id	sid	tid	token	lemma	pos
bibechana-19674	1	1	microsoft	microsoft	PROPN
bibechana-19674	1	2	word	word	PROPN
bibechana-19674	1	3	shah	shah	PROPN
bibechana-19674	1	4	final	final	ADJ
bibechana-19674	1	5	(	(	PUNCT
bibechana-19674	1	6	55	55	NUM
bibechana-19674	1	7	-	-	SYM
bibechana-19674	1	8	63	63	NUM
bibechana-19674	1	9	)	)	PUNCT
bibechana-19674	1	10	riddhi	riddhi	PROPN
bibechana-19674	1	11	jung	jung	PROPN
bibechana-19674	1	12	shah./	shah./	PROPN
bibechana-19674	1	13	bibechana	bibechana	PROPN
bibechana-19674	1	14	16	16	NUM
bibechana-19674	1	15	(	(	PUNCT
bibechana-19674	1	16	2019	2019	NUM
bibechana-19674	1	17	)	)	PUNCT
bibechana-19674	1	18	55	55	NUM
bibechana-19674	1	19	-	-	SYM
bibechana-19674	1	20	63	63	NUM
bibechana-19674	1	21	:	:	PUNCT
bibechana-19674	1	22	rcost	rcost	NOUN
bibechana-19674	1	23	p.55	p.55	NOUN
bibechana-19674	1	24	(	(	PUNCT
bibechana-19674	1	25	online	online	ADJ
bibechana-19674	1	26	publication	publication	NOUN
bibechana-19674	1	27	:	:	PUNCT
bibechana-19674	1	28	dec	dec	PROPN
bibechana-19674	1	29	.	.	PROPN
bibechana-19674	1	30	,	,	PUNCT
bibechana-19674	1	31	2018	2018	NUM
bibechana-19674	1	32	)	)	PUNCT
bibechana-19674	1	33	bibechana	bibechana	NOUN
bibechana-19674	1	34	a	a	DET
bibechana-19674	1	35	multidisciplinary	multidisciplinary	ADJ
bibechana-19674	1	36	journal	journal	NOUN
bibechana-19674	1	37	of	of	ADP
bibechana-19674	1	38	science	science	NOUN
bibechana-19674	1	39	,	,	PUNCT
bibechana-19674	1	40	technology	technology	NOUN
bibechana-19674	1	41	and	and	CCONJ
bibechana-19674	1	42	mathematics	mathematic	NOUN
bibechana-19674	1	43	issn	issn	VERB
bibechana-19674	1	44	2091	2091	NUM
bibechana-19674	1	45	-	-	SYM
bibechana-19674	1	46	0762	0762	NUM
bibechana-19674	1	47	(	(	PUNCT
bibechana-19674	1	48	print	print	NOUN
bibechana-19674	1	49	)	)	PUNCT
bibechana-19674	1	50	,	,	PUNCT
bibechana-19674	1	51	2382	2382	NUM
bibechana-19674	1	52	-	-	SYM
bibechana-19674	1	53	5340	5340	NUM
bibechana-19674	1	54	(	(	PUNCT
bibechana-19674	1	55	0nline	0nline	NUM
bibechana-19674	1	56	)	)	PUNCT
bibechana-19674	1	57	journal	journal	NOUN
bibechana-19674	1	58	homepage	homepage	NOUN
bibechana-19674	1	59	:	:	PUNCT
bibechana-19674	1	60	http://nepjol.info/index.php/bibechana	http://nepjol.info/index.php/bibechana	PROPN
bibechana-19674	1	61	publisher	publisher	NOUN
bibechana-19674	1	62	:	:	PUNCT
bibechana-19674	1	63	research	research	PROPN
bibechana-19674	1	64	council	council	PROPN
bibechana-19674	1	65	of	of	ADP
bibechana-19674	1	66	science	science	NOUN
bibechana-19674	1	67	and	and	CCONJ
bibechana-19674	1	68	technology	technology	NOUN
bibechana-19674	1	69	,	,	PUNCT
bibechana-19674	1	70	biratnagar	biratnagar	NOUN
bibechana-19674	1	71	,	,	PUNCT
bibechana-19674	1	72	nepal	nepal	ADJ
bibechana-19674	1	73	on	on	ADP
bibechana-19674	1	74	some	some	DET
bibechana-19674	1	75	curvature	curvature	NOUN
bibechana-19674	1	76	tensors	tensor	NOUN
bibechana-19674	1	77	in	in	ADP
bibechana-19674	1	78	n(k)-contact	n(k)-contact	PROPN
bibechana-19674	1	79	metric	metric	ADJ
bibechana-19674	1	80	manifolds	manifolds	PROPN
bibechana-19674	1	81	riddhi	riddhi	PROPN
bibechana-19674	1	82	jung	jung	PROPN
bibechana-19674	1	83	shah	shah	PROPN
bibechana-19674	1	84	department	department	PROPN
bibechana-19674	1	85	of	of	ADP
bibechana-19674	1	86	mathematics	mathematics	PROPN
bibechana-19674	1	87	,	,	PUNCT
bibechana-19674	1	88	janata	janata	PROPN
bibechana-19674	1	89	campus	campus	PROPN
bibechana-19674	1	90	,	,	PUNCT
bibechana-19674	1	91	nepal	nepal	PROPN
bibechana-19674	1	92	sanskrit	sanskrit	PROPN
bibechana-19674	1	93	university	university	PROPN
bibechana-19674	1	94	,	,	PUNCT
bibechana-19674	1	95	dang	dang	INTJ
bibechana-19674	1	96	,	,	PUNCT
bibechana-19674	1	97	nepal	nepal	ADJ
bibechana-19674	1	98	email	email	NOUN
bibechana-19674	1	99	:	:	PUNCT
bibechana-19674	1	100	shahrjgeo@gmail.com	shahrjgeo@gmail.com	X
bibechana-19674	1	101	article	article	NOUN
bibechana-19674	1	102	history	history	NOUN
bibechana-19674	1	103	:	:	PUNCT
bibechana-19674	1	104	received	receive	VERB
bibechana-19674	1	105	25	25	NUM
bibechana-19674	1	106	april	april	PROPN
bibechana-19674	1	107	,	,	PUNCT
bibechana-19674	1	108	2018	2018	NUM
bibechana-19674	1	109	;	;	PUNCT
bibechana-19674	1	110	accepted	accept	VERB
bibechana-19674	1	111	14	14	NUM
bibechana-19674	1	112	september	september	PROPN
bibechana-19674	1	113	,	,	PUNCT
bibechana-19674	1	114	2018	2018	NUM
bibechana-19674	1	115	doi	doi	NOUN
bibechana-19674	1	116	:	:	PUNCT
bibechana-19674	1	117	http://dx.doi.org/10.3126/bibechana.v16i0.19674	http://dx.doi.org/10.3126/bibechana.v16i0.19674	DET
bibechana-19674	1	118	this	this	DET
bibechana-19674	1	119	work	work	NOUN
bibechana-19674	1	120	is	be	AUX
bibechana-19674	1	121	licensed	license	VERB
bibechana-19674	1	122	under	under	ADP
bibechana-19674	1	123	the	the	DET
bibechana-19674	1	124	creative	creative	ADJ
bibechana-19674	1	125	commons	common	NOUN
bibechana-19674	1	126	cc	cc	ADP
bibechana-19674	1	127	by	by	ADP
bibechana-19674	1	128	-	-	PUNCT
bibechana-19674	1	129	nc	nc	NOUN
bibechana-19674	1	130	license	license	NOUN
bibechana-19674	1	131	.	.	PUNCT
bibechana-19674	2	1	https://creativecommons.org/licenses/by-nc/4.0/	https://creativecommons.org/licenses/by-nc/4.0/	DET
bibechana-19674	2	2	abstract	abstract	ADJ
bibechana-19674	2	3	the	the	DET
bibechana-19674	2	4	purpose	purpose	NOUN
bibechana-19674	2	5	of	of	ADP
bibechana-19674	2	6	this	this	DET
bibechana-19674	2	7	paper	paper	NOUN
bibechana-19674	2	8	is	be	AUX
bibechana-19674	2	9	to	to	PART
bibechana-19674	2	10	study	study	VERB
bibechana-19674	2	11	7w	7w	NOUN
bibechana-19674	2	12	and	and	CCONJ
bibechana-19674	2	13	9w	9w	NOUN
bibechana-19674	2	14	-curvature	-curvature	NOUN
bibechana-19674	2	15	tensors	tensor	NOUN
bibechana-19674	2	16	on	on	ADP
bibechana-19674	2	17	)	)	PUNCT
bibechana-19674	2	18	(	(	PUNCT
bibechana-19674	2	19	kn	kn	NOUN
bibechana-19674	2	20	-contact	-contact	NOUN
bibechana-19674	2	21	metric	metric	ADJ
bibechana-19674	2	22	manifolds	manifold	NOUN
bibechana-19674	2	23	.	.	PUNCT
bibechana-19674	3	1	we	we	PRON
bibechana-19674	3	2	prove	prove	VERB
bibechana-19674	3	3	that	that	SCONJ
bibechana-19674	3	4	a	a	X
bibechana-19674	3	5	)	)	PUNCT
bibechana-19674	3	6	(	(	PUNCT
bibechana-19674	3	7	kn	kn	NOUN
bibechana-19674	3	8	-contact	-contact	PROPN
bibechana-19674	3	9	metric	metric	ADJ
bibechana-19674	3	10	manifold	manifold	NOUN
bibechana-19674	3	11	satisfying	satisfy	VERB
bibechana-19674	3	12	the	the	DET
