	ADJ
ejpam-7	145	3	1	1	NUM
ejpam-7	145	4	)	)	PUNCT
ejpam-7	145	5	+	+	CCONJ
ejpam-7	145	6	b(3n−	b(3n−	PROPN
ejpam-7	145	7	5	5	NUM
ejpam-7	145	8	)	)	PUNCT
ejpam-7	145	9	]	]	PUNCT
ejpam-7	145	10	g(φy	g(φy	PROPN
ejpam-7	145	11	,	,	PUNCT
ejpam-7	145	12	φz	φz	PROPN
ejpam-7	145	13	)	)	PUNCT
ejpam-7	145	14	(	(	PUNCT
ejpam-7	145	15	3.11	3.11	NUM
ejpam-7	145	16	)	)	PUNCT
ejpam-7	145	17	interchanging	interchange	VERB
ejpam-7	145	18	y	y	PROPN
ejpam-7	145	19	and	and	CCONJ
ejpam-7	145	20	z	z	PROPN
ejpam-7	145	21	in	in	ADP
ejpam-7	145	22	(	(	PUNCT
ejpam-7	145	23	3.11	3.11	NUM
ejpam-7	145	24	)	)	PUNCT
ejpam-7	145	25	,	,	PUNCT
ejpam-7	145	26	we	we	PRON
ejpam-7	145	27	have	have	VERB
ejpam-7	145	28	−(a+	−(a+	NOUN
ejpam-7	145	29	b)s(φy	b)s(φy	X
ejpam-7	145	30	,	,	PUNCT
ejpam-7	145	31	φz)−	φz)−	NUM
ejpam-7	145	32	(	(	PUNCT
ejpam-7	145	33	a−	a−	PROPN
ejpam-7	145	34	b)s(φy	b)s(φy	ADJ
ejpam-7	145	35	,	,	PUNCT
ejpam-7	145	36	z	z	NOUN
ejpam-7	145	37	)	)	PUNCT
ejpam-7	145	38	[	[	PUNCT
ejpam-7	145	39	a	a	DET
ejpam-7	145	40	(	(	PUNCT
ejpam-7	145	41	a+	a+	SYM
ejpam-7	145	42	3	3	NUM
ejpam-7	145	43	2	2	NUM
ejpam-7	145	44	)	)	PUNCT
ejpam-7	146	1	+	+	CCONJ
ejpam-7	146	2	b(3n−	b(3n−	PROPN
ejpam-7	146	3	5	5	NUM
ejpam-7	146	4	)	)	PUNCT
ejpam-7	146	5	]	]	PUNCT
ejpam-7	147	1	g(φy	g(φy	PROPN
ejpam-7	147	2	,	,	PUNCT
ejpam-7	147	3	z	z	NOUN
ejpam-7	147	4	)	)	PUNCT
ejpam-7	147	5	+	+	CCONJ
ejpam-7	148	1	[	[	X
ejpam-7	148	2	a(n+	a(n+	ADJ
ejpam-7	148	3	1	1	NUM
ejpam-7	148	4	)	)	PUNCT
ejpam-7	148	5	+	+	CCONJ
ejpam-7	148	6	b(3n−	b(3n−	PROPN
ejpam-7	148	7	5	5	NUM
ejpam-7	148	8	)	)	PUNCT
ejpam-7	148	9	]	]	PUNCT
ejpam-7	148	10	g(φy	g(φy	PROPN
ejpam-7	148	11	,	,	PUNCT
ejpam-7	148	12	φz	φz	NOUN
ejpam-7	148	13	)	)	PUNCT
ejpam-7	148	14	(	(	PUNCT
ejpam-7	148	15	3.12	3.12	NUM
ejpam-7	148	16	)	)	PUNCT
ejpam-7	148	17	by	by	ADP
ejpam-7	148	18	adding	add	VERB
ejpam-7	148	19	(	(	PUNCT
ejpam-7	148	20	3.11	3.11	NUM
ejpam-7	148	21	)	)	PUNCT
ejpam-7	148	22	with	with	ADP
ejpam-7	148	23	(	(	PUNCT
ejpam-7	148	24	3.12	3.12	NUM
ejpam-7	148	25	)	)	PUNCT
ejpam-7	148	26	,	,	PUNCT
ejpam-7	148	27	and	and	CCONJ
ejpam-7	148	28	then	then	ADV
ejpam-7	148	29	by	by	ADP
ejpam-7	148	30	using	use	VERB
ejpam-7	148	31	the	the	DET
ejpam-7	148	32	skew	skew	ADJ
ejpam-7	148	33	-	-	PUNCT
ejpam-7	148	34	symmetric	symmetric	ADJ
ejpam-7	148	35	property	property	NOUN
ejpam-7	148	36	of	of	ADP
ejpam-7	148	37	φ	φ	PROPN
ejpam-7	148	38	,	,	PUNCT
ejpam-7	148	39	one	one	PRON
ejpam-7	148	40	can	can	AUX
ejpam-7	148	41	get	get	VERB
ejpam-7	148	42	s(y	s(y	NOUN
ejpam-7	148	43	,	,	PUNCT
ejpam-7	148	44	z	z	NOUN
ejpam-7	148	45	)	)	PUNCT
ejpam-7	148	46	=	=	SYM
ejpam-7	148	47	p1.g(y	p1.g(y	PROPN
ejpam-7	148	48	,	,	PUNCT
ejpam-7	148	49	z	z	NOUN
ejpam-7	148	50	)	)	PUNCT
ejpam-7	148	51	+	+	VERB
ejpam-7	148	52	q1.η(y	q1.η(y	NOUN
ejpam-7	148	53	)	)	PUNCT
ejpam-7	148	54	η(z	η(z	PROPN
ejpam-7	148	55	)	)	PUNCT
ejpam-7	148	56	(	(	PUNCT
ejpam-7	148	57	3.13	3.13	NUM
ejpam-7	148	58	)	)	PUNCT
ejpam-7	148	59	wherep1	wherep1	NOUN
ejpam-7	148	60	=	=	PUNCT
ejpam-7	149	1	[	[	PUNCT
ejpam-7	149	2	−	−	X
ejpam-7	149	3	a	a	DET
ejpam-7	149	4	a+	a+	X
ejpam-7	149	5	b	b	NOUN
ejpam-7	149	6	(	(	PUNCT
ejpam-7	149	7	n−	n−	PROPN
ejpam-7	149	8	1)−	1)−	PROPN
ejpam-7	149	9	b	b	PROPN
ejpam-7	149	10	a+	a+	PUNCT
ejpam-7	149	11	b	b	PROPN
ejpam-7	149	12	(	(	PUNCT
ejpam-7	149	13	3n−	3n−	PROPN
ejpam-7	149	14	5	5	NUM
ejpam-7	149	15	)	)	PUNCT
ejpam-7	149	16	]	]	PUNCT
ejpam-7	149	17	and	and	CCONJ
ejpam-7	149	18	q1	q1	PROPN
ejpam-7	149	19	=	=	PUNCT
ejpam-7	149	20	[	[	PUNCT
ejpam-7	149	21	2a+	2a+	NUM
ejpam-7	149	22	b	b	PROPN
ejpam-7	149	23	a+	a+	PUNCT
ejpam-7	149	24	b	b	PROPN
ejpam-7	149	25	(	(	PUNCT
ejpam-7	149	26	n−	n−	NOUN
ejpam-7	149	27	1	1	NUM
ejpam-7	149	28	)	)	PUNCT
ejpam-7	149	29	+	+	CCONJ
ejpam-7	149	30	b	b	X
ejpam-7	149	31	a+	a+	SYM
ejpam-7	149	32	b	b	NOUN
ejpam-7	149	33	(	(	PUNCT
ejpam-7	149	34	3n−	3n−	PROPN
ejpam-7	149	35	5	5	NUM
ejpam-7	149	36	)	)	PUNCT
ejpam-7	149	37	]	]	PUNCT
ejpam-7	149	38	.	.	PUNCT
ejpam-7	150	1	there	there	ADV
ejpam-7	150	2	fore	fore	NOUN
ejpam-7	150	3	the	the	DET
ejpam-7	150	4	manifold	manifold	NOUN
ejpam-7	150	5	is	be	AUX
ejpam-7	150	6	η	η	NOUN
ejpam-7	150	7	-	-	NOUN
ejpam-7	150	8	einstein	einstein	NOUN
ejpam-7	150	9	.	.	PUNCT
ejpam-7	151	1	let	let	VERB
ejpam-7	151	2	ei	ei	PART
ejpam-7	151	3	be	be	AUX
ejpam-7	151	4	an	an	DET
ejpam-7	151	5	orthogonal	orthogonal	ADJ
ejpam-7	151	6	basis	basis	NOUN
ejpam-7	151	7	of	of	ADP
ejpam-7	151	8	the	the	DET
ejpam-7	151	9	tangent	tangent	ADJ
ejpam-7	151	10	space	space	NOUN
ejpam-7	151	11	at	at	ADP
ejpam-7	151	12	each	each	DET
ejpam-7	151	13	point	point	NOUN
ejpam-7	151	14	of	of	ADP
ejpam-7	151	15	the	the	DET
ejpam-7	151	16	manifold	manifold	ADJ
ejpam-7	151	17	mn	mn	PROPN
ejpam-7	151	18	for	for	ADP
ejpam-7	151	19	i	i	PROPN
ejpam-7	151	20	=	=	NOUN
ejpam-7	151	21	1	1	NUM
ejpam-7	151	22	,	,	PUNCT
ejpam-7	151	23	2	2	NUM
ejpam-7	151	24	,	,	PUNCT
ejpam-7	151	25	....	....	PUNCT
ejpam-7	151	26	,	,	PUNCT
ejpam-7	151	27	n.	n.	PROPN
ejpam-7	151	28	putting	put	VERB
ejpam-7	151	29	y	y	NOUN
ejpam-7	151	30	=	=	PUNCT
ejpam-7	151	31	z	z	NOUN
ejpam-7	151	32	=	=	PUNCT
ejpam-7	151	33	ei	ei	NOUN
ejpam-7	151	34	in	in	ADP
ejpam-7	151	35	(	(	PUNCT
ejpam-7	151	36	3.13	3.13	NUM
ejpam-7	151	37	)	)	PUNCT
ejpam-7	151	38	and	and	CCONJ
ejpam-7	151	39	then	then	ADV
ejpam-7	151	40	taking	take	VERB
ejpam-7	151	41	summation	summation	NOUN
ejpam-7	151	42	over	over	ADP
ejpam-7	151	43	the	the	DET
ejpam-7	151	44	index	index	NOUN
ejpam-7	151	45	i	i	PRON
ejpam-7	151	46	,	,	PUNCT
ejpam-7	151	47	we	we	PRON
ejpam-7	151	48	get	get	VERB
ejpam-7	151	49	r	r	NOUN
ejpam-7	151	50	=	=	PRON
ejpam-7	151	51	−(n−	−(n−	ADJ
ejpam-7	151	52	1)(n−	1)(n−	NUM
ejpam-7	151	53	2	2	NUM
ejpam-7	151	54	)	)	PUNCT
ejpam-7	151	55	(	(	PUNCT
ejpam-7	151	56	a+	a+	X
ejpam-7	151	57	3b	3b	NUM
ejpam-7	151	58	)	)	PUNCT
ejpam-7	151	59	(	(	PUNCT
ejpam-7	151	60	a+	a+	PUNCT
ejpam-7	151	61	b	b	NOUN
ejpam-7	151	62	)	)	PUNCT
ejpam-7	151	63	.	.	PUNCT
ejpam-7	152	1	(	(	PUNCT
ejpam-7	152	2	3.14	3.14	NUM
ejpam-7	152	3	)	)	PUNCT
ejpam-7	152	4	this	this	PRON
ejpam-7	152	5	proves	prove	VERB
ejpam-7	152	6	the	the	DET
ejpam-7	152	7	theorem	theorem	NOUN
ejpam-7	152	8	.	.	PUNCT
ejpam-7	152	9	suppose	suppose	VERB
ejpam-7	152	10	in	in	ADP
ejpam-7	152	11	k	k	ADJ
ejpam-7	152	12	-	-	NOUN
ejpam-7	152	13	contact	contact	NOUN
ejpam-7	152	14	manifold	manifold	NOUN
ejpam-7	152	15	admitting	admit	VERB
ejpam-7	152	16	a	a	DET
ejpam-7	152	17	semi	semi	ADJ
ejpam-7	152	18	-	-	ADJ
ejpam-7	152	19	symmetric	symmetric	ADJ
ejpam-7	152	20	metric	metric	ADJ
ejpam-7	152	21	connection	connection	NOUN
ejpam-7	152	22	,	,	PUNCT
ejpam-7	152	23	the	the	DET
ejpam-7	152	24	pseudo	pseudo	NOUN
ejpam-7	152	25	projective	projective	NOUN
ejpam-7	152	26	curvature	curvature	NOUN
ejpam-7	152	27	tensor	tensor	NOUN
ejpam-7	152	28	with	with	ADP
ejpam-7	152	29	respect	respect	NOUN
ejpam-7	152	30	to	to	ADP
ejpam-7	152	31	this	this	DET
ejpam-7	152	32	connection	connection	NOUN
ejpam-7	152	33	is	be	AUX
ejpam-7	152	34	conservative	conservative	ADJ
ejpam-7	152	35	.	.	PUNCT
ejpam-7	153	1	then	then	ADV
ejpam-7	153	2	the	the	DET
ejpam-7	153	3	manifold	manifold	NOUN
ejpam-7	153	4	has	have	VERB
ejpam-7	153	5	a	a	DET
ejpam-7	153	6	cyclic	cyclic	ADJ
ejpam-7	153	7	-	-	PUNCT
ejpam-7	153	8	ricci	ricci	NOUN
ejpam-7	153	9	tensor	tensor	NOUN
ejpam-7	153	10	with	with	ADP
ejpam-7	153	11	respect	respect	NOUN
ejpam-7	153	12	to	to	ADP
ejpam-7	153	13	levi	levi	PROPN
ejpam-7	153	14	-	-	PUNCT
ejpam-7	153	15	civita	civita	NOUN
ejpam-7	153	16	connection	connection	NOUN
ejpam-7	153	17	;	;	PUNCT
ejpam-7	153	18	and	and	CCONJ
ejpam-7	153	19	moreover	moreover	ADV
ejpam-7	153	20	the	the	DET
ejpam-7	153	21	scalar	scalar	ADJ
ejpam-7	153	22	curvature	curvature	NOUN
ejpam-7	153	23	of	of	ADP
ejpam-7	153	24	the	the	DET
ejpam-7	153	25	manifold	manifold	NOUN
ejpam-7	153	26	is	be	AUX
ejpam-7	153	27	constant	constant	ADJ
ejpam-7	153	28	if	if	SCONJ
ejpam-7	153	29	and	and	CCONJ
ejpam-7	153	30	only	only	ADV
ejpam-7	153	31	if	if	SCONJ
ejpam-7	153	32	the	the	DET
ejpam-7	153	33	vector	vector	NOUN
ejpam-7	153	34	field	field	NOUN
ejpam-7	153	35	ξ	ξ	PROPN
ejpam-7	153	36	is	be	AUX
ejpam-7	153	37	harmonic	harmonic	ADJ
ejpam-7	153	38	provided	provide	VERB
ejpam-7	153	39	(	(	PUNCT
ejpam-7	153	40	a+	a+	PRON
ejpam-7	153	41	b	b	NOUN
ejpam-7	153	42	)	)	PUNCT
ejpam-7	153	43	6=	6=	ADP
ejpam-7	153	44	0	0	X
ejpam-7	153	45	.	.	PUNCT
ejpam-7	154	1	bagewadi	bagewadi	PROPN
ejpam-7	154	2	c.s	c.s	PROPN
ejpam-7	154	3	.	.	PROPN
ejpam-7	154	4	et	et	PROPN
ejpam-7	154	5	al	al	PROPN
ejpam-7	154	6	.	.	PUNCT
ejpam-7	154	7	/	/	SYM
ejpam-7	154	8	eur	eur	PROPN
ejpam-7	154	9	.	.	PUNCT
ejpam-7	155	1	j.	j.	PROPN
ejpam-7	155	2	pure	pure	PROPN
ejpam-7	155	3	appl	appl	PROPN
ejpam-7	155	4	.	.	PROPN
ejpam-7	155	5	math	math	PROPN
ejpam-7	155	6	,	,	PUNCT
ejpam-7	155	7	1	1	NUM
ejpam-7	155	8	(	(	PUNCT
ejpam-7	155	9	2008	2008	NUM
ejpam-7	155	10	)	)	PUNCT
ejpam-7	155	11	,	,	PUNCT
ejpam-7	155	12	(	(	PUNCT
ejpam-7	155	13	21	21	NUM
ejpam-7	155	14	-	-	SYM
ejpam-7	155	15	31	31	NUM
ejpam-7	155	16	)	)	PUNCT
ejpam-7	155	17	27	27	NUM
ejpam-7	155	18	proof	proof	NOUN
ejpam-7	155	19	.	.	PUNCT
ejpam-7	156	1	differentiating	differentiate	VERB
ejpam-7	156	2	(	(	PUNCT
ejpam-7	156	3	3.13	3.13	NUM
ejpam-7	156	4	)	)	PUNCT
ejpam-7	156	5	covariantly	covariantly	ADV
ejpam-7	156	6	with	with	ADP
ejpam-7	156	7	respect	respect	NOUN
ejpam-7	156	8	to	to	ADP
ejpam-7	156	9	x	x	PRON
ejpam-7	156	10	,	,	PUNCT
ejpam-7	156	11	we	we	PRON
ejpam-7	156	12	have	have	VERB
ejpam-7	156	13	(	(	PUNCT
ejpam-7	156	14	∇xs)(y	∇xs)(y	ADJ
ejpam-7	156	15	,	,	PUNCT
ejpam-7	156	16	z	z	NOUN
ejpam-7	156	17	)	)	PUNCT
ejpam-7	156	18	=	=	PUNCT
ejpam-7	157	1	[	[	PUNCT
ejpam-7	157	2	2a+	2a+	NUM
ejpam-7	157	3	b	b	PROPN
ejpam-7	157	4	a+	a+	PUNCT
ejpam-7	157	5	b	b	PROPN
ejpam-7	157	6	(	(	PUNCT
ejpam-7	157	7	n−	n−	NOUN
ejpam-7	157	8	1	1	NUM
ejpam-7	157	9	)	)	PUNCT
ejpam-7	158	1	+	+	CCONJ
ejpam-7	158	2	b	b	X
ejpam-7	158	3	a+	a+	SYM
ejpam-7	158	4	b	b	NOUN
ejpam-7	158	5	(	(	PUNCT
ejpam-7	158	6	3n−	3n−	PROPN
ejpam-7	158	7	5	5	NUM
ejpam-7	158	8	)	)	PUNCT
ejpam-7	158	9	]	]	PUNCT
ejpam-7	159	1	[	[	X
ejpam-7	159	2	g(φy	g(φy	NUM
ejpam-7	159	3	,	,	PUNCT
ejpam-7	159	4	x)η(z	x)η(z	PRON
ejpam-7	159	5	)	)	PUNCT
ejpam-7	160	1	+	+	CCONJ
ejpam-7	160	2	g(φx	g(φx	NOUN
ejpam-7	160	3	,	,	PUNCT
ejpam-7	160	4	z)η(y	z)η(y	NOUN
ejpam-7	160	5	)	)	PUNCT
ejpam-7	160	6	]	]	PUNCT
ejpam-7	160	7	(	(	PUNCT
ejpam-7	160	8	3.15	3.15	NUM
ejpam-7	160	9	)	)	PUNCT
ejpam-7	160	10	similarly	similarly	ADV
ejpam-7	160	11	(	(	PUNCT
ejpam-7	160	12	∇y	∇y	PROPN
ejpam-7	160	13	s)(z	s)(z	PROPN
ejpam-7	160	14	,	,	PUNCT
ejpam-7	160	15	x	x	X
ejpam-7	160	16	)	)	PUNCT
ejpam-7	161	1	=	=	PUNCT
ejpam-7	161	2	[	[	PUNCT
ejpam-7	161	3	2a+	2a+	NUM
ejpam-7	161	4	b	b	PROPN
ejpam-7	161	5	a+	a+	PUNCT
ejpam-7	161	6	b	b	PROPN
ejpam-7	161	7	(	(	PUNCT
ejpam-7	161	8	n−	n−	NOUN
ejpam-7	161	9	1	1	NUM
ejpam-7	161	10	)	)	PUNCT
ejpam-7	162	1	+	+	CCONJ
ejpam-7	162	2	b	b	X
ejpam-7	162	3	a+	a+	SYM
ejpam-7	162	4	b	b	NOUN
ejpam-7	162	5	(	(	PUNCT
ejpam-7	162	6	3n−	3n−	PROPN
ejpam-7	162	7	5	5	NUM
ejpam-7	162	8	)	)	PUNCT
ejpam-7	162	9	]	]	PUNCT
ejpam-7	163	1	[	[	X
ejpam-7	163	2	g(φy	g(φy	PRON
ejpam-7	163	3	,	,	PUNCT
ejpam-7	163	4	z)η(x	z)η(x	NOUN
ejpam-7	163	5	)	)	PUNCT
ejpam-7	164	1	+	+	NUM
ejpam-7	164	2	g(φx	g(φx	NOUN
ejpam-7	164	3	,	,	PUNCT
ejpam-7	164	4	y	y	NOUN
ejpam-7	164	5	)	)	PUNCT
ejpam-7	164	6	η(z)](3.16	η(z)](3.16	PROPN
ejpam-7	164	7	)	)	PUNCT
ejpam-7	164	8	(	(	PUNCT
ejpam-7	164	9	∇zs)(x	∇zs)(x	PROPN
ejpam-7	164	10	,	,	PUNCT
ejpam-7	164	11	y	y	PROPN
ejpam-7	164	12	)	)	PUNCT
ejpam-7	165	1	=	=	PUNCT
ejpam-7	165	2	[	[	PUNCT
ejpam-7	165	3	2a+	2a+	NUM
ejpam-7	165	4	b	b	PROPN
ejpam-7	165	5	a+	a+	PUNCT
ejpam-7	165	6	b	b	PROPN
ejpam-7	165	7	(	(	PUNCT
ejpam-7	165	8	n−	n−	NOUN
ejpam-7	165	9	1	1	NUM
ejpam-7	165	10	)	)	PUNCT
ejpam-7	166	1	+	+	CCONJ
ejpam-7	166	2	b	b	X
ejpam-7	166	3	a+	a+	SYM
ejpam-7	166	4	b	b	NOUN
ejpam-7	166	5	(	(	PUNCT
ejpam-7	166	6	3n−	3n−	PROPN
ejpam-7	166	7	5	5	NUM
ejpam-7	166	8	)	)	PUNCT
ejpam-7	166	9	]	]	PUNCT
ejpam-7	167	1	[	[	X
ejpam-7	167	2	g(φx	g(φx	NOUN
ejpam-7	167	3	,	,	PUNCT
ejpam-7	167	4	z)η(y	z)η(y	NOUN
ejpam-7	167	5	)	)	PUNCT
ejpam-7	167	6	+	+	CCONJ
ejpam-7	167	7	g(φz	g(φz	NOUN
ejpam-7	167	8	,	,	PUNCT
ejpam-7	167	9	y	y	NOUN
ejpam-7	167	10	)	)	PUNCT
ejpam-7	167	11	η(x)].(3.17	η(x)].(3.17	X
ejpam-7	167	12	)	)	PUNCT
ejpam-7	167	13	adding	add	VERB
ejpam-7	167	14	the	the	DET
ejpam-7	167	15	equations	equation	NOUN
ejpam-7	167	16	(	(	PUNCT
ejpam-7	167	17	3.15	3.15	NUM
ejpam-7	167	18	)	)	PUNCT
ejpam-7	167	19	,	,	PUNCT
ejpam-7	167	20	(	(	PUNCT
ejpam-7	167	21	3.16	3.16	NUM
ejpam-7	167	22	)	)	PUNCT
ejpam-7	167	23	and	and	CCONJ
ejpam-7	167	24	(	(	PUNCT
ejpam-7	167	25	3.17	3.17	NUM
ejpam-7	167	26	)	)	PUNCT
ejpam-7	167	27	,	,	PUNCT
ejpam-7	167	28	then	then	ADV
ejpam-7	167	29	using	use	VERB
ejpam-7	167	30	skew	skew	NOUN
ejpam-7	167	31	-	-	PUNCT
ejpam-7	167	32	symmetry	symmetry	NOUN
ejpam-7	167	33	of	of	ADP
ejpam-7	167	34	φ	φ	PROPN
ejpam-7	167	35	,	,	PUNCT
ejpam-7	167	36	we	we	PRON
ejpam-7	167	37	obtain	obtain	VERB
ejpam-7	167	38	(	(	PUNCT
ejpam-7	167	39	∇xs)(y	∇xs)(y	PROPN
ejpam-7	167	40	,	,	PUNCT
ejpam-7	167	41	z	z	NOUN
ejpam-7	167	42	)	)	PUNCT
ejpam-7	168	1	+	+	CCONJ
ejpam-7	169	1	(	(	PUNCT
ejpam-7	169	2	∇y	∇y	PROPN
ejpam-7	169	3	s)(z	s)(z	PROPN
ejpam-7	169	4	,	,	PUNCT
ejpam-7	169	5	x	x	X
ejpam-7	169	6	)	)	PUNCT
ejpam-7	169	7	+	+	CCONJ
ejpam-7	169	8	(	(	PUNCT
ejpam-7	169	9	∇zs)(x	∇zs)(x	PROPN
ejpam-7	169	10	,	,	PUNCT
ejpam-7	169	11	y	y	PROPN
ejpam-7	169	12	)	)	PUNCT
ejpam-7	170	1	=	=	SYM
ejpam-7	170	2	0	0	NUM
ejpam-7	170	3	(	(	PUNCT
ejpam-7	170	4	3.18	3.18	NUM
ejpam-7	170	5	)	)	PUNCT
ejpam-7	170	6	thus	thus	ADV
ejpam-7	170	7	the	the	DET
ejpam-7	170	8	manifold	manifold	NOUN
ejpam-7	170	9	has	have	VERB
ejpam-7	170	10	a	a	DET
ejpam-7	170	11	cyclic	cyclic	ADJ
ejpam-7	170	12	-	-	PUNCT
ejpam-7	170	13	ricci	ricci	NOUN
ejpam-7	170	14	tensor	tensor	NOUN
ejpam-7	170	15	.	.	PUNCT
ejpam-7	171	1	taking	take	VERB
ejpam-7	171	2	an	an	DET
ejpam-7	171	3	orthonormal	orthonormal	ADJ
ejpam-7	171	4	frame	frame	NOUN
ejpam-7	171	5	field	field	NOUN
ejpam-7	171	6	and	and	CCONJ
ejpam-7	171	7	contracting	contracting	NOUN
ejpam-7	171	8	(	(	PUNCT
ejpam-7	171	9	3.15	3.15	NUM
ejpam-7	171	10	)	)	PUNCT
ejpam-7	171	11	over	over	ADP
ejpam-7	171	12	x	x	PROPN
ejpam-7	171	13	and	and	CCONJ
ejpam-7	171	14	z	z	NOUN
ejpam-7	171	15	,	,	PUNCT
ejpam-7	171	16	we	we	PRON
ejpam-7	171	17	obtain	obtain	AUX
ejpam-7	171	18	dr(y	dr(y	VERB
ejpam-7	171	19	)	)	PUNCT
ejpam-7	171	20	=	=	PUNCT
ejpam-7	172	1	[	[	PUNCT
ejpam-7	172	2	2a+	2a+	NUM
ejpam-7	172	3	b	b	PROPN
ejpam-7	172	4	a+	a+	PUNCT
ejpam-7	172	5	b	b	PROPN
ejpam-7	172	6	(	(	PUNCT
ejpam-7	172	7	n−	n−	NOUN
ejpam-7	172	8	1	1	NUM
ejpam-7	172	9	)	)	PUNCT
ejpam-7	173	1	+	+	CCONJ
ejpam-7	173	2	b	b	X
ejpam-7	173	3	a+	a+	SYM
ejpam-7	173	4	b	b	NOUN
ejpam-7	173	5	(	(	PUNCT
ejpam-7	173	6	3n−	3n−	PROPN
ejpam-7	173	7	5	5	NUM
ejpam-7	173	8	)	)	PUNCT
ejpam-7	173	9	]	]	PUNCT
ejpam-7	173	10	ψη(y	ψη(y	X
ejpam-7	173	11	)	)	PUNCT
ejpam-7	173	12	(	(	PUNCT
ejpam-7	173	13	3.19	3.19	NUM
ejpam-7	173	14	)	)	PUNCT
ejpam-7	173	15	where	where	SCONJ
ejpam-7	173	16	ψ	ψ	NOUN
ejpam-7	173	17	=	=	SYM
ejpam-7	173	18	tr.φ	tr.φ	PROPN
ejpam-7	173	19	.	.	PUNCT
ejpam-7	174	1	from	from	ADP
ejpam-7	174	2	(	(	PUNCT
ejpam-7	174	3	3.19	3.19	NUM
ejpam-7	174	4	)	)	PUNCT
ejpam-7	174	5	,	,	PUNCT
ejpam-7	174	6	it	it	PRON
ejpam-7	174	7	follows	follow	VERB
ejpam-7	174	8	that	that	SCONJ
ejpam-7	174	9	dr(y	dr(y	VERB
ejpam-7	174	10	)	)	PUNCT
ejpam-7	175	1	=	=	SYM
ejpam-7	175	2	0	0	PUNCT
ejpam-7	176	1	if	if	SCONJ
ejpam-7	176	2	and	and	CCONJ
ejpam-7	176	3	only	only	ADV
ejpam-7	176	4	ψ	ψ	X
ejpam-7	176	5	=	=	SYM
ejpam-7	176	6	0	0	NUM
ejpam-7	176	7	provided	provide	VERB
ejpam-7	176	8	(	(	PUNCT
ejpam-7	176	9	a+	a+	PRON
ejpam-7	176	10	b	b	NOUN
ejpam-7	176	11	)	)	PUNCT
ejpam-7	176	12	6=	6=	ADP
ejpam-7	176	13	0	0	NUM
ejpam-7	176	14	.	.	PUNCT
ejpam-7	177	1	(	(	PUNCT
ejpam-7	177	2	3.20	3.20	NUM
ejpam-7	177	3	)	)	PUNCT
ejpam-7	177	4	4	4	NUM
ejpam-7	177	5	.	.	X
ejpam-7	178	1	trans	trans	ADJ
ejpam-7	178	2	-	-	ADJ
ejpam-7	178	3	sasakian	sasakian	ADJ
ejpam-7	178	4	manifold	manifold	NOUN
ejpam-7	178	5	admitting	admit	VERB
ejpam-7	178	6	a	a	DET
ejpam-7	178	7	semi	semi	ADJ
ejpam-7	178	8	-	-	ADJ
ejpam-7	178	9	symmetric	symmetric	ADJ
ejpam-7	178	10	metric	metric	ADJ
ejpam-7	178	11	connection	connection	NOUN
ejpam-7	178	12	with	with	ADP
ejpam-7	178	13	div.p̃	div.p̃	PROPN