bibechana-19674	3	13	condition	condition	NOUN
bibechana-19674	3	14	0	0	NUM
bibechana-19674	3	15	)	)	PUNCT
bibechana-19674	3	16	.	.	PUNCT
bibechana-19674	4	1	,	,	PUNCT
bibechana-19674	4	2	(	(	PUNCT
bibechana-19674	4	3	97	97	NUM
bibechana-19674	4	4	=	=	NOUN
bibechana-19674	4	5	wxw	wxw	VERB
bibechana-19674	4	6	ξis	ξis	PROPN
bibechana-19674	4	7	η	η	PROPN
bibechana-19674	4	8	-einstein	-einstein	PROPN
bibechana-19674	4	9	manifold	manifold	ADJ
bibechana-19674	4	10	.	.	PUNCT
bibechana-19674	5	1	we	we	PRON
bibechana-19674	5	2	also	also	ADV
bibechana-19674	5	3	obtain	obtain	VERB
bibechana-19674	5	4	the	the	DET
bibechana-19674	5	5	ricci	ricci	PROPN
bibechana-19674	5	6	tensor	tensor	NOUN
bibechana-19674	5	7	s	s	PROPN
bibechana-19674	5	8	of	of	ADP
bibechana-19674	5	9	type	type	NOUN
bibechana-19674	5	10	(	(	PUNCT
bibechana-19674	5	11	0	0	NUM
bibechana-19674	5	12	,	,	PUNCT
bibechana-19674	5	13	2	2	NUM
bibechana-19674	5	14	)	)	PUNCT
bibechana-19674	5	15	for	for	ADP
bibechana-19674	5	16	9w−ϕ	9w−ϕ	NOUN
bibechana-19674	5	17	flat	flat	ADJ
bibechana-19674	5	18	and	and	CCONJ
bibechana-19674	5	19	09	09	NUM
bibechana-19674	5	20	=	=	NOUN
bibechana-19674	5	21	divw	divw	NOUN
bibechana-19674	5	22	conditions	condition	NOUN
bibechana-19674	5	23	on	on	ADP
bibechana-19674	5	24	)	)	PUNCT
bibechana-19674	5	25	(	(	PUNCT
bibechana-19674	5	26	kn	kn	NOUN
bibechana-19674	5	27	-contact	-contact	NOUN
bibechana-19674	5	28	metric	metric	ADJ
bibechana-19674	5	29	manifolds	manifold	NOUN
bibechana-19674	5	30	.	.	PUNCT
bibechana-19674	6	1	finally	finally	ADV
bibechana-19674	6	2	,	,	PUNCT
bibechana-19674	6	3	we	we	PRON
bibechana-19674	6	4	give	give	VERB
bibechana-19674	6	5	an	an	DET
bibechana-19674	6	6	example	example	NOUN
bibechana-19674	6	7	of	of	ADP
bibechana-19674	6	8	3	3	NUM
bibechana-19674	6	9	-	-	PUNCT
bibechana-19674	6	10	dimensional	dimensional	ADJ
bibechana-19674	6	11	)	)	PUNCT
bibechana-19674	6	12	(	(	PUNCT
bibechana-19674	6	13	kn	kn	NOUN
bibechana-19674	6	14	-contact	-contact	PROPN
bibechana-19674	6	15	metric	metric	ADJ
bibechana-19674	6	16	manifold	manifold	NOUN
bibechana-19674	6	17	.	.	PUNCT
bibechana-19674	7	1	keywords	keyword	NOUN
bibechana-19674	7	2	:	:	PUNCT
bibechana-19674	7	3	contact	contact	NOUN
bibechana-19674	7	4	manifold	manifold	ADJ
bibechana-19674	7	5	;	;	PUNCT
bibechana-19674	7	6	)	)	PUNCT
bibechana-19674	8	1	(	(	PUNCT
bibechana-19674	8	2	kn	kn	NOUN
bibechana-19674	8	3	-contact	-contact	PROPN
bibechana-19674	8	4	metric	metric	ADJ
bibechana-19674	8	5	manifold	manifold	NOUN
bibechana-19674	8	6	;	;	PUNCT
bibechana-19674	8	7	η	η	PROPN
bibechana-19674	8	8	-einstein	-einstein	PROPN
bibechana-19674	8	9	manifold	manifold	ADJ
bibechana-19674	8	10	.	.	PUNCT
bibechana-19674	9	1	1	1	X
bibechana-19674	9	2	.	.	X
bibechana-19674	9	3	introduction	introduction	NOUN
bibechana-19674	9	4	in	in	ADP
bibechana-19674	9	5	1988	1988	NUM
bibechana-19674	9	6	,	,	PUNCT
bibechana-19674	9	7	tanno	tanno	VERB
bibechana-19674	10	1	[	[	X
bibechana-19674	10	2	1	1	NUM
bibechana-19674	10	3	]	]	PUNCT
bibechana-19674	10	4	introduced	introduce	VERB
bibechana-19674	10	5	the	the	DET
bibechana-19674	10	6	notion	notion	NOUN
bibechana-19674	10	7	of	of	ADP
bibechana-19674	10	8	k	k	PROPN
bibechana-19674	10	9	-nullity	-nullity	NOUN
bibechana-19674	10	10	distribution	distribution	NOUN
bibechana-19674	10	11	of	of	ADP
bibechana-19674	10	12	a	a	DET
bibechana-19674	10	13	contact	contact	NOUN
bibechana-19674	10	14	metric	metric	NOUN
bibechana-19674	10	15	manifold	manifold	ADJ
bibechana-19674	10	16	as	as	ADP
bibechana-19674	10	17	a	a	DET
bibechana-19674	10	18	distribution	distribution	NOUN
bibechana-19674	10	19	such	such	ADJ
bibechana-19674	10	20	that	that	SCONJ
bibechana-19674	10	21	the	the	DET
bibechana-19674	10	22	characteristic	characteristic	ADJ
bibechana-19674	10	23	vector	vector	NOUN
bibechana-19674	10	24	field	field	NOUN
bibechana-19674	10	25	or	or	CCONJ
bibechana-19674	10	26	reeb	reeb	NOUN
bibechana-19674	10	27	vector	vector	NOUN
bibechana-19674	10	28	field	field	NOUN
bibechana-19674	10	29	(	(	PUNCT
bibechana-19674	10	30	reeb	reeb	NOUN
bibechana-19674	10	31	1952	1952	NUM
bibechana-19674	10	32	)	)	PUNCT
bibechana-19674	11	1	[	[	X
bibechana-19674	11	2	2	2	NUM
bibechana-19674	11	3	]	]	SYM
bibechana-19674	11	4	ξ	ξ	PROPN
bibechana-19674	11	5	of	of	ADP
bibechana-19674	11	6	the	the	DET
bibechana-19674	11	7	contact	contact	NOUN
bibechana-19674	11	8	metric	metric	NOUN
bibechana-19674	11	9	manifold	manifold	PROPN
bibechana-19674	11	10	belongs	belong	VERB
bibechana-19674	11	11	to	to	ADP
bibechana-19674	11	12	the	the	DET
bibechana-19674	11	13	distribution	distribution	NOUN
bibechana-19674	11	14	.	.	PUNCT
bibechana-19674	12	1	a	a	DET
bibechana-19674	12	2	contact	contact	NOUN
bibechana-19674	12	3	metric	metric	NOUN
bibechana-19674	12	4	manifold	manifold	ADJ
bibechana-19674	12	5	with	with	ADP
bibechana-19674	12	6	ξ	ξ	PROPN
bibechana-19674	12	7	belonging	belong	VERB
bibechana-19674	12	8	to	to	ADP
bibechana-19674	12	9	the	the	DET
bibechana-19674	12	10	k	k	PROPN
bibechana-19674	12	11	-nullity	-nullity	NOUN
bibechana-19674	12	12	distribution	distribution	NOUN
bibechana-19674	12	13	is	be	AUX
bibechana-19674	12	14	called	call	VERB
bibechana-19674	12	15	)	)	PUNCT
bibechana-19674	13	1	(	(	PUNCT
bibechana-19674	13	2	kn	kn	NOUN
bibechana-19674	13	3	-contact	-contact	PROPN
bibechana-19674	13	4	metric	metric	ADJ
bibechana-19674	13	5	manifold	manifold	NOUN
bibechana-19674	13	6	.	.	PUNCT
bibechana-19674	14	1	generalizing	generalize	VERB
bibechana-19674	14	2	this	this	DET
bibechana-19674	14	3	notion	notion	NOUN
bibechana-19674	14	4	blair	blair	PROPN
bibechana-19674	14	5	,	,	PUNCT
bibechana-19674	14	6	koufogiorgos	koufogiorgo	NOUN
bibechana-19674	14	7	and	and	CCONJ
bibechana-19674	14	8	popantoniou	popantoniou	VERB
bibechana-19674	14	9	[	[	X
bibechana-19674	14	10	3	3	X
bibechana-19674	14	11	]	]	PUNCT
bibechana-19674	14	12	introduced	introduce	VERB
bibechana-19674	14	13	the	the	DET
bibechana-19674	14	14	notion	notion	NOUN
bibechana-19674	14	15	of	of	ADP
bibechana-19674	14	16	a	a	DET
bibechana-19674	14	17	contact	contact	NOUN
bibechana-19674	14	18	metric	metric	NOUN
bibechana-19674	14	19	manifold	manifold	ADJ
bibechana-19674	14	20	with	with	ADP
bibechana-19674	14	21	ξ	ξ	PROPN
bibechana-19674	14	22	belonging	belong	VERB
bibechana-19674	14	23	to	to	ADP
bibechana-19674	14	24	the	the	PRON
bibechana-19674	14	25	)	)	PUNCT
bibechana-19674	14	26	,	,	PUNCT
bibechana-19674	14	27	(	(	PUNCT