ejpam-7	178	14	=	=	NOUN
ejpam-7	178	15	0	0	NUM
ejpam-7	178	16	here	here	ADV
ejpam-7	178	17	we	we	PRON
ejpam-7	178	18	recall	recall	VERB
ejpam-7	178	19	some	some	DET
ejpam-7	178	20	results	result	NOUN
ejpam-7	178	21	which	which	PRON
ejpam-7	178	22	will	will	AUX
ejpam-7	178	23	be	be	AUX
ejpam-7	178	24	used	use	VERB
ejpam-7	178	25	in	in	ADP
ejpam-7	178	26	further	far	ADV
ejpam-7	178	27	.	.	PUNCT
ejpam-7	179	1	[	[	X
ejpam-7	179	2	5	5	NUM
ejpam-7	179	3	]	]	PUNCT
ejpam-7	179	4	:	:	PUNCT
ejpam-7	179	5	in	in	ADP
ejpam-7	179	6	a	a	DET
ejpam-7	179	7	trans	trans	ADJ
ejpam-7	179	8	-	-	ADJ
ejpam-7	179	9	sasakian	sasakian	ADJ
ejpam-7	179	10	manifold	manifold	NOUN
ejpam-7	179	11	under	under	ADP
ejpam-7	179	12	the	the	DET
ejpam-7	179	13	condition	condition	NOUN
ejpam-7	179	14	(	(	PUNCT
ejpam-7	179	15	2.14	2.14	NUM
ejpam-7	179	16	)	)	PUNCT
ejpam-7	179	17	,	,	PUNCT
ejpam-7	179	18	we	we	PRON
ejpam-7	179	19	have	have	VERB
ejpam-7	179	20	[	[	X
ejpam-7	179	21	(	(	PUNCT
ejpam-7	179	22	∇ξs)(y	∇ξs)(y	PROPN
ejpam-7	179	23	,	,	PUNCT
ejpam-7	179	24	z)−	z)−	PROPN
ejpam-7	180	1	(	(	PUNCT
ejpam-7	180	2	∇y	∇y	PROPN
ejpam-7	180	3	s)(ξ	s)(ξ	NOUN
ejpam-7	180	4	,	,	PUNCT
ejpam-7	180	5	z	z	NOUN
ejpam-7	180	6	)	)	PUNCT
ejpam-7	180	7	]	]	PUNCT
ejpam-7	181	1	=	=	SYM
ejpam-7	181	2	βs(y	βs(y	X
ejpam-7	181	3	,	,	PUNCT
ejpam-7	181	4	z)−	z)−	PROPN
ejpam-7	181	5	(	(	PUNCT
ejpam-7	181	6	n−	n−	NOUN
ejpam-7	181	7	1)(α2	1)(α2	NUM
ejpam-7	181	8	−	−	NOUN
ejpam-7	181	9	β2)βg(y	β2)βg(y	SYM
ejpam-7	181	10	,	,	PUNCT
ejpam-7	181	11	z	z	NOUN
ejpam-7	181	12	)	)	PUNCT
ejpam-7	181	13	(	(	PUNCT
ejpam-7	181	14	4.1	4.1	NUM
ejpam-7	181	15	)	)	PUNCT
ejpam-7	181	16	−(n−	−(n−	NOUN
ejpam-7	181	17	1)(α2	1)(α2	NUM
ejpam-7	181	18	−	−	PROPN
ejpam-7	181	19	β2)αg(y	β2)αg(y	SYM
ejpam-7	181	20	,	,	PUNCT
ejpam-7	181	21	φz	φz	NOUN
ejpam-7	181	22	)	)	PUNCT
ejpam-7	181	23	+	+	CCONJ
ejpam-7	181	24	αs(y	αs(y	NUM
ejpam-7	181	25	,	,	PUNCT
ejpam-7	181	26	φz	φz	NOUN
ejpam-7	181	27	)	)	PUNCT
ejpam-7	181	28	.	.	PUNCT
ejpam-7	182	1	[	[	X
ejpam-7	182	2	5	5	NUM
ejpam-7	182	3	]	]	PUNCT
ejpam-7	182	4	:	:	PUNCT
ejpam-7	182	5	for	for	ADP
ejpam-7	182	6	trans	trans	PROPN
ejpam-7	182	7	-	-	ADJ
ejpam-7	182	8	sasakian	sasakian	ADJ
ejpam-7	182	9	manifold	manifold	NOUN
ejpam-7	182	10	under	under	ADP
ejpam-7	182	11	the	the	DET
ejpam-7	182	12	condition	condition	NOUN
ejpam-7	182	13	(	(	PUNCT
ejpam-7	182	14	2.14	2.14	NUM
ejpam-7	182	15	)	)	PUNCT
ejpam-7	182	16	,	,	PUNCT
ejpam-7	182	17	the	the	DET
ejpam-7	182	18	following	follow	VERB
ejpam-7	182	19	results	result	NOUN
ejpam-7	182	20	are	be	AUX
ejpam-7	182	21	bagewadi	bagewadi	PROPN
ejpam-7	182	22	c.s	c.s	PROPN
ejpam-7	182	23	.	.	PROPN
ejpam-7	182	24	et	et	PROPN
ejpam-7	182	25	al	al	PROPN
ejpam-7	182	26	.	.	PUNCT
ejpam-7	182	27	/	/	SYM
ejpam-7	182	28	eur	eur	PROPN
ejpam-7	182	29	.	.	PUNCT
ejpam-7	183	1	j.	j.	PROPN
ejpam-7	183	2	pure	pure	PROPN
ejpam-7	183	3	appl	appl	PROPN
ejpam-7	183	4	.	.	PROPN
ejpam-7	183	5	math	math	PROPN
ejpam-7	183	6	,	,	PUNCT
ejpam-7	183	7	1	1	NUM
ejpam-7	183	8	(	(	PUNCT
ejpam-7	183	9	2008	2008	NUM
ejpam-7	183	10	)	)	PUNCT
ejpam-7	183	11	,	,	PUNCT
ejpam-7	183	12	(	(	PUNCT
ejpam-7	183	13	21	21	NUM
ejpam-7	183	14	-	-	SYM
ejpam-7	183	15	31	31	NUM
ejpam-7	183	16	)	)	PUNCT
ejpam-7	183	17	28	28	NUM
ejpam-7	183	18	true	true	ADJ
ejpam-7	183	19	(	(	PUNCT
ejpam-7	183	20	i	i	NOUN
ejpam-7	183	21	)	)	PUNCT
ejpam-7	183	22	k(y	k(y	PROPN
ejpam-7	183	23	,	,	PUNCT
ejpam-7	183	24	z	z	NOUN
ejpam-7	183	25	)	)	PUNCT
ejpam-7	183	26	=	=	SYM
ejpam-7	183	27	αg(y	αg(y	NUM
ejpam-7	183	28	,	,	PUNCT
ejpam-7	183	29	φz	φz	NOUN
ejpam-7	183	30	)	)	PUNCT
ejpam-7	183	31	+	+	CCONJ
ejpam-7	183	32	(	(	PUNCT
ejpam-7	183	33	β	β	X
ejpam-7	183	34	+	+	NOUN
ejpam-7	183	35	1	1	NUM
ejpam-7	183	36	2	2	NUM
ejpam-7	183	37	)	)	PUNCT
ejpam-7	183	38	g(y	g(y	PROPN
ejpam-7	183	39	,	,	PUNCT
ejpam-7	183	40	z)−	z)−	PROPN
ejpam-7	183	41	(	(	PUNCT
ejpam-7	183	42	β	β	X
ejpam-7	183	43	+	+	X
ejpam-7	183	44	1)η(y	1)η(y	NUM
ejpam-7	183	45	)	)	PUNCT
ejpam-7	183	46	η(z	η(z	PROPN
ejpam-7	183	47	)	)	PUNCT
ejpam-7	183	48	(	(	PUNCT
ejpam-7	183	49	ii	ii	NOUN
ejpam-7	183	50	)	)	PUNCT
ejpam-7	183	51	k(y	k(y	PROPN
ejpam-7	183	52	,	,	PUNCT
ejpam-7	183	53	ξ	ξ	X
ejpam-7	183	54	)	)	PUNCT
ejpam-7	183	55	=	=	SYM
ejpam-7	184	1	k(ξ	k(ξ	X
ejpam-7	184	2	,	,	PUNCT
ejpam-7	184	3	y	y	PROPN
ejpam-7	184	4	)	)	PUNCT
ejpam-7	184	5	=	=	PUNCT
ejpam-7	184	6	−1	−1	NOUN
ejpam-7	184	7	2	2	NUM
ejpam-7	184	8	η(y	η(y	NOUN
ejpam-7	184	9	)	)	PUNCT
ejpam-7	184	10	(	(	PUNCT
ejpam-7	184	11	iii	iii	NOUN
ejpam-7	184	12	)	)	PUNCT
ejpam-7	184	13	k(∇y	k(∇y	NUM
ejpam-7	184	14	ξ	ξ	PROPN
ejpam-7	184	15	,	,	PUNCT
ejpam-7	184	16	z	z	NOUN
ejpam-7	184	17	)	)	PUNCT
ejpam-7	184	18	=	=	SYM
ejpam-7	184	19	−α2[g(y	−α2[g(y	NOUN
ejpam-7	184	20	,	,	PUNCT
ejpam-7	184	21	z)−	z)−	PROPN
ejpam-7	184	22	η(y	η(y	PROPN
ejpam-7	184	23	)	)	PUNCT
ejpam-7	184	24	η(z)]−	η(z)]−	ADV
ejpam-7	184	25	2αβg(φy	2αβg(φy	NUM
ejpam-7	184	26	,	,	PUNCT
ejpam-7	184	27	z	z	NOUN
ejpam-7	184	28	)	)	PUNCT
ejpam-7	184	29	−α	−α	NOUN
ejpam-7	184	30	2	2	NUM
ejpam-7	184	31	g(φy	g(φy	PROPN
ejpam-7	184	32	,	,	PUNCT
ejpam-7	184	33	z	z	NOUN
ejpam-7	184	34	)	)	PUNCT
ejpam-7	185	1	+	+	CCONJ
ejpam-7	185	2	β	β	X
ejpam-7	185	3	(	(	PUNCT
ejpam-7	185	4	β	β	X
ejpam-7	185	5	+	+	NOUN
ejpam-7	185	6	1	1	NUM
ejpam-7	185	7	2	2	NUM
ejpam-7	185	8	)	)	PUNCT
ejpam-7	186	1	[	[	X
ejpam-7	186	2	g(y	g(y	X
ejpam-7	186	3	,	,	PUNCT
ejpam-7	186	4	z)−	z)−	PROPN
ejpam-7	186	5	η(y	η(y	PROPN
ejpam-7	186	6	)	)	PUNCT
ejpam-7	186	7	η(z	η(z	PROPN
ejpam-7	186	8	)	)	PUNCT
ejpam-7	186	9	]	]	PUNCT
ejpam-7	186	10	(	(	PUNCT
ejpam-7	186	11	4.2	4.2	NUM
ejpam-7	186	12	)	)	PUNCT
ejpam-7	186	13	(	(	PUNCT
ejpam-7	186	14	iv	iv	X
ejpam-7	186	15	)	)	PUNCT
ejpam-7	186	16	k(y,∇zξ	k(y,∇zξ	NOUN
ejpam-7	186	17	)	)	PUNCT
ejpam-7	186	18	=	=	PUNCT
ejpam-7	186	19	α2[g(y	α2[g(y	PROPN
ejpam-7	186	20	,	,	PUNCT
ejpam-7	186	21	z)−	z)−	PROPN
ejpam-7	186	22	η(y	η(y	PROPN
ejpam-7	186	23	)	)	PUNCT
ejpam-7	186	24	η(z	η(z	PROPN
ejpam-7	186	25	)	)	PUNCT
ejpam-7	186	26	]	]	PUNCT
ejpam-7	187	1	+	+	CCONJ
ejpam-7	187	2	α	α	X
ejpam-7	187	3	2	2	NUM
ejpam-7	187	4	g(φy	g(φy	NUM
ejpam-7	187	5	,	,	PUNCT
ejpam-7	187	6	z	z	NOUN
ejpam-7	187	7	)	)	PUNCT
ejpam-7	188	1	+	+	NOUN
ejpam-7	188	2	β	β	X
ejpam-7	188	3	(	(	PUNCT
ejpam-7	188	4	β	β	X
ejpam-7	188	5	+	+	NOUN
ejpam-7	188	6	1	1	NUM
ejpam-7	188	7	2	2	NUM
ejpam-7	188	8	)	)	PUNCT
ejpam-7	189	1	[	[	X
ejpam-7	189	2	g(y	g(y	X
ejpam-7	189	3	,	,	PUNCT
ejpam-7	189	4	z)−	z)−	PROPN
ejpam-7	189	5	η(y	η(y	PROPN
ejpam-7	189	6	)	)	PUNCT
ejpam-7	189	7	η(z	η(z	PROPN
ejpam-7	189	8	)	)	PUNCT
ejpam-7	189	9	]	]	PUNCT
ejpam-7	189	10	.	.	PUNCT
ejpam-7	190	1	[	[	X
ejpam-7	190	2	5	5	NUM
ejpam-7	190	3	]	]	PUNCT
ejpam-7	190	4	:	:	PUNCT
ejpam-7	190	5	in	in	ADP
ejpam-7	190	6	a	a	DET
ejpam-7	190	7	trans	trans	ADJ
ejpam-7	190	8	-	-	ADJ
ejpam-7	190	9	sasakian	sasakian	ADJ
ejpam-7	190	10	manifold	manifold	NOUN
ejpam-7	190	11	under	under	ADP
ejpam-7	190	12	the	the	DET
ejpam-7	190	13	condition	condition	NOUN
ejpam-7	190	14	(	(	PUNCT
ejpam-7	190	15	2.14	2.14	NUM
ejpam-7	190	16	)	)	PUNCT
ejpam-7	190	17	,	,	PUNCT
ejpam-7	190	18	we	we	PRON
ejpam-7	190	19	have	have	VERB
ejpam-7	190	20	[	[	X
ejpam-7	190	21	(	(	PUNCT
ejpam-7	190	22	∇ξk)(y	∇ξk)(y	PROPN
ejpam-7	190	23	,	,	PUNCT
ejpam-7	190	24	z)−	z)−	PROPN
ejpam-7	190	25	(	(	PUNCT
ejpam-7	190	26	∇yk)(ξ	∇yk)(ξ	PROPN
ejpam-7	190	27	,	,	PUNCT
ejpam-7	190	28	z	z	NOUN
ejpam-7	190	29	)	)	PUNCT
ejpam-7	190	30	]	]	PUNCT
ejpam-7	191	1	=	=	PUNCT
ejpam-7	191	2	αg(y	αg(y	NOUN
ejpam-7	191	3	,	,	PUNCT
ejpam-7	191	4	φz)−	φz)−	NUM
ejpam-7	191	5	2αβg(φy	2αβg(φy	NUM
ejpam-7	191	6	,	,	PUNCT
ejpam-7	191	7	z	z	NOUN
ejpam-7	191	8	)	)	PUNCT
ejpam-7	191	9	−[(α2	−[(α2	NOUN
ejpam-7	192	1	−	−	NOUN
ejpam-7	193	1	β2)−	β2)−	PROPN
ejpam-7	193	2	(	(	PUNCT
ejpam-7	193	3	2β	2β	NOUN
ejpam-7	193	4	+	+	CCONJ
ejpam-7	193	5	1)][g(y	1)][g(y	NUM
ejpam-7	193	6	,	,	PUNCT
ejpam-7	193	7	z)−	z)−	PROPN
ejpam-7	193	8	η(y	η(y	NOUN
ejpam-7	193	9	)	)	PUNCT
ejpam-7	193	10	η(z)].(4.3	η(z)].(4.3	SYM
ejpam-7	193	11	)	)	PUNCT
ejpam-7	193	12	in	in	ADP
ejpam-7	193	13	this	this	DET
ejpam-7	193	14	section	section	NOUN
ejpam-7	193	15	we	we	PRON
ejpam-7	193	16	prove	prove	VERB
ejpam-7	193	17	the	the	DET
ejpam-7	193	18	following	following	NOUN
ejpam-7	193	19	:	:	PUNCT
ejpam-7	193	20	let	let	VERB
ejpam-7	193	21	in	in	ADP
ejpam-7	193	22	a	a	DET
ejpam-7	193	23	trans	trans	ADJ
ejpam-7	193	24	-	-	ADJ
ejpam-7	193	25	sasakian	sasakian	ADJ
ejpam-7	193	26	manifoldmn	manifoldmn	NOUN
ejpam-7	193	27	(	(	PUNCT
ejpam-7	193	28	n	n	CCONJ
ejpam-7	193	29	>	>	X
ejpam-7	193	30	2	2	NUM
ejpam-7	193	31	)	)	PUNCT
ejpam-7	193	32	under	under	ADP
ejpam-7	193	33	the	the	DET
ejpam-7	193	34	condition	condition	NOUN
ejpam-7	193	35	(	(	PUNCT
ejpam-7	193	36	2.14	2.14	NUM
ejpam-7	193	37	)	)	PUNCT
ejpam-7	193	38	admits	admit	VERB
ejpam-7	193	39	a	a	DET
ejpam-7	193	40	semi	semi	ADJ
ejpam-7	193	41	-	-	ADJ
ejpam-7	193	42	symmetric	symmetric	ADJ
ejpam-7	193	43	metric	metric	ADJ
ejpam-7	193	44	connection	connection	NOUN
ejpam-7	193	45	the	the	DET
ejpam-7	193	46	pseudo	pseudo	NOUN
ejpam-7	193	47	projective	projective	NOUN
ejpam-7	193	48	curvature	curvature	NOUN
ejpam-7	193	49	tensor	tensor	NOUN
ejpam-7	193	50	with	with	ADP
ejpam-7	193	51	respect	respect	NOUN
ejpam-7	193	52	to	to	ADP
ejpam-7	193	53	this	this	DET
ejpam-7	193	54	connection	connection	NOUN
ejpam-7	193	55	is	be	AUX
ejpam-7	193	56	conservative	conservative	ADJ
ejpam-7	193	57	.	.	PUNCT
ejpam-7	194	1	then	then	ADV
ejpam-7	194	2	the	the	DET
ejpam-7	194	3	manifold	manifold	ADJ
ejpam-7	194	4	mn	mn	PROPN
ejpam-7	194	5	is	be	AUX
ejpam-7	194	6	η	η	NOUN
ejpam-7	194	7	-	-	NOUN
ejpam-7	194	8	einstein	einstein	NOUN
ejpam-7	194	9	with	with	ADP
ejpam-7	194	10	respect	respect	NOUN
ejpam-7	194	11	to	to	ADP
ejpam-7	194	12	levi	levi	PROPN
ejpam-7	194	13	-	-	PUNCT
ejpam-7	194	14	civita	civita	NOUN
ejpam-7	194	15	connection	connection	NOUN
ejpam-7	194	16	;	;	PUNCT
ejpam-7	194	17	the	the	DET
ejpam-7	194	18	scalar	scalar	ADJ
ejpam-7	194	19	curvature	curvature	NOUN
ejpam-7	194	20	of	of	ADP
ejpam-7	194	21	such	such	DET
ejpam-7	194	22	a	a	DET
ejpam-7	194	23	manifold	manifold	NOUN
ejpam-7	194	24	is	be	AUX
ejpam-7	194	25	given	give	VERB
ejpam-7	194	26	by	by	ADP
ejpam-7	194	27	(	(	PUNCT
ejpam-7	194	28	4	4	NUM
ejpam-7	194	29	)	)	PUNCT
ejpam-7	194	30	.	.	PUNCT
ejpam-7	195	1	proof	proof	NOUN
ejpam-7	195	2	.	.	PUNCT
ejpam-7	196	1	let	let	VERB
ejpam-7	196	2	us	we	PRON
ejpam-7	196	3	suppose	suppose	VERB
ejpam-7	196	4	that	that	SCONJ
ejpam-7	196	5	in	in	ADP
ejpam-7	196	6	a	a	DET
ejpam-7	196	7	trans	trans	ADJ
ejpam-7	196	8	-	-	ADJ
ejpam-7	196	9	sasakian	sasakian	ADJ
ejpam-7	196	10	manifold	manifold	ADJ
ejpam-7	196	11	mn	mn	PROPN
ejpam-7	196	12	under	under	ADP
ejpam-7	196	13	the	the	DET
ejpam-7	196	14	condition	condition	NOUN
ejpam-7	196	15	(	(	PUNCT
ejpam-7	196	16	2.14)with	2.14)with	NUM
ejpam-7	196	17	respect	respect	NOUN
ejpam-7	196	18	to	to	ADP
ejpam-7	196	19	semi	semi	ADJ
ejpam-7	196	20	-	-	ADJ
ejpam-7	196	21	symmetric	symmetric	ADJ
ejpam-7	196	22	metric	metric	ADJ
ejpam-7	196	23	connection	connection	NOUN
ejpam-7	196	24	div.p̃	div.p̃	PROPN
ejpam-7	196	25	=	=	SYM
ejpam-7	196	26	0	0	X
ejpam-7	196	27	.	.	PUNCT
ejpam-7	196	28	putting	put	VERB
ejpam-7	196	29	x	x	PUNCT
ejpam-7	196	30	=	=	SYM
ejpam-7	196	31	ξ	ξ	X
ejpam-7	196	32	in	in	ADP
ejpam-7	196	33	(	(	PUNCT
ejpam-7	196	34	3.2	3.2	NUM
ejpam-7	196	35	)	)	PUNCT
ejpam-7	196	36	then	then	ADV
ejpam-7	196	37	using	use	VERB
ejpam-7	196	38	(	(	PUNCT
ejpam-7	196	39	2.1),(2.3	2.1),(2.3	NUM
ejpam-7	196	40	)	)	PUNCT
ejpam-7	196	41	,	,	PUNCT
ejpam-7	196	42	(	(	PUNCT
ejpam-7	196	43	2.16	2.16	NUM
ejpam-7	196	44	)	)	PUNCT
ejpam-7	196	45	and	and	CCONJ
ejpam-7	196	46	(	(	PUNCT
ejpam-7	196	47	4.2(ii	4.2(ii	NUM
ejpam-7	196	48	)	)	PUNCT
ejpam-7	196	49	)	)	PUNCT
ejpam-7	196	50	we	we	PRON
ejpam-7	196	51	get	get	VERB
ejpam-7	196	52	(	(	PUNCT
ejpam-7	196	53	a+	a+	PUNCT
ejpam-7	196	54	b)[(∇ξs)(y	b)[(∇ξs)(y	NOUN
ejpam-7	196	55	,	,	PUNCT
ejpam-7	196	56	z)−	z)−	PROPN
ejpam-7	196	57	(	(	PUNCT
ejpam-7	196	58	∇y	∇y	PROPN
ejpam-7	196	59	s)(ξ	s)(ξ	NOUN
ejpam-7	196	60	,	,	PUNCT
ejpam-7	196	61	z)]−	z)]−	NUM
ejpam-7	196	62	(	(	PUNCT
ejpam-7	196	63	a+	a+	PUNCT
ejpam-7	196	64	b(n−	b(n−	PROPN
ejpam-7	196	65	2))[(∇ξk)(y	2))[(∇ξk)(y	NUM
ejpam-7	196	66	,	,	PUNCT
ejpam-7	196	67	z)−	z)−	PROPN
ejpam-7	196	68	(	(	PUNCT
ejpam-7	196	69	∇yk)(ξ	∇yk)(ξ	PROPN
ejpam-7	196	70	,	,	PUNCT
ejpam-7	196	71	z	z	NOUN
ejpam-7	196	72	)	)	PUNCT
ejpam-7	196	73	]	]	PUNCT
ejpam-7	197	1	=	=	SYM
ejpam-7	197	2	(	(	PUNCT
ejpam-7	197	3	a−	a−	PROPN
ejpam-7	197	4	b)s(y	b)s(y	NOUN
ejpam-7	197	5	,	,	PUNCT
ejpam-7	197	6	z	z	NOUN
ejpam-7	197	7	)	)	PUNCT
ejpam-7	198	1	+	+	CCONJ
ejpam-7	198	2	(	(	PUNCT
ejpam-7	198	3	a+	a+	PUNCT
ejpam-7	198	4	b(n−	b(n−	PROPN
ejpam-7	198	5	2))αg(y	2))αg(y	NUM
ejpam-7	198	6	,	,	PUNCT
ejpam-7	198	7	φz)−	φz)−	X
ejpam-7	198	8	a(n−	a(n−	PROPN
ejpam-7	198	9	1)η(r(ξ	1)η(r(ξ	PROPN
ejpam-7	198	10	,	,	PUNCT
ejpam-7	198	11	y	y	PROPN
ejpam-7	198	12	)	)	PUNCT
ejpam-7	198	13	z	z	X
ejpam-7	198	14	)	)	PUNCT
ejpam-7	199	1	+	+	CCONJ
ejpam-7	199	2	[	[	PUNCT
ejpam-7	199	3	(	(	PUNCT
ejpam-7	199	4	a+	a+	PUNCT
ejpam-7	199	5	b(n−	b(n−	PROPN
ejpam-7	199	6	2	2	NUM
ejpam-7	199	7	)	)	PUNCT
ejpam-7	199	8	)	)	PUNCT
ejpam-7	199	9	(	(	PUNCT
ejpam-7	199	10	β	β	X
ejpam-7	199	11	+	+	NOUN
ejpam-7	199	12	1	1	NUM
ejpam-7	199	13	2	2	NUM
ejpam-7	199	14	)	)	PUNCT
ejpam-7	200	1	+	+	CCONJ
ejpam-7	200	2	a(n−a−	a(n−a−	NOUN
ejpam-7	200	3	1	1	NUM
ejpam-7	200	4	)	)	PUNCT
ejpam-7	200	5	+	+	CCONJ
ejpam-7	200	6	b(n−	b(n−	VERB
ejpam-7	200	7	1)(α2	1)(α2	NUM
ejpam-7	200	8	−	−	NOUN
ejpam-7	200	9	β2	β2	ADJ
ejpam-7	200	10	)	)	PUNCT
ejpam-7	200	11	+	+	CCONJ
ejpam-7	200	12	b	b	X
ejpam-7	200	13	2	2	NUM
ejpam-7	200	14	(	(	PUNCT
ejpam-7	200	15	n−	n−	NOUN
ejpam-7	200	16	2	2	NUM
ejpam-7	200	17	)	)	PUNCT
ejpam-7	200	18	]	]	PUNCT
ejpam-7	200	19	g(y	g(y	PROPN
ejpam-7	200	20	,	,	PUNCT
ejpam-7	200	21	z	z	NOUN
ejpam-7	200	22	)	)	PUNCT
ejpam-7	200	23	−	−	NOUN
ejpam-7	200	24	[	[	PUNCT
ejpam-7	200	25	a(n−a−	a(n−a−	NOUN
ejpam-7	200	26	1	1	NUM
ejpam-7	200	27	)	)	PUNCT
ejpam-7	200	28	+	+	CCONJ
ejpam-7	200	29	(	(	PUNCT
ejpam-7	200	30	a+	a+	PUNCT
ejpam-7	200	31	b(n−	b(n−	PROPN
ejpam-7	200	32	2	2	NUM
ejpam-7	200	33	)	)	PUNCT
ejpam-7	200	34	)	)	PUNCT
ejpam-7	200	35	(	(	PUNCT
ejpam-7	200	36	β	β	X
ejpam-7	200	37	+	+	NOUN
ejpam-7	200	38	1	1	NUM
ejpam-7	200	39	2	2	NUM
ejpam-7	200	40	)	)	PUNCT
ejpam-7	200	41	+	+	CCONJ
ejpam-7	200	42	b	b	X
ejpam-7	200	43	2	2	NUM
ejpam-7	200	44	(	(	PUNCT
ejpam-7	200	45	n−	n−	NOUN
ejpam-7	200	46	2	2	NUM
ejpam-7	200	47	)	)	PUNCT
ejpam-7	200	48	]	]	PUNCT
ejpam-7	200	49	η(y	η(y	PROPN
ejpam-7	200	50	)	)	PUNCT
ejpam-7	200	51	η(z	η(z	PROPN
ejpam-7	200	52	)	)	PUNCT
ejpam-7	200	53	(	(	PUNCT
ejpam-7	200	54	4.4	4.4	NUM
ejpam-7	200	55	)	)	PUNCT
ejpam-7	200	56	+	+	CCONJ
ejpam-7	200	57	[	[	PUNCT
ejpam-7	200	58	1	1	NUM
ejpam-7	200	59	n	n	NOUN
ejpam-7	200	60	a+	a+	PUNCT
ejpam-7	200	61	(	(	PUNCT
ejpam-7	200	62	n−	n−	NOUN
ejpam-7	200	63	1	1	NUM
ejpam-7	200	64	)	)	PUNCT
ejpam-7	200	65	(	(	PUNCT
ejpam-7	200	66	n−	n−	NOUN
ejpam-7	200	67	1	1	NUM
ejpam-7	200	68	)	)	PUNCT
ejpam-7	200	69	(	(	PUNCT
ejpam-7	200	70	n−	n−	NOUN
ejpam-7	200	71	2)−	2)−	PROPN
ejpam-7	200	72	a	a	PRON
ejpam-7	200	73	]	]	X
ejpam-7	200	74	[	[	X
ejpam-7	200	75	η(z)∇ya−	η(z)∇ya−	NOUN
ejpam-7	200	76	g(y	g(y	PROPN
ejpam-7	200	77	,	,	PUNCT
ejpam-7	200	78	z)∇ξa	z)∇ξa	NUM
ejpam-7	200	79	]	]	PUNCT
ejpam-7	200	80	−	−	PROPN
ejpam-7	200	81	1	1	NUM
ejpam-7	200	82	n	n	PROPN
ejpam-7	200	83	[	[	PUNCT
ejpam-7	200	84	a+	a+	PUNCT
ejpam-7	200	85	(	(	PUNCT
ejpam-7	200	86	n−	n−	NOUN
ejpam-7	200	87	1	1	NUM
ejpam-7	200	88	)	)	PUNCT
ejpam-7	200	89	(	(	PUNCT
ejpam-7	200	90	n−	n−	NOUN
ejpam-7	200	91	1	1	NUM
ejpam-7	200	92	)	)	PUNCT
ejpam-7	200	93	]	]	PUNCT
ejpam-7	201	1	[	[	X
ejpam-7	201	2	η(z)∇y	η(z)∇y	NUM
ejpam-7	201	3	r	r	NOUN
ejpam-7	201	4	−	−	PROPN
ejpam-7	201	5	g(y	g(y	PROPN
ejpam-7	201	6	,	,	PUNCT
ejpam-7	201	7	z)∇ξr	z)∇ξr	ADV
ejpam-7	201	8	]	]	PUNCT
ejpam-7	201	9	.	.	PUNCT
ejpam-7	202	1	bagewadi	bagewadi	PROPN
ejpam-7	202	2	c.s	c.s	PROPN
ejpam-7	202	3	.	.	PROPN
ejpam-7	202	4	et	et	PROPN
ejpam-7	202	5	al	al	PROPN
ejpam-7	202	6	.	.	PUNCT
ejpam-7	202	7	/	/	SYM
ejpam-7	202	8	eur	eur	PROPN
ejpam-7	202	9	.	.	PUNCT
ejpam-7	203	1	j.	j.	PROPN
ejpam-7	203	2	pure	pure	PROPN
ejpam-7	203	3	appl	appl	PROPN
ejpam-7	203	4	.	.	PROPN
ejpam-7	203	5	math	math	PROPN
ejpam-7	203	6	,	,	PUNCT
ejpam-7	203	7	1	1	NUM
ejpam-7	203	8	(	(	PUNCT
ejpam-7	203	9	2008	2008	NUM
ejpam-7	203	10	)	)	PUNCT