bibechana-19674	14	28	µk	µk	DET
bibechana-19674	14	29	-nullity	-nullity	NOUN
bibechana-19674	14	30	distribution	distribution	NOUN
bibechana-19674	14	31	,	,	PUNCT
bibechana-19674	14	32	where	where	SCONJ
bibechana-19674	14	33	k	k	PROPN
bibechana-19674	14	34	and	and	CCONJ
bibechana-19674	14	35	µ	µ	PROPN
bibechana-19674	14	36	are	be	AUX
bibechana-19674	14	37	real	real	ADJ
bibechana-19674	14	38	constants	constant	NOUN
bibechana-19674	14	39	.	.	PUNCT
bibechana-19674	15	1	in	in	ADP
bibechana-19674	15	2	particular	particular	ADJ
bibechana-19674	15	3	,	,	PUNCT
bibechana-19674	15	4	if	if	SCONJ
bibechana-19674	15	5	,	,	PUNCT
bibechana-19674	15	6	0=µ	0=µ	PROPN
bibechana-19674	15	7	then	then	ADV
bibechana-19674	15	8	the	the	DET
bibechana-19674	15	9	notion	notion	NOUN
bibechana-19674	15	10	of	of	ADP
bibechana-19674	15	11	)	)	PUNCT
bibechana-19674	15	12	,	,	PUNCT
bibechana-19674	15	13	(	(	PUNCT
bibechana-19674	15	14	µk	µk	PRON
bibechana-19674	15	15	-nullity	-nullity	NOUN
bibechana-19674	15	16	distribution	distribution	NOUN
bibechana-19674	15	17	reduces	reduce	VERB
bibechana-19674	15	18	to	to	ADP
bibechana-19674	15	19	the	the	DET
bibechana-19674	15	20	notion	notion	NOUN
bibechana-19674	15	21	of	of	ADP
bibechana-19674	15	22	k	k	PROPN
bibechana-19674	15	23	-nullity	-nullity	NOUN
bibechana-19674	15	24	distribution	distribution	NOUN
bibechana-19674	15	25	.	.	PUNCT
bibechana-19674	16	1	on	on	ADP
bibechana-19674	16	2	the	the	DET
bibechana-19674	16	3	other	other	ADJ
bibechana-19674	16	4	hand	hand	NOUN
bibechana-19674	16	5	,	,	PUNCT
bibechana-19674	16	6	in	in	ADP
bibechana-19674	16	7	1982	1982	NUM
bibechana-19674	16	8	,	,	PUNCT
bibechana-19674	16	9	pokhariyal	pokhariyal	NOUN
bibechana-19674	17	1	[	[	X
bibechana-19674	17	2	4	4	NUM
bibechana-19674	17	3	]	]	PUNCT
bibechana-19674	17	4	defined	define	VERB
bibechana-19674	17	5	,	,	PUNCT
bibechana-19674	17	6	7w	7w	ADJ
bibechana-19674	17	7	8w	8w	NOUN
bibechana-19674	17	8	and	and	CCONJ
bibechana-19674	17	9	9w	9w	NOUN
bibechana-19674	17	10	-curvature	-curvature	NOUN
bibechana-19674	17	11	tensors	tensor	NOUN
bibechana-19674	17	12	with	with	ADP
bibechana-19674	17	13	the	the	DET
bibechana-19674	17	14	help	help	NOUN
bibechana-19674	17	15	of	of	ADP
bibechana-19674	17	16	the	the	DET
bibechana-19674	17	17	weyl	weyl	PROPN
bibechana-19674	17	18	's	's	PART
bibechana-19674	17	19	projective	projective	ADJ
bibechana-19674	17	20	curvature	curvature	NOUN
bibechana-19674	17	21	tensor	tensor	NOUN
bibechana-19674	17	22	defined	define	VERB
bibechana-19674	17	23	by	by	ADP
bibechana-19674	17	24	eisenhart	eisenhart	NOUN
bibechana-19674	17	25	[	[	X
bibechana-19674	17	26	5	5	NUM
bibechana-19674	17	27	]	]	PUNCT
bibechana-19674	17	28	.	.	PUNCT
bibechana-19674	18	1	in	in	ADP
bibechana-19674	18	2	[	[	X
bibechana-19674	18	3	4	4	X
bibechana-19674	18	4	]	]	PUNCT
bibechana-19674	18	5	it	it	PRON
bibechana-19674	18	6	is	be	AUX
bibechana-19674	18	7	studied	study	VERB
bibechana-19674	18	8	that	that	SCONJ
bibechana-19674	18	9	distribution	distribution	NOUN
bibechana-19674	18	10	of	of	ADP
bibechana-19674	18	11	vector	vector	NOUN
bibechana-19674	18	12	field	field	NOUN
bibechana-19674	18	13	over	over	ADP
bibechana-19674	18	14	the	the	DET
bibechana-19674	18	15	metric	metric	ADJ
bibechana-19674	18	16	potentials	potential	NOUN
bibechana-19674	18	17	and	and	CCONJ
bibechana-19674	18	18	matter	matter	VERB
bibechana-19674	18	19	tensors	tensor	NOUN
bibechana-19674	18	20	plays	play	VERB
bibechana-19674	18	21	an	an	DET
bibechana-19674	18	22	important	important	ADJ
bibechana-19674	18	23	role	role	NOUN
bibechana-19674	18	24	in	in	ADP
bibechana-19674	18	25	shaping	shape	VERB
bibechana-19674	18	26	the	the	DET
bibechana-19674	18	27	various	various	ADJ
bibechana-19674	18	28	physical	physical	ADJ
bibechana-19674	18	29	and	and	CCONJ
bibechana-19674	18	30	geometrical	geometrical	ADJ
bibechana-19674	18	31	properties	property	NOUN
bibechana-19674	18	32	of	of	ADP
bibechana-19674	18	33	a	a	DET
bibechana-19674	18	34	tensor	tensor	NOUN
bibechana-19674	18	35	.	.	PUNCT
bibechana-19674	19	1	in	in	ADP
bibechana-19674	19	2	the	the	DET
bibechana-19674	19	3	same	same	ADJ
bibechana-19674	19	4	paper	paper	NOUN
bibechana-19674	19	5	it	it	PRON
bibechana-19674	19	6	is	be	AUX
bibechana-19674	19	7	proved	prove	VERB
bibechana-19674	19	8	that	that	SCONJ
bibechana-19674	19	9	9w	9w	NOUN
bibechana-19674	19	10	-curvature	-curvature	NOUN
bibechana-19674	19	11	tensor	tensor	NOUN
bibechana-19674	19	12	satisfies	satisfy	VERB
bibechana-19674	19	13	the	the	DET
bibechana-19674	19	14	cyclic	cyclic	ADJ
bibechana-19674	19	15	property	property	NOUN
bibechana-19674	19	16	.	.	PUNCT
bibechana-19674	20	1	in	in	ADP
bibechana-19674	20	2	this	this	DET
bibechana-19674	20	3	paper	paper	NOUN
bibechana-19674	20	4	,	,	PUNCT
bibechana-19674	20	5	we	we	PRON
bibechana-19674	20	6	study	study	VERB
bibechana-19674	20	7	some	some	DET
bibechana-19674	20	8	curvature	curvature	NOUN
bibechana-19674	20	9	conditions	condition	NOUN
bibechana-19674	20	10	of	of	ADP
bibechana-19674	20	11	7w	7w	NUM
bibechana-19674	20	12	and	and	CCONJ
bibechana-19674	20	13	9w	9w	NOUN
bibechana-19674	20	14	-curvature	-curvature	NOUN
bibechana-19674	20	15	tensors	tensor	NOUN
bibechana-19674	20	16	in	in	ADP
bibechana-19674	20	17	)	)	PUNCT
bibechana-19674	20	18	(	(	PUNCT
bibechana-19674	20	19	kn	kn	NOUN
bibechana-19674	20	20	-contact	-contact	NOUN
bibechana-19674	20	21	metric	metric	ADJ
bibechana-19674	20	22	manifolds	manifold	NOUN
bibechana-19674	20	23	and	and	CCONJ
bibechana-19674	20	24	obtain	obtain	VERB
bibechana-19674	20	25	some	some	DET
bibechana-19674	20	26	results	result	NOUN
bibechana-19674	20	27	.	.	PUNCT
bibechana-19674	21	1	riddhi	riddhi	PROPN
bibechana-19674	21	2	jung	jung	PROPN
bibechana-19674	21	3	shah./	shah./	PROPN
bibechana-19674	21	4	bibechana	bibechana	PROPN
bibechana-19674	21	5	16	16	NUM
bibechana-19674	21	6	(	(	PUNCT
bibechana-19674	21	7	2019	2019	NUM
bibechana-19674	21	8	)	)	PUNCT
bibechana-19674	21	9	55	55	NUM
bibechana-19674	21	10	-	-	SYM
bibechana-19674	21	11	63	63	NUM
bibechana-19674	21	12	:	:	PUNCT
bibechana-19674	21	13	rcost	rcost	NOUN
bibechana-19674	21	14	p.56	p.56	X
bibechana-19674	21	15	(	(	PUNCT
bibechana-19674	21	16	online	online	ADJ
bibechana-19674	21	17	publication	publication	NOUN
bibechana-19674	21	18	:	:	PUNCT
bibechana-19674	21	19	dec	dec	PROPN
bibechana-19674	21	20	.	.	PROPN
bibechana-19674	21	21	,	,	PUNCT
bibechana-19674	21	22	2018	2018	NUM
bibechana-19674	21	23	)	)	PUNCT
bibechana-19674	21	24	2	2	NUM
bibechana-19674	21	25	.	.	PUNCT
bibechana-19674	21	26	preliminaries	preliminary	NOUN
bibechana-19674	21	27	a	a	PRON
bibechana-19674	21	28	)	)	PUNCT
bibechana-19674	21	29	12	12	NUM
bibechana-19674	21	30	(	(	PUNCT
bibechana-19674	21	31	+	+	ADJ
bibechana-19674	21	32	n	n	CCONJ
bibechana-19674	21	33	-dimensional	-dimensional	ADJ
bibechana-19674	21	34	smooth	smooth	ADJ
bibechana-19674	21	35	manifold	manifold	NOUN
bibechana-19674	21	36	m	m	VERB
bibechana-19674	21	37	is	be	AUX
bibechana-19674	21	38	said	say	VERB
bibechana-19674	21	39	to	to	PART
bibechana-19674	21	40	be	be	AUX
bibechana-19674	21	41	a	a	DET
bibechana-19674	21	42	contact	contact	NOUN
bibechana-19674	21	43	manifold	manifold	NOUN
bibechana-19674	21	44	,	,	PUNCT
bibechana-19674	21	45	if	if	SCONJ
bibechana-19674	21	46	it	it	PRON
bibechana-19674	21	47	carries	carry	VERB
bibechana-19674	21	48	a	a	DET
bibechana-19674	21	49	global	global	ADJ
bibechana-19674	21	50	1	1	NUM
bibechana-19674	21	51	-	-	PUNCT
bibechana-19674	21	52	form	form	NOUN
bibechana-19674	21	53	η	η	NOUN
bibechana-19674	21	54	such	such	ADJ
bibechana-19674	21	55	that	that	DET
bibechana-19674	21	56	0	0	NUM
bibechana-19674	21	57	)	)	PUNCT
bibechana-19674	21	58	(	(	PUNCT
bibechana-19674	21	59	≠∧	≠∧	NOUN
bibechana-19674	21	60	ndηη	ndηη	VERB
bibechana-19674	21	61	everywhere	everywhere	ADV
bibechana-19674	21	62	.	.	PUNCT
bibechana-19674	22	1	given	give	VERB
bibechana-19674	22	2	a	a	DET
bibechana-19674	22	3	contact	contact	NOUN
bibechana-19674	22	4	form	form	NOUN
bibechana-19674	22	5	η	η	PROPN
bibechana-19674	22	6	,	,	PUNCT
bibechana-19674	22	7	it	it	PRON
bibechana-19674	22	8	is	be	AUX
bibechana-19674	22	9	well	well	ADV
bibechana-19674	22	10	known	know	VERB
bibechana-19674	22	11	that	that	SCONJ
bibechana-19674	22	12	there	there	PRON
bibechana-19674	22	13	exists	exist	VERB
bibechana-19674	22	14	a	a	DET
bibechana-19674	22	15	unique	unique	ADJ
bibechana-19674	22	16	vector	vector	NOUN
bibechana-19674	22	17	field	field	NOUN
bibechana-19674	22	18	ξ	ξ	PROPN
bibechana-19674	22	19	,	,	PUNCT
bibechana-19674	22	20	called	call	VERB
bibechana-19674	22	21	the	the	DET
bibechana-19674	22	22	characteristic	characteristic	ADJ
bibechana-19674	22	23	vector	vector	NOUN
bibechana-19674	22	24	field	field	NOUN
bibechana-19674	22	25	or	or	CCONJ
bibechana-19674	22	26	reeb	reeb	NOUN
bibechana-19674	22	27	vector	vector	NOUN
bibechana-19674	22	28	field	field	NOUN
bibechana-19674	22	29	(	(	PUNCT
bibechana-19674	22	30	reeb	reeb	NOUN
bibechana-19674	22	31	1952	1952	NUM
bibechana-19674	22	32	)	)	PUNCT
bibechana-19674	23	1	[	[	X
bibechana-19674	23	2	2	2	X
bibechana-19674	23	3	]	]	PUNCT
bibechana-19674	23	4	of	of	ADP
bibechana-19674	23	5	η	η	PROPN
bibechana-19674	23	6	,	,	PUNCT
bibechana-19674	23	7	satisfying	satisfying	ADJ
bibechana-19674	23	8	,	,	PUNCT
bibechana-19674	23	9	1	1	NUM
bibechana-19674	23	10	)	)	PUNCT
bibechana-19674	23	11	(	(	PUNCT
bibechana-19674	23	12	=	=	NOUN
bibechana-19674	23	13	ξη	ξη	ADJ
bibechana-19674	23	14	0	0	NUM
bibechana-19674	23	15	)	)	PUNCT
bibechana-19674	23	16	,	,	PUNCT
bibechana-19674	23	17	(	(	PUNCT
bibechana-19674	23	18	=	=	NOUN
bibechana-19674	23	19	xd	xd	INTJ
bibechana-19674	23	20	ξη	ξη	X
bibechana-19674	23	21	(	(	PUNCT
bibechana-19674	23	22	2.1	2.1	NUM
bibechana-19674	23	23	)	)	PUNCT
bibechana-19674	23	24	for	for	ADP
bibechana-19674	23	25	all	all	DET
bibechana-19674	23	26	vector	vector	NOUN
bibechana-19674	23	27	fields	field	NOUN
bibechana-19674	23	28	.x	.x	NOUN
bibechana-19674	24	1	a	a	DET
bibechana-19674	24	2	riemannian	riemannian	ADJ
bibechana-19674	24	3	metric	metric	ADJ
bibechana-19674	24	4	g	g	PROPN
bibechana-19674	24	5	is	be	AUX
bibechana-19674	24	6	said	say	VERB
bibechana-19674	24	7	to	to	PART
bibechana-19674	24	8	be	be	AUX
bibechana-19674	24	9	an	an	DET
bibechana-19674	24	10	associated	associated	ADJ
bibechana-19674	24	11	metric	metric	NOUN
bibechana-19674	24	12	if	if	SCONJ
bibechana-19674	24	13	there	there	PRON
bibechana-19674	24	14	exists	exist	VERB
bibechana-19674	24	15	a	a	DET
bibechana-19674	24	16	tensor	tensor	NOUN
bibechana-19674	24	17	field	field	NOUN
bibechana-19674	24	18	ϕ	ϕ	NOUN
bibechana-19674	24	19	of	of	ADP
bibechana-19674	24	20	type	type	NOUN
bibechana-19674	24	21	(	(	PUNCT
bibechana-19674	24	22	1	1	NUM
bibechana-19674	24	23	,	,	PUNCT
bibechana-19674	24	24	1	1	NUM
bibechana-19674	24	25	)	)	PUNCT
bibechana-19674	24	26	such	such	ADJ
bibechana-19674	24	27	that	that	PRON
bibechana-19674	24	28	)	)	PUNCT
bibechana-19674	24	29	,	,	PUNCT
bibechana-19674	24	30	,	,	PUNCT
bibechana-19674	24	31	(	(	PUNCT
bibechana-19674	24	32	)	)	PUNCT
bibechana-19674	24	33	,	,	PUNCT
bibechana-19674	24	34	(	(	PUNCT
bibechana-19674	24	35	yxgyxd	yxgyxd	NOUN
bibechana-19674	24	36	ϕη	ϕη	ADP
bibechana-19674	24	37	=	=	PUNCT
bibechana-19674	24	38	)	)	PUNCT
bibechana-19674	24	39	,	,	PUNCT
bibechana-19674	24	40	,	,	PUNCT
bibechana-19674	24	41	(	(	PUNCT
bibechana-19674	24	42	)	)	PUNCT
bibechana-19674	24	43	(	(	PUNCT
bibechana-19674	24	44	ξη	ξη	ADP
bibechana-19674	24	45	xgx	xgx	X
bibechana-19674	25	1	=	=	NOUN
bibechana-19674	25	2	ξηϕ	ξηϕ	NOUN
bibechana-19674	25	3	)	)	PUNCT
bibechana-19674	25	4	(	(	PUNCT
bibechana-19674	25	5	)	)	PUNCT
bibechana-19674	25	6	(	(	PUNCT
bibechana-19674	25	7	2	2	NUM
bibechana-19674	25	8	xxx	xxx	X
bibechana-19674	25	9	+	+	NOUN
bibechana-19674	25	10	−=	−=	X
bibechana-19674	25	11	(	(	PUNCT
bibechana-19674	25	12	2.2	2.2	NUM
bibechana-19674	25	13	)	)	PUNCT
bibechana-19674	25	14	for	for	ADP
bibechana-19674	25	15	all	all	DET
bibechana-19674	25	16	vector	vector	NOUN
bibechana-19674	25	17	fields	field	NOUN
bibechana-19674	25	18	yx	yx	NOUN
bibechana-19674	25	19	,	,	PUNCT
bibechana-19674	25	20	on	on	ADP
bibechana-19674	25	21	.12	.12	NUM
bibechana-19674	25	22	+	+	NOUN
bibechana-19674	25	23	nm	nm	NOUN
bibechana-19674	25	24	from	from	ADP
bibechana-19674	25	25	above	above	ADP
bibechana-19674	25	26	conditions	condition	NOUN
bibechana-19674	25	27	one	one	PRON
bibechana-19674	25	28	can	can	AUX
bibechana-19674	25	29	easily	easily	ADV
bibechana-19674	25	30	obtain	obtain	VERB
bibechana-19674	25	31	,	,	PUNCT
bibechana-19674	25	32	0=ϕξ	0=ϕξ	ADJ
bibechana-19674	25	33	,	,	PUNCT
bibechana-19674	25	34	0=ϕη	0=ϕη	NOUN
bibechana-19674	25	35	o	o	NOUN
bibechana-19674	25	36	)	)	PUNCT
bibechana-19674	25	37	.	.	PUNCT
bibechana-19674	26	1	(	(	PUNCT
bibechana-19674	26	2	)	)	PUNCT
bibechana-19674	26	3	(	(	PUNCT
bibechana-19674	26	4	)	)	PUNCT