ejpam-7	203	11	,	,	PUNCT
ejpam-7	203	12	(	(	PUNCT
ejpam-7	203	13	21	21	NUM
ejpam-7	203	14	-	-	SYM
ejpam-7	203	15	31	31	NUM
ejpam-7	203	16	)	)	PUNCT
ejpam-7	203	17	29	29	NUM
ejpam-7	203	18	using	use	VERB
ejpam-7	203	19	(	(	PUNCT
ejpam-7	203	20	2.15	2.15	NUM
ejpam-7	203	21	)	)	PUNCT
ejpam-7	203	22	,	,	PUNCT
ejpam-7	203	23	(	(	PUNCT
ejpam-7	203	24	4.1	4.1	NUM
ejpam-7	203	25	)	)	PUNCT
ejpam-7	203	26	,	,	PUNCT
ejpam-7	203	27	(	(	PUNCT
ejpam-7	203	28	4.2(i	4.2(i	NUM
ejpam-7	203	29	)	)	PUNCT
ejpam-7	203	30	)	)	PUNCT
ejpam-7	204	1	and	and	CCONJ
ejpam-7	204	2	(	(	PUNCT
ejpam-7	204	3	4.3	4.3	NUM
ejpam-7	204	4	)	)	PUNCT
ejpam-7	204	5	in	in	ADP
ejpam-7	204	6	above	above	ADV
ejpam-7	204	7	,	,	PUNCT
ejpam-7	204	8	we	we	PRON
ejpam-7	204	9	get	get	VERB
ejpam-7	204	10	(	(	PUNCT
ejpam-7	204	11	a+	a+	PRON
ejpam-7	204	12	b)(β	b)(β	NOUN
ejpam-7	204	13	−	−	PROPN
ejpam-7	204	14	1)s(y	1)s(y	NUM
ejpam-7	204	15	,	,	PUNCT
ejpam-7	204	16	z	z	NOUN
ejpam-7	204	17	)	)	PUNCT
ejpam-7	205	1	+	+	CCONJ
ejpam-7	205	2	(	(	PUNCT
ejpam-7	205	3	a+	a+	PRON
ejpam-7	205	4	b)αs(y	b)αs(y	NOUN
ejpam-7	205	5	,	,	PUNCT
ejpam-7	205	6	φz	φz	NOUN
ejpam-7	205	7	)	)	PUNCT
ejpam-7	205	8	=	=	PUNCT
ejpam-7	206	1	−[2α(β	−[2α(β	X
ejpam-7	206	2	+	+	NUM
ejpam-7	207	1	1)(a+	1)(a+	NUM
ejpam-7	207	2	b(n−	b(n−	VERB
ejpam-7	207	3	2	2	NUM
ejpam-7	207	4	)	)	PUNCT
ejpam-7	207	5	)	)	PUNCT
ejpam-7	208	1	+	+	CCONJ
ejpam-7	208	2	(	(	PUNCT
ejpam-7	208	3	a+	a+	PUNCT
ejpam-7	208	4	b)(n−	b)(n−	NOUN
ejpam-7	208	5	1)(α2	1)(α2	NUM
ejpam-7	209	1	−	−	NOUN
ejpam-7	209	2	β2)α]g(φy	β2)α]g(φy	ADJ
ejpam-7	209	3	,	,	PUNCT
ejpam-7	209	4	z	z	NOUN
ejpam-7	209	5	)	)	PUNCT
ejpam-7	210	1	+	+	PROPN
ejpam-7	210	2	p̀	p̀	PROPN
ejpam-7	210	3	.g(y	.g(y	PROPN
ejpam-7	210	4	,	,	PUNCT
ejpam-7	210	5	z	z	NOUN
ejpam-7	210	6	)	)	PUNCT
ejpam-7	210	7	+	+	CCONJ
ejpam-7	210	8	q̀.η(y	q̀.η(y	ADJ
ejpam-7	210	9	)	)	PUNCT
ejpam-7	210	10	η(z	η(z	PROPN
ejpam-7	210	11	)	)	PUNCT
ejpam-7	211	1	+	+	CCONJ
ejpam-7	211	2	[	[	PUNCT
ejpam-7	211	3	1	1	NUM
ejpam-7	211	4	n	n	NOUN
ejpam-7	211	5	a+	a+	PUNCT
ejpam-7	211	6	(	(	PUNCT
ejpam-7	211	7	n−	n−	NOUN
ejpam-7	211	8	1	1	NUM
ejpam-7	211	9	)	)	PUNCT
ejpam-7	211	10	(	(	PUNCT
ejpam-7	211	11	n−	n−	NOUN
ejpam-7	211	12	1	1	NUM
ejpam-7	211	13	)	)	PUNCT
ejpam-7	211	14	(	(	PUNCT
ejpam-7	211	15	n−	n−	NOUN
ejpam-7	211	16	2)−	2)−	PROPN
ejpam-7	211	17	a	a	PRON
ejpam-7	211	18	]	]	X
ejpam-7	212	1	[	[	X
ejpam-7	212	2	η(z)∇ya−	η(z)∇ya−	NOUN
ejpam-7	212	3	g(y	g(y	PROPN
ejpam-7	212	4	,	,	PUNCT
ejpam-7	212	5	z)∇ξa	z)∇ξa	NUM
ejpam-7	212	6	]	]	PUNCT
ejpam-7	212	7	(	(	PUNCT
ejpam-7	212	8	4.5	4.5	NUM
ejpam-7	212	9	)	)	PUNCT
ejpam-7	212	10	−	−	PROPN
ejpam-7	212	11	1	1	NUM
ejpam-7	212	12	n	n	PROPN
ejpam-7	212	13	[	[	PUNCT
ejpam-7	212	14	a+	a+	PUNCT
ejpam-7	212	15	(	(	PUNCT
ejpam-7	212	16	n−	n−	NOUN
ejpam-7	212	17	1	1	NUM
ejpam-7	212	18	)	)	PUNCT
ejpam-7	212	19	(	(	PUNCT
ejpam-7	212	20	n−	n−	NOUN
ejpam-7	212	21	1	1	NUM
ejpam-7	212	22	)	)	PUNCT
ejpam-7	212	23	]	]	PUNCT
ejpam-7	213	1	[	[	X
ejpam-7	213	2	η(z)∇y	η(z)∇y	NUM
ejpam-7	213	3	r	r	NOUN
ejpam-7	213	4	−	−	PROPN
ejpam-7	213	5	g(y	g(y	PROPN
ejpam-7	213	6	,	,	PUNCT
ejpam-7	213	7	z)∇ξr	z)∇ξr	ADV
ejpam-7	213	8	]	]	PUNCT
ejpam-7	213	9	.	.	PUNCT
ejpam-7	214	1	where	where	SCONJ
ejpam-7	214	2	p̀	p̀	NOUN
ejpam-7	214	3	=	=	PUNCT
ejpam-7	215	1	[	[	X
ejpam-7	215	2	a(β	a(β	NOUN
ejpam-7	215	3	−	−	PROPN
ejpam-7	215	4	1	1	NUM
ejpam-7	215	5	)	)	PUNCT
ejpam-7	215	6	+	+	CCONJ
ejpam-7	216	1	b(β	b(β	PROPN
ejpam-7	216	2	+	+	CCONJ
ejpam-7	216	3	1)](n−	1)](n−	NUM
ejpam-7	216	4	1)(α2	1)(α2	NUM
ejpam-7	216	5	−	−	NOUN
ejpam-7	216	6	β2	β2	ADJ
ejpam-7	216	7	)	)	PUNCT
ejpam-7	216	8	+	+	CCONJ
ejpam-7	216	9	a(n−a−	a(n−a−	NOUN
ejpam-7	216	10	1	1	NUM
ejpam-7	216	11	)	)	PUNCT
ejpam-7	216	12	+	+	CCONJ
ejpam-7	216	13	b	b	SYM
ejpam-7	216	14	2	2	NUM
ejpam-7	216	15	(	(	PUNCT
ejpam-7	216	16	n−	n−	NOUN
ejpam-7	216	17	2	2	NUM
ejpam-7	216	18	)	)	PUNCT
ejpam-7	216	19	+	+	CCONJ
ejpam-7	217	1	[	[	X
ejpam-7	217	2	a+	a+	PUNCT
ejpam-7	217	3	b(n−	b(n−	PROPN
ejpam-7	217	4	2	2	NUM
ejpam-7	217	5	)	)	PUNCT
ejpam-7	217	6	]	]	PUNCT
ejpam-7	217	7	[	[	PUNCT
ejpam-7	217	8	2	2	NUM
ejpam-7	217	9	(	(	PUNCT
ejpam-7	217	10	β	β	X
ejpam-7	217	11	+	+	NOUN
ejpam-7	217	12	1	1	NUM
ejpam-7	217	13	4	4	NUM
ejpam-7	217	14	)	)	PUNCT
ejpam-7	217	15	−	−	PROPN
ejpam-7	217	16	(	(	PUNCT
ejpam-7	217	17	α2	α2	ADV
ejpam-7	217	18	−	−	PROPN
ejpam-7	217	19	β2	β2	PROPN
ejpam-7	217	20	)	)	PUNCT
ejpam-7	217	21	]	]	PUNCT
ejpam-7	217	22	and	and	CCONJ
ejpam-7	217	23	q̀	q̀	X
ejpam-7	217	24	=	=	SYM
ejpam-7	218	1	[	[	X
ejpam-7	218	2	(	(	PUNCT
ejpam-7	218	3	a−	a−	PROPN
ejpam-7	218	4	b)(α2	b)(α2	NOUN
ejpam-7	218	5	−	−	PROPN
ejpam-7	218	6	β2)−	β2)−	PROPN
ejpam-7	218	7	b](n−	b](n−	PROPN
ejpam-7	218	8	2)−	2)−	NUM
ejpam-7	218	9	a	a	DET
ejpam-7	218	10	(	(	PUNCT
ejpam-7	218	11	n−a−	n−a−	NUM
ejpam-7	218	12	1	1	NUM
ejpam-7	218	13	2	2	NUM
ejpam-7	218	14	)	)	PUNCT
ejpam-7	218	15	.	.	PUNCT
ejpam-7	219	1	next	next	ADV
ejpam-7	219	2	,	,	PUNCT
ejpam-7	219	3	by	by	ADP
ejpam-7	219	4	replacing	replace	VERB
ejpam-7	219	5	z	z	NOUN
ejpam-7	219	6	by	by	ADP
ejpam-7	219	7	φz	φz	X
ejpam-7	219	8	in	in	ADP
ejpam-7	219	9	(	(	PUNCT
ejpam-7	219	10	4.5	4.5	NUM
ejpam-7	219	11	)	)	PUNCT
ejpam-7	219	12	and	and	CCONJ
ejpam-7	219	13	then	then	ADV
ejpam-7	219	14	using	use	VERB
ejpam-7	219	15	(	(	PUNCT
ejpam-7	219	16	2.1	2.1	NUM
ejpam-7	219	17	)	)	PUNCT
ejpam-7	219	18	,	,	PUNCT
ejpam-7	219	19	we	we	PRON
ejpam-7	219	20	obtain	obtain	VERB
ejpam-7	219	21	−(a+	−(a+	NUM
ejpam-7	219	22	b)αs(y	b)αs(y	NOUN
ejpam-7	219	23	,	,	PUNCT
ejpam-7	219	24	z)−	z)−	PROPN
ejpam-7	219	25	(	(	PUNCT
ejpam-7	219	26	a+	a+	PUNCT
ejpam-7	219	27	b)(β	b)(β	NOUN
ejpam-7	219	28	−	−	PROPN
ejpam-7	219	29	1)s(φy	1)s(φy	NUM
ejpam-7	219	30	,	,	PUNCT
ejpam-7	219	31	z	z	NOUN
ejpam-7	219	32	)	)	PUNCT
ejpam-7	219	33	=	=	SYM
ejpam-7	220	1	−[2α(β	−[2α(β	X
ejpam-7	220	2	+	+	NOUN
ejpam-7	220	3	1)[a+	1)[a+	NUM
ejpam-7	220	4	b(n−	b(n−	VERB
ejpam-7	220	5	2	2	NUM
ejpam-7	220	6	)	)	PUNCT
ejpam-7	220	7	+	+	CCONJ
ejpam-7	220	8	(	(	PUNCT
ejpam-7	220	9	a+	a+	PUNCT
ejpam-7	220	10	b)(n−	b)(n−	NOUN
ejpam-7	220	11	1)(α2	1)(α2	NUM
ejpam-7	220	12	−	−	PROPN
ejpam-7	220	13	β2)α]g(y	β2)α]g(y	NOUN
ejpam-7	220	14	,	,	PUNCT
ejpam-7	220	15	z	z	NOUN
ejpam-7	220	16	)	)	PUNCT
ejpam-7	220	17	−p̀	−p̀	PROPN
ejpam-7	220	18	.g(y	.g(y	PROPN
ejpam-7	220	19	,	,	PUNCT
ejpam-7	220	20	φz	φz	PROPN
ejpam-7	220	21	)	)	PUNCT
ejpam-7	220	22	+	+	PUNCT
ejpam-7	221	1	[	[	X
ejpam-7	221	2	2α(β	2α(β	NUM
ejpam-7	221	3	+	+	NOUN
ejpam-7	221	4	1)(a+	1)(a+	NUM
ejpam-7	221	5	b(n−	b(n−	VERB
ejpam-7	221	6	2))]η(y	2))]η(y	NUM
ejpam-7	221	7	)	)	PUNCT
ejpam-7	221	8	η(z	η(z	PROPN
ejpam-7	221	9	)	)	PUNCT
ejpam-7	221	10	(	(	PUNCT
ejpam-7	221	11	4.6	4.6	NUM
ejpam-7	221	12	)	)	PUNCT
ejpam-7	221	13	+	+	CCONJ
ejpam-7	221	14	[	[	PUNCT
ejpam-7	221	15	1	1	NUM
ejpam-7	221	16	n	n	NOUN
ejpam-7	221	17	a+	a+	PUNCT
ejpam-7	221	18	(	(	PUNCT
ejpam-7	221	19	n−	n−	NOUN
ejpam-7	221	20	1	1	NUM
ejpam-7	221	21	)	)	PUNCT
ejpam-7	221	22	(	(	PUNCT
ejpam-7	221	23	n−	n−	NOUN
ejpam-7	221	24	1	1	NUM
ejpam-7	221	25	)	)	PUNCT
ejpam-7	221	26	(	(	PUNCT
ejpam-7	221	27	n−	n−	NOUN
ejpam-7	221	28	2)−	2)−	PROPN
ejpam-7	221	29	a	a	DET
ejpam-7	221	30	]	]	X
ejpam-7	221	31	g(y	g(y	PROPN
ejpam-7	221	32	,	,	PUNCT
ejpam-7	221	33	φz)∇ξa−	φz)∇ξa−	NOUN
ejpam-7	221	34	1	1	NUM
ejpam-7	221	35	n	n	PROPN
ejpam-7	221	36	[	[	PUNCT
ejpam-7	221	37	a+	a+	PUNCT
ejpam-7	221	38	(	(	PUNCT
ejpam-7	221	39	n−	n−	NOUN
ejpam-7	221	40	1	1	NUM
ejpam-7	221	41	)	)	PUNCT
ejpam-7	221	42	(	(	PUNCT
ejpam-7	221	43	n−	n−	NOUN
ejpam-7	221	44	1	1	NUM
ejpam-7	221	45	)	)	PUNCT
ejpam-7	221	46	]	]	PUNCT
ejpam-7	222	1	g(y	g(y	NOUN
ejpam-7	222	2	,	,	PUNCT
ejpam-7	222	3	φz)∇ξr	φz)∇ξr	NOUN
ejpam-7	222	4	.	.	PUNCT
ejpam-7	223	1	interchanging	interchange	VERB
ejpam-7	223	2	y	y	PROPN
ejpam-7	223	3	and	and	CCONJ
ejpam-7	223	4	z	z	PROPN
ejpam-7	223	5	in	in	ADP
ejpam-7	223	6	above	above	ADV
ejpam-7	223	7	,	,	PUNCT
ejpam-7	223	8	we	we	PRON
ejpam-7	223	9	have	have	VERB
ejpam-7	223	10	−(a+	−(a+	NUM
ejpam-7	223	11	b)αs(y	b)αs(y	NOUN
ejpam-7	223	12	,	,	PUNCT
ejpam-7	223	13	z)−	z)−	PROPN
ejpam-7	223	14	(	(	PUNCT
ejpam-7	223	15	a+	a+	PUNCT
ejpam-7	223	16	b)(β	b)(β	NOUN
ejpam-7	223	17	−	−	PROPN
ejpam-7	223	18	1)s(y	1)s(y	NUM
ejpam-7	223	19	,	,	PUNCT
ejpam-7	223	20	φz	φz	NOUN