bibechana-19674	26	5	,	,	PUNCT
bibechana-19674	26	6	(	(	PUNCT
bibechana-19674	26	7	)	)	PUNCT
bibechana-19674	26	8	,	,	PUNCT
bibechana-19674	26	9	(	(	PUNCT
bibechana-19674	26	10	yxyxgyxg	yxyxgyxg	PROPN
bibechana-19674	26	11	ηηϕϕ	ηηϕϕ	NOUN
bibechana-19674	26	12	−=	−=	X
bibechana-19674	26	13	(	(	PUNCT
bibechana-19674	26	14	2.3	2.3	NUM
bibechana-19674	26	15	)	)	PUNCT
bibechana-19674	26	16	the	the	DET
bibechana-19674	26	17	structure	structure	NOUN
bibechana-19674	26	18	)	)	PUNCT
bibechana-19674	26	19	,	,	PUNCT
bibechana-19674	26	20	,	,	PUNCT
bibechana-19674	26	21	,	,	PUNCT
bibechana-19674	26	22	(	(	PUNCT
bibechana-19674	26	23	gηξϕ	gηξϕ	PROPN
bibechana-19674	26	24	is	be	AUX
bibechana-19674	26	25	called	call	VERB
bibechana-19674	26	26	a	a	DET
bibechana-19674	26	27	contact	contact	NOUN
bibechana-19674	26	28	metric	metric	ADJ
bibechana-19674	26	29	structure	structure	NOUN
bibechana-19674	26	30	and	and	CCONJ
bibechana-19674	26	31	a	a	DET
bibechana-19674	26	32	manifold	manifold	ADJ
bibechana-19674	26	33	12	12	NUM
bibechana-19674	26	34	+	+	NOUN
bibechana-19674	26	35	nm	nm	NOUN
bibechana-19674	26	36	with	with	ADP
bibechana-19674	26	37	a	a	DET
bibechana-19674	26	38	contact	contact	NOUN
bibechana-19674	26	39	metric	metric	ADJ
bibechana-19674	26	40	structure	structure	NOUN
bibechana-19674	26	41	)	)	PUNCT
bibechana-19674	26	42	,	,	PUNCT
bibechana-19674	26	43	,	,	PUNCT
bibechana-19674	26	44	,	,	PUNCT
bibechana-19674	26	45	(	(	PUNCT
bibechana-19674	26	46	gηξϕ	gηξϕ	PROPN
bibechana-19674	26	47	is	be	AUX
bibechana-19674	26	48	said	say	VERB
bibechana-19674	26	49	to	to	PART
bibechana-19674	26	50	be	be	AUX
bibechana-19674	26	51	a	a	DET
bibechana-19674	26	52	contact	contact	NOUN
bibechana-19674	26	53	metric	metric	NOUN
bibechana-19674	26	54	manifold	manifold	ADJ
bibechana-19674	27	1	[	[	X
bibechana-19674	27	2	6	6	NUM
bibechana-19674	27	3	]	]	PUNCT
bibechana-19674	27	4	.	.	PUNCT
bibechana-19674	28	1	now	now	ADV
bibechana-19674	28	2	,	,	PUNCT
bibechana-19674	28	3	we	we	PRON
bibechana-19674	28	4	define	define	VERB
bibechana-19674	28	5	the	the	DET
bibechana-19674	28	6	operators	operator	NOUN
bibechana-19674	28	7	l	l	NOUN
bibechana-19674	28	8	and	and	CCONJ
bibechana-19674	28	9	h	h	NOUN
bibechana-19674	28	10	by	by	ADP
bibechana-19674	28	11	,	,	PUNCT
bibechana-19674	28	12	)	)	PUNCT
bibechana-19674	28	13	,	,	PUNCT
bibechana-19674	28	14	(	(	PUNCT
bibechana-19674	28	15	ξξxrlx	ξξxrlx	NOUN
bibechana-19674	28	16	=	=	SYM
bibechana-19674	28	17	h	h	NOUN
bibechana-19674	28	18	=	=	SYM
bibechana-19674	28	19	21	21	NUM
bibechana-19674	28	20	ëξ	ëξ	PROPN
bibechana-19674	28	21	ϕ	ϕ	PROPN
bibechana-19674	28	22	(	(	PUNCT
bibechana-19674	28	23	2.4	2.4	NUM
bibechana-19674	28	24	)	)	PUNCT
bibechana-19674	28	25	where	where	SCONJ
bibechana-19674	28	26	r	r	NOUN
bibechana-19674	28	27	and	and	CCONJ
bibechana-19674	28	28	ë	ë	PROPN
bibechana-19674	28	29	denote	denote	VERB
bibechana-19674	28	30	the	the	DET
bibechana-19674	28	31	curvature	curvature	NOUN
bibechana-19674	28	32	tensor	tensor	NOUN
bibechana-19674	28	33	and	and	CCONJ
bibechana-19674	28	34	lie	lie	VERB
bibechana-19674	28	35	differentiation	differentiation	NOUN
bibechana-19674	28	36	respectively	respectively	ADV
bibechana-19674	28	37	.	.	PUNCT
bibechana-19674	29	1	the	the	DET
bibechana-19674	29	2	(	(	PUNCT
bibechana-19674	29	3	1	1	NUM
bibechana-19674	29	4	,	,	PUNCT
bibechana-19674	29	5	1)-type	1)-type	NUM
bibechana-19674	29	6	tensors	tensor	NOUN
bibechana-19674	29	7	h	h	NOUN
bibechana-19674	29	8	and	and	CCONJ
bibechana-19674	29	9	l	l	NOUN
bibechana-19674	29	10	are	be	AUX
bibechana-19674	29	11	symmetric	symmetric	ADJ
bibechana-19674	29	12	and	and	CCONJ
bibechana-19674	29	13	satisfy	satisfy	VERB
bibechana-19674	29	14	,	,	PUNCT
bibechana-19674	29	15	0	0	PUNCT
bibechana-19674	29	16	=	=	NUM
bibechana-19674	29	17	ξh	ξh	PROPN
bibechana-19674	29	18	,	,	PUNCT
bibechana-19674	29	19	0	0	PUNCT
bibechana-19674	29	20	=	=	SYM
bibechana-19674	29	21	ξl	ξl	PROPN
bibechana-19674	29	22	,	,	PUNCT
bibechana-19674	29	23	0	0	NUM
bibechana-19674	29	24	.	.	PUNCT
bibechana-19674	30	1	=	=	NOUN
bibechana-19674	30	2	htr	htr	NOUN
bibechana-19674	30	3	0	0	NUM
bibechana-19674	30	4	.	.	PUNCT
bibechana-19674	31	1	=	=	NOUN
bibechana-19674	31	2	ϕhtr	ϕhtr	NOUN
bibechana-19674	31	3	and	and	CCONJ
bibechana-19674	31	4	.hh	.hh	PUNCT
bibechana-19674	31	5	ϕϕ	ϕϕ	PROPN
bibechana-19674	31	6	−=	−=	PUNCT
bibechana-19674	31	7	(	(	PUNCT
bibechana-19674	31	8	2.5	2.5	NUM
bibechana-19674	31	9	)	)	PUNCT
bibechana-19674	31	10	we	we	PRON
bibechana-19674	31	11	also	also	ADV
bibechana-19674	31	12	have	have	VERB
bibechana-19674	31	13	the	the	DET
bibechana-19674	31	14	following	follow	VERB
bibechana-19674	31	15	relations	relation	NOUN
bibechana-19674	31	16	for	for	ADP
bibechana-19674	31	17	a	a	DET
bibechana-19674	31	18	contact	contact	NOUN
bibechana-19674	31	19	metric	metric	ADJ
bibechana-19674	31	20	manifold	manifold	ADJ
bibechana-19674	31	21	:	:	PUNCT
bibechana-19674	31	22	hxxx	hxxx	NOUN
bibechana-19674	31	23	ϕϕξ	ϕϕξ	PROPN
bibechana-19674	31	24	−−=∇	−−=∇	NOUN
bibechana-19674	31	25	(	(	PUNCT
bibechana-19674	31	26	2.6	2.6	NUM
bibechana-19674	31	27	)	)	PUNCT
bibechana-19674	31	28	0=∇	0=∇	PUNCT
bibechana-19674	32	1	ϕ	ϕ	X
bibechana-19674	32	2	ξ	ξ	X
bibechana-19674	32	3	(	(	PUNCT
bibechana-19674	32	4	2.7	2.7	NUM
bibechana-19674	32	5	)	)	PUNCT
bibechana-19674	32	6	2.2	2.2	NUM
bibechana-19674	32	7	)	)	PUNCT
bibechana-19674	32	8	,	,	PUNCT
bibechana-19674	32	9	(	(	PUNCT
bibechana-19674	32	10	.	.	PUNCT
bibechana-19674	32	11	htrnqgltr	htrnqgltr	PROPN
bibechana-19674	32	12	−==	−==	ADJ
bibechana-19674	32	13	ξξ	ξξ	ADP
bibechana-19674	32	14	(	(	PUNCT
bibechana-19674	32	15	2.8	2.8	NUM
bibechana-19674	32	16	)	)	PUNCT
bibechana-19674	32	17	)	)	PUNCT
bibechana-19674	32	18	(	(	PUNCT
bibechana-19674	32	19	2	2	NUM
bibechana-19674	32	20	22	22	NUM
bibechana-19674	32	21	hll	hll	NOUN
bibechana-19674	32	22	+	+	NOUN
bibechana-19674	32	23	=	=	PROPN
bibechana-19674	32	24	−	−	PROPN
bibechana-19674	32	25	ϕϕϕ	ϕϕϕ	NOUN
bibechana-19674	32	26	(	(	PUNCT
bibechana-19674	32	27	2.9	2.9	NUM
bibechana-19674	32	28	)	)	PUNCT
bibechana-19674	32	29	2hlh	2hlh	NUM
bibechana-19674	32	30	ϕϕϕ	ϕϕϕ	NOUN
bibechana-19674	32	31	ξ	ξ	X
bibechana-19674	32	32	−−=∇	−−=∇	NOUN
bibechana-19674	32	33	(	(	PUNCT
bibechana-19674	32	34	2.10	2.10	NUM
bibechana-19674	32	35	)	)	PUNCT
bibechana-19674	32	36	where	where	SCONJ
bibechana-19674	32	37	q	q	NOUN
bibechana-19674	32	38	is	be	AUX
bibechana-19674	32	39	the	the	DET
bibechana-19674	32	40	ricci	ricci	NOUN
bibechana-19674	32	41	operator	operator	NOUN
bibechana-19674	32	42	defined	define	VERB
bibechana-19674	32	43	by	by	ADP
bibechana-19674	32	44	)	)	PUNCT
bibechana-19674	32	45	,	,	PUNCT
bibechana-19674	32	46	,	,	PUNCT
bibechana-19674	32	47	(	(	PUNCT
bibechana-19674	32	48	)	)	PUNCT
bibechana-19674	32	49	,	,	PUNCT
bibechana-19674	32	50	(	(	PUNCT
bibechana-19674	32	51	yxsyqxg	yxsyqxg	ADJ
bibechana-19674	32	52	=	=	SYM
bibechana-19674	32	53	∇	∇	X
bibechana-19674	32	54	is	be	AUX
bibechana-19674	32	55	the	the	DET
bibechana-19674	32	56	levi	levi	PROPN
bibechana-19674	32	57	-	-	PUNCT
bibechana-19674	32	58	civita	civita	PROPN
bibechana-19674	32	59	connection	connection	NOUN
bibechana-19674	32	60	of	of	ADP
bibechana-19674	32	61	the	the	DET
bibechana-19674	32	62	riemannian	riemannian	ADJ
bibechana-19674	32	63	metric	metric	ADJ
bibechana-19674	32	64	g	g	PROPN
bibechana-19674	32	65	and	and	CCONJ
bibechana-19674	32	66	s	s	VERB
bibechana-19674	32	67	the	the	DET
bibechana-19674	32	68	ricci	ricci	PROPN
bibechana-19674	32	69	tensor	tensor	NOUN
bibechana-19674	32	70	[	[	NOUN
bibechana-19674	32	71	6,7	6,7	NUM
bibechana-19674	32	72	]	]	PUNCT
bibechana-19674	32	73	.	.	PUNCT
bibechana-19674	33	1	an	an	DET
bibechana-19674	33	2	almost	almost	ADV
bibechana-19674	33	3	contact	contact	NOUN
bibechana-19674	33	4	metric	metric	ADJ
bibechana-19674	33	5	manifold	manifold	NOUN
bibechana-19674	33	6	is	be	AUX
bibechana-19674	33	7	an	an	DET
bibechana-19674	33	8	odd	odd	ADJ
bibechana-19674	33	9	dimensional	dimensional	ADJ
bibechana-19674	33	10	smooth	smooth	ADJ
bibechana-19674	33	11	manifold	manifold	ADJ
bibechana-19674	33	12	12	12	NUM
bibechana-19674	33	13	+	+	NOUN
bibechana-19674	33	14	nm	nm	NOUN
bibechana-19674	33	15	equipped	equip	VERB
bibechana-19674	33	16	with	with	ADP
bibechana-19674	33	17	an	an	DET
bibechana-19674	33	18	almost	almost	ADV
bibechana-19674	33	19	contact	contact	NOUN
bibechana-19674	33	20	metric	metric	ADJ
bibechana-19674	33	21	structure	structure	NOUN
bibechana-19674	33	22	)	)	PUNCT
bibechana-19674	33	23	,	,	PUNCT
bibechana-19674	33	24	,	,	PUNCT
bibechana-19674	33	25	,	,	PUNCT
bibechana-19674	33	26	(	(	PUNCT
bibechana-19674	33	27	gηξϕ	gηξϕ	PROPN
bibechana-19674	33	28	satisfying	satisfy	VERB
bibechana-19674	33	29	the	the	DET
bibechana-19674	33	30	conditions	condition	NOUN
bibechana-19674	33	31	(	(	PUNCT
bibechana-19674	33	32	2.1	2.1	NUM
bibechana-19674	33	33	)	)	PUNCT
bibechana-19674	33	34	(	(	PUNCT
bibechana-19674	33	35	2.3	2.3	NUM
bibechana-19674	33	36	)	)	PUNCT
bibechana-19674	33	37	except	except	SCONJ
bibechana-19674	33	38	the	the	DET
bibechana-19674	33	39	condition	condition	NOUN
bibechana-19674	33	40	)	)	PUNCT
bibechana-19674	33	41	,	,	PUNCT
bibechana-19674	33	42	(	(	PUNCT
bibechana-19674	33	43	)	)	PUNCT
bibechana-19674	33	44	,	,	PUNCT
bibechana-19674	33	45	(	(	PUNCT
bibechana-19674	33	46	yxgyxd	yxgyxd	NOUN
bibechana-19674	33	47	ϕη	ϕη	ADP
bibechana-19674	33	48	=	=	PUNCT
bibechana-19674	33	49	or	or	CCONJ
bibechana-19674	33	50	.0	.0	NUM
bibechana-19674	33	51	)	)	PUNCT
bibechana-19674	33	52	,	,	PUNCT
bibechana-19674	33	53	(	(	PUNCT
bibechana-19674	33	54	=	=	NOUN
bibechana-19674	33	55	xd	xd	NOUN
bibechana-19674	33	56	ξη	ξη	VERB
bibechana-19674	33	57	sasaki	sasaki	PROPN
bibechana-19674	33	58	and	and	CCONJ
bibechana-19674	33	59	hatakeyama	hatakeyama	NOUN
bibechana-19674	33	60	[	[	X
bibechana-19674	33	61	8	8	NUM
bibechana-19674	33	62	]	]	PUNCT
bibechana-19674	33	63	defined	define	VERB
bibechana-19674	33	64	an	an	DET
bibechana-19674	33	65	almost	almost	ADV
bibechana-19674	33	66	complex	complex	ADJ
bibechana-19674	33	67	structure	structure	NOUN
bibechana-19674	33	68	j	j	PROPN
bibechana-19674	33	69	on	on	ADP
bibechana-19674	33	70	rm	rm	PROPN
bibechana-19674	33	71	n	n	CCONJ
bibechana-19674	33	72	×+12	×+12	PROPN
bibechana-19674	33	73	by	by	ADP
bibechana-19674	33	74			NOUN
bibechana-19674	33	75			PUNCT
bibechana-19674	34	1			PROPN
bibechana-19674	34	2			NOUN
bibechana-19674	34	3			NOUN
bibechana-19674	34	4			VERB
bibechana-19674	34	5	−=	−=	PROPN
bibechana-19674	34	6			PUNCT
bibechana-19674	35	1			PROPN
bibechana-19674	35	2			PROPN
bibechana-19674	35	3			NOUN
bibechana-19674	35	4			VERB
bibechana-19674	35	5	dtdxfxdtdfxj	dtdxfxdtdfxj	NOUN
bibechana-19674	35	6	)	)	PUNCT
bibechana-19674	35	7	(	(	PUNCT
bibechana-19674	35	8	,	,	PUNCT
bibechana-19674	35	9	,	,	PUNCT
bibechana-19674	35	10	ηξϕ	ηξϕ	X
bibechana-19674	35	11	(	(	PUNCT
bibechana-19674	35	12	2.11	2.11	NUM
bibechana-19674	35	13	)	)	PUNCT
bibechana-19674	35	14	where	where	SCONJ
bibechana-19674	35	15	f	f	PROPN
bibechana-19674	35	16	is	be	AUX
bibechana-19674	35	17	a	a	DET
bibechana-19674	35	18	smooth	smooth	ADJ
bibechana-19674	35	19	real	real	ADV
bibechana-19674	35	20	valued	value	VERB
bibechana-19674	35	21	function	function	NOUN
bibechana-19674	35	22	on	on	ADP
bibechana-19674	35	23	.12	.12	NUM
bibechana-19674	35	24	rm	rm	NOUN
bibechana-19674	35	25	n	n	PROPN
bibechana-19674	35	26	×+	×+	PROPN
bibechana-19674	35	27	an	an	DET
bibechana-19674	35	28	almost	almost	ADV
bibechana-19674	35	29	contact	contact	NOUN
bibechana-19674	35	30	metric	metric	ADJ
bibechana-19674	35	31	structure	structure	NOUN
bibechana-19674	35	32	is	be	AUX
bibechana-19674	35	33	said	say	VERB
bibechana-19674	35	34	to	to	PART
bibechana-19674	35	35	be	be	AUX
bibechana-19674	35	36	normal	normal	ADJ
bibechana-19674	35	37	if	if	SCONJ
bibechana-19674	35	38	j	j	PROPN
bibechana-19674	35	39	is	be	AUX
bibechana-19674	35	40	integrable	integrable	ADJ
bibechana-19674	35	41	.	.	PUNCT
bibechana-19674	36	1	an	an	DET
bibechana-19674	36	2	almost	almost	ADV
bibechana-19674	36	3	contact	contact	NOUN
bibechana-19674	36	4	metric	metric	ADJ
bibechana-19674	36	5	manifold	manifold	NOUN
bibechana-19674	36	6	is	be	AUX
bibechana-19674	36	7	sasakian	sasakian	ADJ
bibechana-19674	36	8	if	if	SCONJ
bibechana-19674	37	1	and	and	CCONJ
bibechana-19674	37	2	only	only	ADV
bibechana-19674	37	3	if	if	SCONJ
bibechana-19674	37	4	(	(	PUNCT
bibechana-19674	37	5	)	)	PUNCT
bibechana-19674	37	6	.	.	PUNCT
bibechana-19674	37	7	)	)	PUNCT
bibechana-19674	38	1	(	(	PUNCT
bibechana-19674	38	2	)	)	PUNCT
bibechana-19674	38	3	,	,	PUNCT
bibechana-19674	38	4	(	(	PUNCT
bibechana-19674	38	5	)	)	PUNCT
bibechana-19674	38	6	(	(	PUNCT
bibechana-19674	38	7	xyyxgyx	xyyxgyx	VERB
bibechana-19674	38	8	ηξϕ	ηξϕ	PROPN
bibechana-19674	38	9	−=∇	−=∇	PROPN
bibechana-19674	38	10	(	(	PUNCT
bibechana-19674	38	11	2.12	2.12	NUM