ejpam-7	223	21	)	)	PUNCT
ejpam-7	223	22	=	=	PUNCT
ejpam-7	224	1	−[2α(β	−[2α(β	PROPN
ejpam-7	224	2	+	+	NOUN
ejpam-7	224	3	1)[a+	1)[a+	NUM
ejpam-7	224	4	b(n−	b(n−	VERB
ejpam-7	224	5	2	2	NUM
ejpam-7	224	6	)	)	PUNCT
ejpam-7	224	7	+	+	CCONJ
ejpam-7	224	8	(	(	PUNCT
ejpam-7	224	9	a+	a+	PUNCT
ejpam-7	224	10	b)(n−	b)(n−	NOUN
ejpam-7	224	11	1)(α2	1)(α2	NUM
ejpam-7	224	12	−	−	PROPN
ejpam-7	224	13	β2)α]g(y	β2)α]g(y	NOUN
ejpam-7	224	14	,	,	PUNCT
ejpam-7	224	15	z	z	NOUN
ejpam-7	224	16	)	)	PUNCT
ejpam-7	224	17	−p̀	−p̀	PROPN
ejpam-7	225	1	.g(φy	.g(φy	PROPN
ejpam-7	225	2	,	,	PUNCT
ejpam-7	225	3	z	z	X
ejpam-7	225	4	)	)	PUNCT
ejpam-7	225	5	+	+	CCONJ
ejpam-7	226	1	[	[	X
ejpam-7	226	2	2α(β	2α(β	NUM
ejpam-7	226	3	+	+	NOUN
ejpam-7	226	4	1)(a+	1)(a+	NUM
ejpam-7	226	5	b(n−	b(n−	VERB
ejpam-7	226	6	2))]η(y	2))]η(y	NUM
ejpam-7	226	7	)	)	PUNCT
ejpam-7	226	8	η(z	η(z	PROPN
ejpam-7	226	9	)	)	PUNCT
ejpam-7	226	10	(	(	PUNCT
ejpam-7	226	11	4.7	4.7	NUM
ejpam-7	226	12	)	)	PUNCT
ejpam-7	226	13	+	+	CCONJ
ejpam-7	226	14	[	[	PUNCT
ejpam-7	226	15	1	1	NUM
ejpam-7	226	16	n	n	NOUN
ejpam-7	226	17	a+	a+	PUNCT
ejpam-7	226	18	(	(	PUNCT
ejpam-7	226	19	n−	n−	NOUN
ejpam-7	226	20	1	1	NUM
ejpam-7	226	21	)	)	PUNCT
ejpam-7	226	22	(	(	PUNCT
ejpam-7	226	23	n−	n−	NOUN
ejpam-7	226	24	1	1	NUM
ejpam-7	226	25	)	)	PUNCT
ejpam-7	226	26	(	(	PUNCT
ejpam-7	226	27	n−	n−	NOUN
ejpam-7	226	28	2)−	2)−	NUM
ejpam-7	226	29	a	a	PRON
ejpam-7	226	30	]	]	X
ejpam-7	226	31	g(φy	g(φy	PROPN
ejpam-7	226	32	,	,	PUNCT
ejpam-7	226	33	z)∇ξa−	z)∇ξa−	NOUN
ejpam-7	226	34	1	1	NUM
ejpam-7	226	35	n	n	PROPN
ejpam-7	226	36	[	[	PUNCT
ejpam-7	226	37	a+	a+	PUNCT
ejpam-7	226	38	(	(	PUNCT
ejpam-7	226	39	n−	n−	NOUN
ejpam-7	226	40	1	1	NUM
ejpam-7	226	41	)	)	PUNCT
ejpam-7	226	42	(	(	PUNCT
ejpam-7	226	43	n−	n−	NOUN
ejpam-7	226	44	1	1	NUM
ejpam-7	226	45	)	)	PUNCT
ejpam-7	226	46	]	]	PUNCT
ejpam-7	227	1	g(φy	g(φy	X
ejpam-7	227	2	,	,	PUNCT
ejpam-7	227	3	z)∇ξr	z)∇ξr	ADV
ejpam-7	227	4	.	.	PUNCT
ejpam-7	227	5	by	by	ADP
ejpam-7	227	6	adding	add	VERB
ejpam-7	227	7	(	(	PUNCT
ejpam-7	227	8	4.6	4.6	NUM
ejpam-7	227	9	)	)	PUNCT
ejpam-7	227	10	and	and	CCONJ
ejpam-7	227	11	(	(	PUNCT
ejpam-7	227	12	4.7	4.7	NUM
ejpam-7	227	13	)	)	PUNCT
ejpam-7	227	14	,	,	PUNCT
ejpam-7	227	15	then	then	ADV
ejpam-7	227	16	by	by	ADP
ejpam-7	227	17	using	use	VERB
ejpam-7	227	18	skew	skew	ADJ
ejpam-7	227	19	-	-	PUNCT
ejpam-7	227	20	symmetric	symmetric	ADJ
ejpam-7	227	21	property	property	NOUN
ejpam-7	227	22	of	of	ADP
ejpam-7	227	23	φ	φ	PROPN
ejpam-7	227	24	,	,	PUNCT
ejpam-7	227	25	one	one	PRON
ejpam-7	227	26	can	can	AUX
ejpam-7	227	27	obtain	obtain	VERB
ejpam-7	227	28	s(y	s(y	PROPN
ejpam-7	227	29	,	,	PUNCT
ejpam-7	227	30	z	z	NOUN
ejpam-7	227	31	)	)	PUNCT
ejpam-7	228	1	=	=	SYM
ejpam-7	228	2	p2.g(y	p2.g(y	PROPN
ejpam-7	228	3	,	,	PUNCT
ejpam-7	228	4	z	z	NOUN
ejpam-7	228	5	)	)	PUNCT
ejpam-7	229	1	+	+	ADJ
ejpam-7	229	2	q2.η(y	q2.η(y	PROPN
ejpam-7	229	3	)	)	PUNCT
ejpam-7	229	4	η(z	η(z	PROPN
ejpam-7	229	5	)	)	PUNCT
ejpam-7	229	6	.	.	PUNCT
ejpam-7	230	1	(	(	PUNCT
ejpam-7	230	2	4.8	4.8	NUM
ejpam-7	230	3	)	)	PUNCT
ejpam-7	230	4	where	where	SCONJ
ejpam-7	230	5	p2	p2	X
ejpam-7	230	6	=	=	PUNCT
ejpam-7	230	7	[	[	PUNCT
ejpam-7	230	8	2	2	NUM
ejpam-7	230	9	(	(	PUNCT
ejpam-7	230	10	β	β	X
ejpam-7	230	11	+	+	NOUN
ejpam-7	230	12	1	1	NUM
ejpam-7	230	13	)	)	PUNCT
ejpam-7	230	14	(	(	PUNCT
ejpam-7	230	15	a+	a+	PUNCT
ejpam-7	230	16	b	b	X
ejpam-7	230	17	)	)	PUNCT
ejpam-7	231	1	[	[	X
ejpam-7	231	2	a+	a+	PUNCT
ejpam-7	231	3	b(n−	b(n−	PROPN
ejpam-7	231	4	2	2	NUM
ejpam-7	231	5	)	)	PUNCT
ejpam-7	231	6	]	]	PUNCT
ejpam-7	232	1	+	+	CCONJ
ejpam-7	232	2	(	(	PUNCT
ejpam-7	232	3	n−	n−	NOUN
ejpam-7	232	4	1)(α2	1)(α2	NUM
ejpam-7	232	5	−	−	NOUN
ejpam-7	232	6	β2	β2	ADJ
ejpam-7	232	7	)	)	PUNCT
ejpam-7	232	8	]	]	PUNCT
ejpam-7	232	9	and	and	CCONJ
ejpam-7	232	10	q2	q2	NOUN
ejpam-7	232	11	=	=	SYM
ejpam-7	233	1	−2	−2	PROPN
ejpam-7	233	2	(	(	PUNCT
ejpam-7	233	3	β	β	X
ejpam-7	233	4	+	+	NOUN
ejpam-7	233	5	1	1	NUM
ejpam-7	233	6	)	)	PUNCT
ejpam-7	233	7	(	(	PUNCT
ejpam-7	233	8	a+	a+	PUNCT
ejpam-7	233	9	b	b	X
ejpam-7	233	10	)	)	PUNCT
ejpam-7	234	1	[	[	X
ejpam-7	234	2	a+	a+	PUNCT
ejpam-7	234	3	b(n−	b(n−	PROPN
ejpam-7	234	4	2	2	NUM
ejpam-7	234	5	)	)	PUNCT
ejpam-7	234	6	]	]	PUNCT
ejpam-7	234	7	.	.	PUNCT
ejpam-7	235	1	references	reference	NOUN
ejpam-7	235	2	30	30	NUM
ejpam-7	235	3	therefore	therefore	ADV
ejpam-7	235	4	the	the	DET
ejpam-7	235	5	manifold	manifold	NOUN
ejpam-7	235	6	is	be	AUX
ejpam-7	235	7	η	η	NOUN
ejpam-7	235	8	-	-	NOUN
ejpam-7	235	9	einstein	einstein	NOUN
ejpam-7	235	10	.	.	PUNCT
ejpam-7	236	1	let	let	VERB
ejpam-7	236	2	ei	ei	PART
ejpam-7	236	3	be	be	AUX
ejpam-7	236	4	an	an	DET
ejpam-7	236	5	orthogonal	orthogonal	ADJ
ejpam-7	236	6	basis	basis	NOUN
ejpam-7	236	7	of	of	ADP
ejpam-7	236	8	the	the	DET
ejpam-7	236	9	tangent	tangent	ADJ
ejpam-7	236	10	space	space	NOUN
ejpam-7	236	11	at	at	ADP
ejpam-7	236	12	each	each	DET
ejpam-7	236	13	point	point	NOUN
ejpam-7	236	14	of	of	ADP
ejpam-7	236	15	the	the	DET
ejpam-7	236	16	manifold	manifold	ADJ
ejpam-7	236	17	mn	mn	PROPN
ejpam-7	236	18	for	for	ADP
ejpam-7	236	19	i	i	PROPN
ejpam-7	236	20	=	=	NOUN
ejpam-7	236	21	1	1	NUM
ejpam-7	236	22	,	,	PUNCT
ejpam-7	236	23	2	2	NUM
ejpam-7	236	24	,	,	PUNCT
ejpam-7	236	25	....	....	PUNCT
ejpam-7	236	26	,	,	PUNCT
ejpam-7	236	27	n.	n.	PROPN
ejpam-7	236	28	putting	put	VERB
ejpam-7	236	29	y	y	NOUN
ejpam-7	236	30	=	=	PUNCT
ejpam-7	236	31	z	z	NOUN
ejpam-7	236	32	=	=	PUNCT
ejpam-7	236	33	ei	ei	NOUN
ejpam-7	236	34	in	in	ADP
ejpam-7	236	35	(	(	PUNCT
ejpam-7	236	36	4.8	4.8	NUM
ejpam-7	236	37	)	)	PUNCT
ejpam-7	236	38	and	and	CCONJ
ejpam-7	236	39	then	then	ADV
ejpam-7	236	40	taking	take	VERB
ejpam-7	236	41	summation	summation	NOUN
ejpam-7	236	42	over	over	ADP
ejpam-7	236	43	the	the	DET
ejpam-7	236	44	index	index	NOUN
ejpam-7	236	45	i	i	PRON
ejpam-7	236	46	,	,	PUNCT
ejpam-7	236	47	we	we	PRON
ejpam-7	236	48	get	get	VERB
ejpam-7	236	49	r	r	NOUN
ejpam-7	236	50	=	=	PUNCT
ejpam-7	236	51	(	(	PUNCT
ejpam-7	236	52	n−	n−	NOUN
ejpam-7	236	53	1	1	NUM
ejpam-7	236	54	)	)	PUNCT
ejpam-7	236	55	[	[	PUNCT
ejpam-7	236	56	2	2	NUM
ejpam-7	236	57	(	(	PUNCT
ejpam-7	236	58	β	β	X
ejpam-7	236	59	+	+	NOUN
ejpam-7	236	60	1	1	NUM
ejpam-7	236	61	)	)	PUNCT
ejpam-7	236	62	(	(	PUNCT
ejpam-7	236	63	a+	a+	PUNCT
ejpam-7	236	64	b	b	X
ejpam-7	236	65	)	)	PUNCT
ejpam-7	237	1	[	[	X
ejpam-7	237	2	a+	a+	PUNCT
ejpam-7	237	3	b(n−	b(n−	PROPN
ejpam-7	237	4	2	2	NUM
ejpam-7	237	5	)	)	PUNCT
ejpam-7	237	6	]	]	PUNCT
ejpam-7	238	1	+	+	CCONJ
ejpam-7	238	2	n(α2	n(α2	PROPN
ejpam-7	238	3	−	−	PROPN
ejpam-7	238	4	β2	β2	PROPN
ejpam-7	238	5	)	)	PUNCT
ejpam-7	238	6	]	]	PUNCT
ejpam-7	238	7	.	.	PUNCT
ejpam-7	239	1	this	this	PRON
ejpam-7	239	2	proves	prove	VERB
ejpam-7	239	3	the	the	DET
ejpam-7	239	4	theorem	theorem	NOUN
ejpam-7	239	5	.	.	PROPN
ejpam-7	239	6	5	5	NUM
ejpam-7	239	7	.	.	X
ejpam-7	239	8	acknowledgment	acknowledgment	NOUN
ejpam-7	239	9	the	the	DET
ejpam-7	239	10	authors	author	NOUN
ejpam-7	239	11	are	be	AUX
ejpam-7	239	12	grateful	grateful	ADJ
ejpam-7	239	13	to	to	ADP
ejpam-7	239	14	the	the	DET
ejpam-7	239	15	referrers	referrer	NOUN
ejpam-7	239	16	and	and	CCONJ
ejpam-7	239	17	eyüp	eyüp	NOUN
ejpam-7	239	18	çetin	çetin	NOUN
ejpam-7	239	19	for	for	ADP
ejpam-7	239	20	their	their	PRON
ejpam-7	239	21	valuable	valuable	ADJ
ejpam-7	239	22	suggestions	suggestion	NOUN
ejpam-7	239	23	in	in	ADP
ejpam-7	239	24	the	the	DET
ejpam-7	239	25	improvement	improvement	NOUN
ejpam-7	239	26	of	of	ADP
ejpam-7	239	27	the	the	DET
ejpam-7	239	28	paper	paper	NOUN
ejpam-7	239	29	.	.	PUNCT
ejpam-7	240	1	references	reference	NOUN
ejpam-7	240	2	[	[	X
ejpam-7	240	3	1	1	NUM
ejpam-7	240	4	]	]	X
ejpam-7	240	5	k.amur	k.amur	ADJ
ejpam-7	240	6	and	and	CCONJ
ejpam-7	240	7	s.s.pujar	s.s.pujar	NOUN
ejpam-7	240	8	,	,	PUNCT
ejpam-7	240	9	on	on	ADP
ejpam-7	240	10	submanifolds	submanifold	NOUN
ejpam-7	240	11	of	of	ADP
ejpam-7	240	12	a	a	DET
ejpam-7	240	13	riemannian	riemannian	ADJ
ejpam-7	240	14	manifold	manifold	NOUN
ejpam-7	240	15	admitting	admit	VERB
ejpam-7	240	16	a	a	DET
ejpam-7	240	17	metric	metric	ADJ
ejpam-7	240	18	semisymmetric	semisymmetric	ADJ
ejpam-7	240	19	connection	connection	NOUN
ejpam-7	240	20	,	,	PUNCT
ejpam-7	240	21	,	,	PUNCT
ejpam-7	240	22	tensor	tensor	NOUN
ejpam-7	240	23	,	,	PUNCT