bibechana-19674	38	12	)	)	PUNCT
bibechana-19674	38	13	a	a	DET
bibechana-19674	38	14	contact	contact	NOUN
bibechana-19674	38	15	metric	metric	ADJ
bibechana-19674	38	16	manifold	manifold	NOUN
bibechana-19674	38	17	is	be	AUX
bibechana-19674	38	18	sasakian	sasakian	ADJ
bibechana-19674	38	19	if	if	SCONJ
bibechana-19674	38	20	and	and	CCONJ
bibechana-19674	38	21	only	only	ADV
bibechana-19674	38	22	if	if	SCONJ
bibechana-19674	38	23	yxxyyxr	yxxyyxr	PROPN
bibechana-19674	38	24	)	)	PUNCT
bibechana-19674	38	25	(	(	PUNCT
bibechana-19674	38	26	)	)	PUNCT
bibechana-19674	38	27	(	(	PUNCT
bibechana-19674	38	28	)	)	PUNCT
bibechana-19674	38	29	,	,	PUNCT
bibechana-19674	38	30	(	(	PUNCT
bibechana-19674	38	31	ηηξ	ηηξ	NOUN
bibechana-19674	38	32	−=	−=	NOUN
bibechana-19674	38	33	(	(	PUNCT
bibechana-19674	38	34	2.13	2.13	NUM
bibechana-19674	38	35	)	)	PUNCT
bibechana-19674	38	36	for	for	ADP
bibechana-19674	38	37	all	all	DET
bibechana-19674	38	38	vector	vector	NOUN
bibechana-19674	38	39	fields	field	NOUN
bibechana-19674	38	40	x	x	PUNCT
bibechana-19674	38	41	and	and	CCONJ
bibechana-19674	38	42	y	y	PROPN
bibechana-19674	39	1	[	[	X
bibechana-19674	39	2	6	6	NUM
bibechana-19674	39	3	]	]	PUNCT
bibechana-19674	39	4	.	.	PUNCT
bibechana-19674	40	1	riddhi	riddhi	PROPN
bibechana-19674	40	2	jung	jung	PROPN
bibechana-19674	40	3	shah./	shah./	PROPN
bibechana-19674	40	4	bibechana	bibechana	PROPN
bibechana-19674	40	5	16	16	NUM
bibechana-19674	40	6	(	(	PUNCT
bibechana-19674	40	7	2019	2019	NUM
bibechana-19674	40	8	)	)	PUNCT
bibechana-19674	40	9	55	55	NUM
bibechana-19674	40	10	-	-	SYM
bibechana-19674	40	11	63	63	NUM
bibechana-19674	40	12	:	:	PUNCT
bibechana-19674	40	13	rcost	rcost	ADJ
bibechana-19674	40	14	p.57	p.57	PROPN
bibechana-19674	40	15	(	(	PUNCT
bibechana-19674	40	16	online	online	ADJ
bibechana-19674	40	17	publication	publication	NOUN
bibechana-19674	40	18	:	:	PUNCT
bibechana-19674	40	19	dec	dec	PROPN
bibechana-19674	40	20	.	.	PROPN
bibechana-19674	40	21	,	,	PUNCT
bibechana-19674	40	22	2018	2018	NUM
bibechana-19674	40	23	)	)	PUNCT
bibechana-19674	40	24	a	a	DET
bibechana-19674	40	25	contact	contact	NOUN
bibechana-19674	40	26	metric	metric	NOUN
bibechana-19674	40	27	manifold	manifold	NOUN
bibechana-19674	40	28	for	for	ADP
bibechana-19674	40	29	which	which	PRON
bibechana-19674	40	30	ξ	ξ	PROPN
bibechana-19674	40	31	is	be	AUX
bibechana-19674	40	32	a	a	DET
bibechana-19674	40	33	killing	kill	VERB
bibechana-19674	40	34	vector	vector	NOUN
bibechana-19674	40	35	is	be	AUX
bibechana-19674	40	36	called	call	VERB
bibechana-19674	40	37	a	a	DET
bibechana-19674	40	38	k	k	ADJ
bibechana-19674	40	39	-contact	-contact	NOUN
bibechana-19674	40	40	manifold	manifold	ADJ
bibechana-19674	40	41	.	.	PUNCT
bibechana-19674	41	1	it	it	PRON
bibechana-19674	41	2	is	be	AUX
bibechana-19674	41	3	well	well	ADV
bibechana-19674	41	4	known	know	VERB
bibechana-19674	41	5	that	that	SCONJ
bibechana-19674	41	6	a	a	DET
bibechana-19674	41	7	contact	contact	NOUN
bibechana-19674	41	8	manifold	manifold	NOUN
bibechana-19674	41	9	is	be	AUX
bibechana-19674	41	10	k	k	PROPN
bibechana-19674	41	11	-contact	-contact	NOUN
bibechana-19674	41	12	if	if	SCONJ
bibechana-19674	42	1	and	and	CCONJ
bibechana-19674	42	2	only	only	ADV
bibechana-19674	42	3	if	if	SCONJ
bibechana-19674	42	4	.0	.0	NUM
bibechana-19674	42	5	=	=	NOUN
bibechana-19674	43	1	h	h	NOUN
bibechana-19674	43	2	we	we	PRON
bibechana-19674	43	3	note	note	VERB
bibechana-19674	43	4	that	that	SCONJ
bibechana-19674	43	5	a	a	DET
bibechana-19674	43	6	sasakian	sasakian	PROPN
bibechana-19674	43	7	manifold	manifold	NOUN
bibechana-19674	43	8	is	be	AUX
bibechana-19674	43	9	k	k	PROPN
bibechana-19674	43	10	-contact	-contact	NOUN
bibechana-19674	43	11	,	,	PUNCT
bibechana-19674	43	12	but	but	CCONJ
bibechana-19674	43	13	the	the	DET
bibechana-19674	43	14	converse	converse	NOUN
bibechana-19674	43	15	holds	hold	VERB
bibechana-19674	43	16	only	only	ADV
bibechana-19674	43	17	if	if	SCONJ
bibechana-19674	43	18	dim	dim	ADJ
bibechana-19674	43	19	.3	.3	NUM
bibechana-19674	44	1	=	=	NOUN
bibechana-19674	44	2	m	m	VERB
bibechana-19674	44	3	the	the	DET
bibechana-19674	44	4	k	k	PROPN
bibechana-19674	44	5	-nullity	-nullity	NOUN
bibechana-19674	44	6	distribution	distribution	NOUN
bibechana-19674	44	7	[	[	X
bibechana-19674	44	8	1	1	X
bibechana-19674	44	9	]	]	PUNCT
bibechana-19674	44	10	of	of	ADP
bibechana-19674	44	11	a	a	DET
bibechana-19674	44	12	riemannian	riemannian	ADJ
bibechana-19674	44	13	manifold	manifold	NOUN
bibechana-19674	44	14	)	)	PUNCT
bibechana-19674	44	15	,	,	PUNCT
bibechana-19674	44	16	(	(	PUNCT
bibechana-19674	44	17	gm	gm	PROPN
bibechana-19674	44	18	for	for	ADP
bibechana-19674	44	19	a	a	DET
bibechana-19674	44	20	real	real	ADJ
bibechana-19674	44	21	number	number	NOUN
bibechana-19674	44	22	k	k	PROPN
bibechana-19674	44	23	is	be	AUX
bibechana-19674	44	24	a	a	DET
bibechana-19674	44	25	distribution	distribution	NOUN
bibechana-19674	44	26	]	]	PUNCT
bibechana-19674	44	27	}	}	PUNCT
bibechana-19674	44	28	)	)	PUNCT
bibechana-19674	44	29	,	,	PUNCT
bibechana-19674	44	30	(	(	PUNCT
bibechana-19674	44	31	)	)	PUNCT
bibechana-19674	44	32	,	,	PUNCT
bibechana-19674	44	33	(	(	PUNCT
bibechana-19674	44	34	[	[	NOUN
bibechana-19674	44	35	)	)	PUNCT
bibechana-19674	44	36	,	,	PUNCT
bibechana-19674	44	37	(:	(:	PROPN
bibechana-19674	44	38	)	)	PUNCT
bibechana-19674	44	39	(	(	PUNCT
bibechana-19674	44	40	{	{	PUNCT
bibechana-19674	44	41	)	)	PUNCT
bibechana-19674	44	42	(:	(:	NOUN
bibechana-19674	44	43	)	)	PUNCT
bibechana-19674	44	44	(	(	PUNCT
bibechana-19674	44	45	yzxgxzygkzyxrmtzknpkn	yzxgxzygkzyxrmtzknpkn	NOUN
bibechana-19674	44	46	pp	pp	ADP
bibechana-19674	44	47	−=∈=→	−=∈=→	NOUN
bibechana-19674	44	48	(	(	PUNCT
bibechana-19674	44	49	2.14	2.14	NUM
bibechana-19674	44	50	)	)	PUNCT
bibechana-19674	44	51	for	for	ADP
bibechana-19674	44	52	any	any	PRON
bibechana-19674	44	53	)	)	PUNCT
bibechana-19674	44	54	.	.	PUNCT
bibechana-19674	45	1	(	(	PUNCT
bibechana-19674	45	2	,	,	PUNCT
bibechana-19674	45	3	mtyx	mtyx	NOUN
bibechana-19674	45	4	p∈	p∈	PROPN
bibechana-19674	45	5	if	if	SCONJ
bibechana-19674	45	6	the	the	DET
bibechana-19674	45	7	characteristic	characteristic	ADJ
bibechana-19674	45	8	vector	vector	NOUN
bibechana-19674	45	9	field	field	NOUN
bibechana-19674	45	10	)	)	PUNCT
bibechana-19674	45	11	,	,	PUNCT
bibechana-19674	45	12	(	(	PUNCT
bibechana-19674	45	13	kn∈ξ	kn∈ξ	VERB
bibechana-19674	45	14	then	then	ADV
bibechana-19674	45	15	the	the	DET
bibechana-19674	45	16	relation	relation	NOUN