ejpam-7	240	24	n.s	n.s	PROPN
ejpam-7	240	25	.	.	PROPN
ejpam-7	240	26	,	,	PUNCT
ejpam-7	240	27	32	32	NUM
ejpam-7	240	28	(	(	PUNCT
ejpam-7	240	29	1978	1978	NUM
ejpam-7	240	30	)	)	PUNCT
ejpam-7	240	31	,	,	PUNCT
ejpam-7	240	32	35	35	NUM
ejpam-7	240	33	-	-	SYM
ejpam-7	240	34	38	38	NUM
ejpam-7	240	35	.	.	PUNCT
ejpam-7	241	1	[	[	X
ejpam-7	241	2	2	2	NUM
ejpam-7	241	3	]	]	X
ejpam-7	241	4	c.s.bagewadi	c.s.bagewadi	NOUN
ejpam-7	241	5	,	,	PUNCT
ejpam-7	241	6	on	on	ADP
ejpam-7	241	7	totally	totally	ADV
ejpam-7	241	8	real	real	ADJ
ejpam-7	241	9	submanifolds	submanifold	NOUN
ejpam-7	241	10	of	of	ADP
ejpam-7	241	11	a	a	DET
ejpam-7	241	12	kahlerian	kahlerian	ADJ
ejpam-7	241	13	manifold	manifold	ADJ
ejpam-7	241	14	admitting	admit	VERB
ejpam-7	241	15	semi	semi	ADV
ejpam-7	241	16	symmetric	symmetric	ADJ
ejpam-7	241	17	metric	metric	ADJ
ejpam-7	241	18	f	f	NOUN
ejpam-7	241	19	-	-	PUNCT
ejpam-7	241	20	connection	connection	NOUN
ejpam-7	241	21	,	,	PUNCT
ejpam-7	241	22	indian	indian	PROPN
ejpam-7	241	23	.	.	PUNCT
ejpam-7	242	1	j.	j.	PROPN
ejpam-7	242	2	pure	pure	PROPN
ejpam-7	242	3	.	.	PUNCT
ejpam-7	243	1	appl	appl	PROPN
ejpam-7	243	2	.	.	PUNCT
ejpam-7	244	1	math,13(5);528	math,13(5);528	PROPN
ejpam-7	244	2	-	-	SYM
ejpam-7	244	3	536	536	NUM
ejpam-7	244	4	,	,	PUNCT
ejpam-7	244	5	may	may	PROPN
ejpam-7	244	6	1982	1982	NUM
ejpam-7	244	7	.	.	PUNCT
ejpam-7	245	1	[	[	X
ejpam-7	245	2	3	3	NUM
ejpam-7	245	3	]	]	X
ejpam-7	245	4	c.s.bagewadi	c.s.bagewadi	NOUN
ejpam-7	245	5	and	and	CCONJ
ejpam-7	245	6	e.girish	e.girish	ADJ
ejpam-7	245	7	kumar	kumar	PROPN
ejpam-7	245	8	,	,	PUNCT
ejpam-7	245	9	note	note	NOUN
ejpam-7	245	10	on	on	ADP
ejpam-7	245	11	trans	trans	ADJ
ejpam-7	245	12	-	-	ADJ
ejpam-7	245	13	sasakian	sasakian	ADJ
ejpam-7	245	14	manifolds	manifold	NOUN
ejpam-7	245	15	,	,	PUNCT
ejpam-7	245	16	tensor.n.s	tensor.n.s	PROPN
ejpam-7	245	17	.	.	PUNCT
ejpam-7	245	18	,	,	PUNCT
ejpam-7	245	19	65	65	NUM
ejpam-7	245	20	(	(	PUNCT
ejpam-7	245	21	2004	2004	NUM
ejpam-7	245	22	)	)	PUNCT
ejpam-7	245	23	,	,	PUNCT
ejpam-7	245	24	no.1	no.1	NUM
ejpam-7	245	25	,	,	PUNCT
ejpam-7	245	26	80	80	NUM
ejpam-7	245	27	-	-	SYM
ejpam-7	245	28	88	88	NUM
ejpam-7	245	29	.	.	PUNCT
ejpam-7	246	1	[	[	X
ejpam-7	246	2	4	4	NUM
ejpam-7	246	3	]	]	X
ejpam-7	246	4	c.s.bagewadi	c.s.bagewadi	NOUN
ejpam-7	246	5	and	and	CCONJ
ejpam-7	246	6	venkatesha	venkatesha	PROPN
ejpam-7	246	7	,	,	PUNCT
ejpam-7	246	8	some	some	DET
ejpam-7	246	9	curvature	curvature	NOUN
ejpam-7	246	10	tensors	tensor	NOUN
ejpam-7	246	11	on	on	ADP
ejpam-7	246	12	trans	trans	PROPN
ejpam-7	246	13	sasakian	sasakian	PROPN
ejpam-7	246	14	manifolds	manifold	NOUN
ejpam-7	246	15	,	,	PUNCT
ejpam-7	246	16	turk	turk	PROPN
ejpam-7	246	17	.	.	PUNCT
ejpam-7	247	1	j.	j.	PROPN
ejpam-7	247	2	math	math	PROPN
ejpam-7	247	3	,	,	PUNCT
ejpam-7	247	4	31(2007	31(2007	NUM
ejpam-7	247	5	)	)	PUNCT
ejpam-7	247	6	,	,	PUNCT
ejpam-7	247	7	111	111	NUM
ejpam-7	247	8	-	-	SYM
ejpam-7	247	9	121	121	NUM
ejpam-7	247	10	.	.	PUNCT
ejpam-7	248	1	[	[	X
ejpam-7	248	2	5	5	NUM
ejpam-7	248	3	]	]	X
ejpam-7	248	4	c.s.bagewadi	c.s.bagewadi	NOUN
ejpam-7	248	5	,	,	PUNCT
ejpam-7	248	6	d.g.prakasha	d.g.prakasha	PROPN
ejpam-7	248	7	and	and	CCONJ
ejpam-7	248	8	venkatesha	venkatesha	PROPN
ejpam-7	248	9	,	,	PUNCT
ejpam-7	248	10	conservative	conservative	ADJ
ejpam-7	248	11	projective	projective	ADJ
ejpam-7	248	12	curvature	curvature	NOUN
ejpam-7	248	13	tensor	tensor	NOUN
ejpam-7	248	14	on	on	ADP
ejpam-7	248	15	trans	trans	PROPN
ejpam-7	248	16	-	-	ADJ
ejpam-7	248	17	sasakian	sasakian	ADJ
ejpam-7	248	18	manifold	manifold	NOUN
ejpam-7	248	19	with	with	ADP
ejpam-7	248	20	respect	respect	NOUN
ejpam-7	248	21	to	to	ADP
ejpam-7	248	22	semi	semi	ADJ
ejpam-7	248	23	-	-	ADJ
ejpam-7	248	24	symmetric	symmetric	ADJ
ejpam-7	248	25	metric	metric	ADJ
ejpam-7	248	26	connection	connection	NOUN
ejpam-7	248	27	,	,	PUNCT
ejpam-7	248	28	analele	analele	PROPN
ejpam-7	248	29	st	st	PROPN
ejpam-7	248	30	.	.	PROPN
ejpam-7	248	31	ale	ale	PROPN
ejpam-7	248	32	univ	univ	PROPN
ejpam-7	248	33	.	.	PUNCT
ejpam-7	249	1	ovidius	ovidius	PROPN
ejpam-7	249	2	constanta	constanta	PROPN
ejpam-7	249	3	,	,	PUNCT
ejpam-7	249	4	seria	seria	PROPN
ejpam-7	249	5	matematica	matematica	PROPN
ejpam-7	249	6	,	,	PUNCT
ejpam-7	249	7	vol	vol	NOUN
ejpam-7	249	8	.	.	PUNCT
ejpam-7	249	9	15(2	15(2	NUM
ejpam-7	249	10	)	)	PUNCT
ejpam-7	249	11	,	,	PUNCT
ejpam-7	249	12	2007	2007	NUM
ejpam-7	249	13	,	,	PUNCT
ejpam-7	249	14	518	518	NUM
ejpam-7	249	15	.	.	PUNCT
ejpam-7	250	1	[	[	X
ejpam-7	250	2	6	6	NUM
ejpam-7	250	3	]	]	X
ejpam-7	250	4	c.s.bagewadi	c.s.bagewadi	NOUN
ejpam-7	250	5	,	,	PUNCT
ejpam-7	250	6	d.g.prakasha	d.g.prakasha	PROPN
ejpam-7	250	7	and	and	CCONJ
ejpam-7	250	8	venkatesha	venkatesha	PROPN
ejpam-7	250	9	,	,	PUNCT
ejpam-7	250	10	conservative	conservative	ADJ
ejpam-7	250	11	conformal	conformal	NOUN
ejpam-7	250	12	and	and	CCONJ
ejpam-7	250	13	quasi	quasi	ADJ
ejpam-7	250	14	-	-	ADJ
ejpam-7	250	15	conformal	conformal	ADJ
ejpam-7	250	16	curvature	curvature	NOUN
ejpam-7	250	17	tensor	tensor	NOUN
ejpam-7	250	18	on	on	ADP
ejpam-7	250	19	k	k	ADJ
ejpam-7	250	20	-	-	NOUN
ejpam-7	250	21	contact	contact	NOUN
ejpam-7	250	22	manifold	manifold	NOUN
ejpam-7	250	23	manifold	manifold	ADJ
ejpam-7	250	24	with	with	ADP
ejpam-7	250	25	respect	respect	NOUN
ejpam-7	250	26	to	to	ADP
ejpam-7	250	27	semi	semi	ADJ
ejpam-7	250	28	-	-	ADJ
ejpam-7	250	29	symmetric	symmetric	ADJ
ejpam-7	250	30	metric	metric	ADJ
ejpam-7	250	31	connection	connection	NOUN
ejpam-7	250	32	,	,	PUNCT
ejpam-7	250	33	to	to	PART
ejpam-7	250	34	appear	appear	VERB
ejpam-7	250	35	in	in	ADP
ejpam-7	250	36	tamsui	tamsui	NOUN
ejpam-7	250	37	oxford	oxford	PROPN
ejpam-7	250	38	j.	j.	PROPN
ejpam-7	250	39	math.sci	math.sci	PROPN
ejpam-7	250	40	.	.	PROPN
ejpam-7	250	41	,	,	PUNCT
ejpam-7	250	42	[	[	X
ejpam-7	250	43	7	7	NUM
ejpam-7	250	44	]	]	PUNCT
ejpam-7	250	45	bhagwat	bhagwat	NOUN
ejpam-7	250	46	prasad	prasad	PROPN
ejpam-7	250	47	,	,	PUNCT
ejpam-7	250	48	on	on	ADP
ejpam-7	250	49	pseudo	pseudo	NOUN
ejpam-7	250	50	-	-	ADJ
ejpam-7	250	51	projective	projective	ADJ
ejpam-7	250	52	curvature	curvature	NOUN
ejpam-7	250	53	tensor	tensor	NOUN
ejpam-7	250	54	on	on	ADP
ejpam-7	250	55	a	a	DET
ejpam-7	250	56	riemanian	riemanian	ADJ
ejpam-7	250	57	manifold	manifold	ADJ
ejpam-7	250	58	,	,	PUNCT
ejpam-7	250	59	bull	bull	NOUN
ejpam-7	250	60	.	.	PUNCT
ejpam-7	251	1	cal	cal	PROPN
ejpam-7	251	2	.	.	PUNCT
ejpam-7	252	1	math	math	NOUN
ejpam-7	252	2	.	.	PUNCT
ejpam-7	253	1	soc	soc	PROPN
ejpam-7	253	2	.	.	PUNCT
ejpam-7	253	3	,	,	PUNCT
ejpam-7	253	4	94(3	94(3	NUM
ejpam-7	253	5	)	)	PUNCT
ejpam-7	253	6	(	(	PUNCT
ejpam-7	253	7	2002	2002	NUM
ejpam-7	253	8	)	)	PUNCT
ejpam-7	253	9	,	,	PUNCT
ejpam-7	253	10	163	163	NUM
ejpam-7	253	11	-	-	SYM
ejpam-7	253	12	166	166	NUM
ejpam-7	253	13	.	.	PUNCT
ejpam-7	254	1	[	[	X
ejpam-7	254	2	8	8	NUM
ejpam-7	254	3	]	]	X
ejpam-7	254	4	d.e.blair	d.e.blair	NOUN
ejpam-7	254	5	and	and	CCONJ
ejpam-7	254	6	j.a.oubina	j.a.oubina	PROPN
ejpam-7	254	7	,	,	PUNCT
ejpam-7	254	8	conformal	conformal	ADJ
ejpam-7	254	9	and	and	CCONJ
ejpam-7	254	10	related	related	ADJ
ejpam-7	254	11	changes	change	NOUN
ejpam-7	254	12	of	of	ADP
ejpam-7	254	13	metric	metric	NOUN
ejpam-7	254	14	on	on	ADP
ejpam-7	254	15	the	the	DET
ejpam-7	254	16	product	product	NOUN
ejpam-7	254	17	of	of	ADP
ejpam-7	254	18	two	two	NUM
ejpam-7	254	19	almost	almost	ADV
ejpam-7	254	20	contact	contact	NOUN
ejpam-7	254	21	metric	metric	ADJ
ejpam-7	254	22	manifolds	manifold	NOUN
ejpam-7	254	23	,	,	PUNCT
ejpam-7	254	24	publ	publ	NOUN
ejpam-7	254	25	.	.	PUNCT
ejpam-7	255	1	mat	mat	NOUN
ejpam-7	255	2	.	.	NOUN
ejpam-7	256	1	34	34	NUM
ejpam-7	256	2	(	(	PUNCT
ejpam-7	256	3	1990	1990	NUM
ejpam-7	256	4	)	)	PUNCT
ejpam-7	256	5	,	,	PUNCT
ejpam-7	256	6	no.1	no.1	NUM
ejpam-7	256	7	,	,	PUNCT
ejpam-7	256	8	199	199	NUM
ejpam-7	256	9	-	-	SYM
ejpam-7	256	10	207	207	NUM
ejpam-7	256	11	.	.	PUNCT
ejpam-7	257	1	references	reference	NOUN
ejpam-7	257	2	31	31	NUM
ejpam-7	257	3	[	[	X
ejpam-7	257	4	9	9	NUM
ejpam-7	257	5	]	]	PUNCT
ejpam-7	257	6	d.e.blair	d.e.blair	NOUN
ejpam-7	257	7	,	,	PUNCT
ejpam-7	257	8	contact	contact	NOUN
ejpam-7	257	9	manifolds	manifold	NOUN
ejpam-7	257	10	in	in	ADP
ejpam-7	257	11	riemannian	riemannian	ADJ
ejpam-7	257	12	geometry	geometry	NOUN
ejpam-7	257	13	,	,	PUNCT
ejpam-7	257	14	lecture	lecture	NOUN
ejpam-7	257	15	notes	note	NOUN
ejpam-7	257	16	in	in	ADP
ejpam-7	257	17	mathematics	mathematic	NOUN
ejpam-7	257	18	,	,	PUNCT
ejpam-7	257	19	509	509	NUM
ejpam-7	257	20	,	,	PUNCT
ejpam-7	257	21	springer	springer	NOUN
ejpam-7	257	22	-	-	PUNCT
ejpam-7	257	23	verlag	verlag	PROPN
ejpam-7	257	24	,	,	PUNCT
ejpam-7	257	25	berlin	berlin	PROPN
ejpam-7	257	26	,	,	PUNCT
ejpam-7	257	27	1976	1976	NUM
ejpam-7	257	28	.	.	PUNCT
ejpam-7	258	1	[	[	X
ejpam-7	258	2	10	10	NUM
ejpam-7	258	3	]	]	PUNCT
ejpam-7	258	4	u.c.de	u.c.de	PROPN
ejpam-7	258	5	and	and	CCONJ
ejpam-7	258	6	absos	absos	PROPN
ejpam-7	258	7	ali	ali	PROPN
ejpam-7	258	8	shaikh	shaikh	PROPN
ejpam-7	258	9	,	,	PUNCT
ejpam-7	258	10	k	k	NOUN
ejpam-7	258	11	-	-	NOUN
ejpam-7	258	12	contact	contact	NOUN
ejpam-7	258	13	and	and	CCONJ
ejpam-7	258	14	sasakian	sasakian	NOUN
ejpam-7	258	15	manifolds	manifold	NOUN
ejpam-7	258	16	with	with	ADP
ejpam-7	258	17	conservative	conservative	ADJ
ejpam-7	258	18	quasiconformal	quasiconformal	ADJ
ejpam-7	258	19	curvature	curvature	NOUN
ejpam-7	258	20	tensor	tensor	NOUN
ejpam-7	258	21	,	,	PUNCT
ejpam-7	258	22	bull	bull	NOUN
ejpam-7	258	23	.	.	PUNCT
ejpam-7	259	1	cal	cal	PROPN
ejpam-7	259	2	.	.	PUNCT
ejpam-7	260	1	math	math	NOUN
ejpam-7	260	2	.	.	PUNCT
ejpam-7	261	1	soc	soc	PROPN
ejpam-7	261	2	.	.	PUNCT
ejpam-7	261	3	,	,	PUNCT
ejpam-7	261	4	89	89	NUM
ejpam-7	261	5	(	(	PUNCT
ejpam-7	261	6	1997	1997	NUM
ejpam-7	261	7	)	)	PUNCT
ejpam-7	261	8	,	,	PUNCT
ejpam-7	261	9	349	349	NUM
ejpam-7	261	10	-	-	SYM
ejpam-7	261	11	354	354	NUM
ejpam-7	261	12	[	[	X
ejpam-7	261	13	11	11	NUM
ejpam-7	261	14	]	]	SYM
ejpam-7	261	15	a.friedmann	a.friedmann	NOUN
ejpam-7	261	16	and	and	CCONJ
ejpam-7	261	17	j.a.schouten	j.a.schouten	ADJ
ejpam-7	261	18	,	,	PUNCT
ejpam-7	261	19	uber	uber	ADJ
ejpam-7	261	20	die	die	VERB
ejpam-7	261	21	geometric	geometric	ADJ
ejpam-7	261	22	der	der	NOUN
ejpam-7	261	23	holbsymmetrischen	holbsymmetrischen	PROPN
ejpam-7	261	24	ubertragurgen	ubertragurgen	PROPN
ejpam-7	261	25	,	,	PUNCT
ejpam-7	261	26	math	math	NOUN
ejpam-7	261	27	.	.	PUNCT
ejpam-7	262	1	zeitschr	zeitschr	PROPN
ejpam-7	262	2	.	.	PROPN
ejpam-7	262	3	21	21	NUM
ejpam-7	262	4	(	(	PUNCT
ejpam-7	262	5	1924	1924	NUM
ejpam-7	262	6	)	)	PUNCT
ejpam-7	262	7	,	,	PUNCT
ejpam-7	262	8	211	211	NUM
ejpam-7	262	9	-	-	SYM
ejpam-7	262	10	233	233	NUM
ejpam-7	262	11	.	.	PUNCT
ejpam-7	263	1	[	[	X
ejpam-7	263	2	12	12	NUM
ejpam-7	263	3	]	]	X
ejpam-7	263	4	n.b.gatti	n.b.gatti	NOUN
ejpam-7	263	5	and	and	CCONJ
ejpam-7	263	6	c.s.bagewadi	c.s.bagewadi	NOUN
ejpam-7	263	7	,	,	PUNCT
ejpam-7	263	8	on	on	ADP
ejpam-7	263	9	irrotational	irrotational	ADJ
ejpam-7	263	10	quasi	quasi	ADJ
ejpam-7	263	11	-	-	ADJ
ejpam-7	263	12	conformal	conformal	ADJ
ejpam-7	263	13	curvature	curvature	NOUN
ejpam-7	263	14	tensor	tensor	NOUN
ejpam-7	263	15	,	,	PUNCT
ejpam-7	263	16	tensor.n.s	tensor.n.s	PROPN
ejpam-7	263	17	.	.	PUNCT
ejpam-7	263	18	,	,	PUNCT
ejpam-7	263	19	64	64	NUM
ejpam-7	263	20	(	(	PUNCT
ejpam-7	263	21	2003),no.3	2003),no.3	NUM
ejpam-7	263	22	,	,	PUNCT
ejpam-7	263	23	248	248	NUM
ejpam-7	263	24	-	-	SYM
ejpam-7	263	25	258	258	NUM
ejpam-7	263	26	.	.	PUNCT
ejpam-7	264	1	[	[	X
ejpam-7	264	2	13	13	NUM
ejpam-7	264	3	]	]	PUNCT
ejpam-7	264	4	a.gray	a.gray	NOUN
ejpam-7	264	5	and	and	CCONJ
ejpam-7	264	6	l.m.harvella	l.m.harvella	ADV
ejpam-7	264	7	,	,	PUNCT
ejpam-7	264	8	the	the	DET
ejpam-7	264	9	sixteen	sixteen	NUM
ejpam-7	264	10	clases	clase	NOUN
ejpam-7	264	11	of	of	ADP
ejpam-7	264	12	almost	almost	ADV
ejpam-7	264	13	hermitian	hermitian	ADJ
ejpam-7	264	14	manifolds	manifold	NOUN
ejpam-7	264	15	and	and	CCONJ
ejpam-7	264	16	their	their	PRON
ejpam-7	264	17	linear	linear	ADJ
ejpam-7	264	18	invariants	invariant	NOUN
ejpam-7	264	19	,	,	PUNCT
ejpam-7	264	20	ann	ann	PROPN
ejpam-7	264	21	.	.	PROPN
ejpam-7	264	22	mat	mat	PROPN
ejpam-7	264	23	.	.	PUNCT
ejpam-7	264	24	pura	pura	NOUN
ejpam-7	264	25	appl	appl	PROPN
ejpam-7	264	26	.	.	PROPN
ejpam-7	264	27	,	,	PUNCT
ejpam-7	264	28	123(1980),no.4	123(1980),no.4	NUM
ejpam-7	264	29	,	,	PUNCT
ejpam-7	264	30	35	35	NUM
ejpam-7	264	31	-	-	SYM
ejpam-7	264	32	58	58	NUM
ejpam-7	264	33	.	.	PUNCT
ejpam-7	265	1	[	[	X
ejpam-7	265	2	14	14	NUM
ejpam-7	265	3	]	]	X
ejpam-7	265	4	h.a.hayden	h.a.hayden	ADJ
ejpam-7	265	5	,	,	PUNCT
ejpam-7	265	6	subspaces	subspace	NOUN
ejpam-7	265	7	of	of	ADP
ejpam-7	265	8	space	space	NOUN
ejpam-7	265	9	with	with	ADP
ejpam-7	265	10	torsion	torsion	NOUN
ejpam-7	265	11	,	,	PUNCT
ejpam-7	265	12	proc	proc	NOUN
ejpam-7	265	13	.	.	PUNCT
ejpam-7	266	1	lond	lond	PROPN
ejpam-7	266	2	.	.	PUNCT
ejpam-7	267	1	math	math	NOUN
ejpam-7	267	2	.	.	PUNCT
ejpam-7	268	1	soc	soc	PROPN
ejpam-7	268	2	.	.	PUNCT
ejpam-7	269	1	34(1932	34(1932	NUM
ejpam-7	269	2	)	)	PUNCT
ejpam-7	269	3	,	,	PUNCT
ejpam-7	269	4	27	27	NUM
ejpam-7	269	5	-	-	SYM
ejpam-7	269	6	50	50	NUM
ejpam-7	269	7	.	.	PUNCT
ejpam-7	270	1	[	[	X
ejpam-7	270	2	15	15	NUM
ejpam-7	270	3	]	]	X
ejpam-7	270	4	j.a.oubina	j.a.oubina	PROPN
ejpam-7	270	5	,	,	PUNCT
ejpam-7	270	6	new	new	ADJ
ejpam-7	270	7	classes	class	NOUN
ejpam-7	270	8	of	of	ADP
ejpam-7	270	9	almost	almost	ADV
ejpam-7	270	10	contact	contact	VERB
ejpam-7	270	11	metric	metric	ADJ
ejpam-7	270	12	structures	structure	NOUN
ejpam-7	270	13	,	,	PUNCT
ejpam-7	270	14	publ.math.debrecen	publ.math.debrecen	NOUN
ejpam-7	270	15	.	.	PUNCT
ejpam-7	271	1	32(1985	32(1985	NUM
ejpam-7	271	2	)	)	PUNCT
ejpam-7	271	3	,	,	PUNCT
ejpam-7	271	4	no.3	no.3	PROPN
ejpam-7	271	5	-	-	PUNCT
ejpam-7	271	6	4,187	4,187	NUM
ejpam-7	271	7	-	-	PUNCT
ejpam-7	271	8	193	193	NUM
ejpam-7	271	9	.	.	PUNCT
ejpam-7	272	1	[	[	X
ejpam-7	272	2	16	16	NUM
ejpam-7	272	3	]	]	PUNCT
ejpam-7	272	4	a.sharafuddin	a.sharafuddin	NOUN
ejpam-7	272	5	and	and	CCONJ
ejpam-7	272	6	s.i.hussain	s.i.hussain	NOUN
ejpam-7	272	7	,	,	PUNCT
ejpam-7	272	8	semi	semi	ADJ
ejpam-7	272	9	-	-	ADJ
ejpam-7	272	10	symmetric	symmetric	ADJ
ejpam-7	272	11	metric	metric	ADJ
ejpam-7	272	12	connections	connection	NOUN
ejpam-7	272	13	in	in	ADP
ejpam-7	272	14	almost	almost	ADV
ejpam-7	272	15	contact	contact	NOUN
ejpam-7	272	16	manifolds	manifold	NOUN
ejpam-7	272	17	,	,	PUNCT
ejpam-7	272	18	tensor	tensor	NOUN
ejpam-7	272	19	,	,	PUNCT
ejpam-7	272	20	n.s	n.s	PROPN
ejpam-7	272	21	.	.	PROPN
ejpam-7	272	22	,30	,30	PUNCT
ejpam-7	272	23	(	(	PUNCT
ejpam-7	272	24	1976	1976	NUM
ejpam-7	272	25	)	)	PUNCT
ejpam-7	272	26	,	,	PUNCT
ejpam-7	272	27	133	133	NUM
ejpam-7	272	28	-	-	SYM
ejpam-7	272	29	139	139	NUM
ejpam-7	272	30	.	.	PUNCT
ejpam-7	273	1	[	[	X
ejpam-7	273	2	17	17	NUM
ejpam-7	273	3	]	]	X
ejpam-7	273	4	venkatesha	venkatesha	NOUN
ejpam-7	273	5	and	and	CCONJ
ejpam-7	273	6	c.s.bagewadi	c.s.bagewadi	NOUN
ejpam-7	273	7	,	,	PUNCT
ejpam-7	273	8	on	on	ADP
ejpam-7	273	9	pseudo	pseudo	NOUN
ejpam-7	273	10	projective	projective	NOUN
ejpam-7	273	11	φ	φ	VERB
ejpam-7	273	12	-	-	ADJ
ejpam-7	273	13	recurrent	recurrent	ADJ
ejpam-7	273	14	kenmotsu	kenmotsu	NOUN
ejpam-7	273	15	manifolds	manifold	NOUN
ejpam-7	273	16	,	,	PUNCT
ejpam-7	273	17	soochow	soochow	PROPN
ejpam-7	273	18	journal	journal	NOUN
ejpam-7	273	19	of	of	ADP
ejpam-7	273	20	mathematics	mathematic	NOUN
ejpam-7	273	21	,	,	PUNCT
ejpam-7	273	22	32(2006	32(2006	NUM
ejpam-7	273	23	)	)	PUNCT
ejpam-7	273	24	,	,	PUNCT
ejpam-7	273	25	no.3	no.3	PROPN
ejpam-7	273	26	,	,	PUNCT
ejpam-7	273	27	433	433	NUM
ejpam-7	273	28	-	-	SYM
ejpam-7	273	29	439	439	NUM
ejpam-7	273	30	.	.	PUNCT
ejpam-7	274	1	[	[	X
ejpam-7	274	2	18	18	NUM
ejpam-7	274	3	]	]	X
ejpam-7	274	4	k.yano	k.yano	NOUN
ejpam-7	274	5	,	,	PUNCT
ejpam-7	274	6	on	on	ADP
ejpam-7	274	7	semi	semi	ADJ
ejpam-7	274	8	-	-	ADJ
ejpam-7	274	9	symmetric	symmetric	ADJ
ejpam-7	274	10	metric	metric	ADJ
ejpam-7	274	11	connections	connection	NOUN
ejpam-7	274	12	,	,	PUNCT
ejpam-7	274	13	revue	revue	NOUN
ejpam-7	274	14	roumaine	roumaine	NOUN
ejpam-7	274	15	de	de	PROPN
ejpam-7	274	16	math	math	NOUN
ejpam-7	274	17	.	.	PUNCT
ejpam-7	275	1	pures	pure	NOUN
ejpam-7	275	2	et	et	PROPN
ejpam-7	275	3	appliques	applique	VERB
ejpam-7	275	4	15	15	NUM
ejpam-7	275	5	(	(	PUNCT
ejpam-7	275	6	1970	1970	NUM
ejpam-7	275	7	)	)	PUNCT
ejpam-7	275	8	,	,	PUNCT
ejpam-7	275	9	1579	1579	NUM
ejpam-7	275	10	-	-	SYM
ejpam-7	275	11	1586	1586	NUM
ejpam-7	275	12	.	.	PUNCT