bibechana-19674	45	17	]	]	PUNCT
bibechana-19674	45	18	)	)	PUNCT
bibechana-19674	45	19	(	(	PUNCT
bibechana-19674	45	20	)	)	PUNCT
bibechana-19674	45	21	(	(	PUNCT
bibechana-19674	45	22	[	[	NOUN
bibechana-19674	45	23	)	)	PUNCT
bibechana-19674	45	24	,	,	PUNCT
bibechana-19674	45	25	(	(	PUNCT
bibechana-19674	45	26	yxxykyxr	yxxykyxr	NOUN
bibechana-19674	45	27	ηηξ	ηηξ	PROPN
bibechana-19674	45	28	−=	−=	PROPN
bibechana-19674	45	29	(	(	PUNCT
bibechana-19674	45	30	2.15	2.15	NUM
bibechana-19674	45	31	)	)	PUNCT
bibechana-19674	45	32	hods	hod	NOUN
bibechana-19674	45	33	.	.	PUNCT
bibechana-19674	46	1	a	a	DET
bibechana-19674	46	2	contact	contact	NOUN
bibechana-19674	46	3	metric	metric	NOUN
bibechana-19674	46	4	manifold	manifold	ADJ
bibechana-19674	46	5	satisfying	satisfy	VERB
bibechana-19674	46	6	the	the	DET
bibechana-19674	46	7	relation	relation	NOUN
bibechana-19674	46	8	(	(	PUNCT
bibechana-19674	46	9	2.15	2.15	NUM
bibechana-19674	46	10	)	)	PUNCT
bibechana-19674	46	11	is	be	AUX
bibechana-19674	46	12	called	call	VERB
bibechana-19674	46	13	a	a	PRON
bibechana-19674	46	14	)	)	PUNCT
bibechana-19674	46	15	(	(	PUNCT
bibechana-19674	46	16	kn	kn	NOUN
bibechana-19674	46	17	-contact	-contact	PROPN
bibechana-19674	46	18	metric	metric	ADJ
bibechana-19674	46	19	manifold	manifold	NOUN
bibechana-19674	46	20	.	.	PUNCT
bibechana-19674	47	1	from	from	ADP
bibechana-19674	47	2	(	(	PUNCT
bibechana-19674	47	3	2.13	2.13	NUM
bibechana-19674	47	4	)	)	PUNCT
bibechana-19674	47	5	and	and	CCONJ
bibechana-19674	47	6	(	(	PUNCT
bibechana-19674	47	7	2.15	2.15	NUM
bibechana-19674	47	8	)	)	PUNCT
bibechana-19674	47	9	it	it	PRON
bibechana-19674	47	10	follows	follow	VERB
bibechana-19674	47	11	that	that	SCONJ
bibechana-19674	47	12	a	a	X
bibechana-19674	47	13	)	)	PUNCT
bibechana-19674	47	14	(	(	PUNCT
bibechana-19674	47	15	kn	kn	NOUN
bibechana-19674	47	16	-contact	-contact	PROPN
bibechana-19674	47	17	metric	metric	ADJ
bibechana-19674	47	18	manifold	manifold	NOUN
bibechana-19674	47	19	is	be	AUX
bibechana-19674	47	20	a	a	DET
bibechana-19674	47	21	sasakian	sasakian	ADJ
bibechana-19674	47	22	manifold	manifold	NOUN
bibechana-19674	47	23	if	if	SCONJ
bibechana-19674	47	24	and	and	CCONJ
bibechana-19674	47	25	only	only	ADV
bibechana-19674	47	26	if	if	SCONJ
bibechana-19674	47	27	.1	.1	PROPN
bibechana-19674	47	28	=	=	PROPN
bibechana-19674	47	29	k	k	X
bibechana-19674	47	30	if	if	SCONJ
bibechana-19674	47	31	0	0	PROPN
bibechana-19674	47	32	=	=	SYM
bibechana-19674	47	33	k	k	X
bibechana-19674	47	34	i.e.	i.e.	X
bibechana-19674	47	35	,	,	PUNCT
bibechana-19674	47	36	,	,	PUNCT
bibechana-19674	47	37	0	0	NUM
bibechana-19674	47	38	)	)	PUNCT
bibechana-19674	47	39	,	,	PUNCT
bibechana-19674	47	40	(	(	PUNCT
bibechana-19674	47	41	=	=	PRON
bibechana-19674	47	42	ξyxr	ξyxr	NOUN
bibechana-19674	47	43	then	then	ADV
bibechana-19674	47	44	)	)	PUNCT
bibechana-19674	47	45	(	(	PUNCT
bibechana-19674	47	46	kn	kn	NOUN
bibechana-19674	47	47	-contact	-contact	PROPN
bibechana-19674	47	48	metric	metric	ADJ
bibechana-19674	47	49	manifold	manifold	NOUN
bibechana-19674	47	50	is	be	AUX
bibechana-19674	47	51	locally	locally	ADV
bibechana-19674	47	52	isometric	isometric	ADJ
bibechana-19674	47	53	to	to	ADP
bibechana-19674	47	54	the	the	DET
bibechana-19674	47	55	riemannian	riemannian	ADJ
bibechana-19674	47	56	product	product	NOUN
bibechana-19674	47	57	)	)	PUNCT
bibechana-19674	47	58	4()0(1	4()0(1	NUM
bibechana-19674	47	59	nn	nn	X
bibechana-19674	47	60	se	se	PROPN
bibechana-19674	47	61	×+	×+	PROPN
bibechana-19674	47	62	for	for	ADP
bibechana-19674	47	63	1	1	NUM
bibechana-19674	47	64	>	>	SYM
bibechana-19674	47	65	n	n	NOUN
bibechana-19674	47	66	and	and	CCONJ
bibechana-19674	47	67	flat	flat	ADJ
bibechana-19674	47	68	for	for	ADP
bibechana-19674	47	69	.1	.1	NOUN
bibechana-19674	48	1	=	=	NOUN
bibechana-19674	48	2	n	n	NOUN
bibechana-19674	48	3	if	if	SCONJ
bibechana-19674	48	4	,	,	PUNCT
bibechana-19674	48	5	1	1	NUM
bibechana-19674	48	6	<	<	X
bibechana-19674	48	7	k	k	X
bibechana-19674	48	8	the	the	DET
bibechana-19674	48	9	scalar	scalar	ADJ
bibechana-19674	48	10	curvature	curvature	NOUN
bibechana-19674	48	11	is	be	AUX
bibechana-19674	48	12	}	}	PUNCT
bibechana-19674	48	13	.)1(2{2	.)1(2{2	PUNCT
bibechana-19674	49	1	knnr	knnr	PROPN
bibechana-19674	49	2	+	+	ADV
bibechana-19674	49	3	−=	−=	NOUN
bibechana-19674	49	4	in	in	ADP
bibechana-19674	49	5	a	a	DET
bibechana-19674	49	6	)	)	PUNCT
bibechana-19674	49	7	12	12	NUM
bibechana-19674	49	8	(	(	PUNCT
bibechana-19674	49	9	+	+	NOUN
bibechana-19674	49	10	n	n	CCONJ
bibechana-19674	49	11	-dimensional	-dimensional	ADJ
bibechana-19674	49	12	)	)	PUNCT
bibechana-19674	49	13	(	(	PUNCT
bibechana-19674	49	14	kn	kn	NOUN
bibechana-19674	49	15	-contact	-contact	PROPN
bibechana-19674	49	16	metric	metric	ADJ
bibechana-19674	49	17	manifold	manifold	NOUN
bibechana-19674	49	18	,	,	PUNCT
bibechana-19674	49	19	m	m	VERB
bibechana-19674	49	20	the	the	DET
bibechana-19674	49	21	following	follow	VERB
bibechana-19674	49	22	relations	relation	NOUN
bibechana-19674	49	23	hold	hold	VERB
bibechana-19674	49	24	:	:	PUNCT
bibechana-19674	49	25	,	,	PUNCT
bibechana-19674	49	26	)	)	PUNCT
bibechana-19674	49	27	1	1	NUM
bibechana-19674	49	28	(	(	PUNCT
bibechana-19674	49	29	22	22	NUM
bibechana-19674	49	30	ϕ−=	ϕ−=	PROPN
bibechana-19674	50	1	kh	kh	PROPN
bibechana-19674	50	2	1≤k	1≤k	PROPN
bibechana-19674	50	3	(	(	PUNCT
bibechana-19674	50	4	2.16	2.16	NUM
bibechana-19674	50	5	)	)	PUNCT
bibechana-19674	50	6	)	)	PUNCT
bibechana-19674	51	1	(	(	PUNCT
bibechana-19674	51	2	2),(,2	2),(,2	NUM
bibechana-19674	51	3	xnkxsnkq	xnkxsnkq	X
bibechana-19674	51	4	ηξξξ	ηξξξ	NOUN
bibechana-19674	51	5	=	=	NOUN
bibechana-19674	51	6	=	=	X
bibechana-19674	51	7	(	(	PUNCT
bibechana-19674	51	8	2.17	2.17	NUM
bibechana-19674	51	9	)	)	PUNCT
bibechana-19674	51	10	]	]	PUNCT
bibechana-19674	51	11	)	)	PUNCT
bibechana-19674	51	12	(	(	PUNCT
bibechana-19674	51	13	)	)	PUNCT
bibechana-19674	51	14	,	,	PUNCT
bibechana-19674	51	15	(	(	PUNCT
bibechana-19674	51	16	[	[	X
bibechana-19674	51	17	)	)	PUNCT
bibechana-19674	51	18	,	,	PUNCT
bibechana-19674	51	19	(	(	PUNCT
bibechana-19674	51	20	xyyxgkyxr	xyyxgkyxr	PROPN
bibechana-19674	51	21	ηξξ	ηξξ	PROPN
bibechana-19674	51	22	−=	−=	NOUN
bibechana-19674	51	23	(	(	PUNCT
bibechana-19674	51	24	2.18	2.18	NUM
bibechana-19674	51	25	)	)	PUNCT
bibechana-19674	51	26	(	(	PUNCT
bibechana-19674	51	27	)	)	PUNCT
bibechana-19674	51	28	)	)	PUNCT
bibechana-19674	51	29	)	)	PUNCT
bibechana-19674	51	30	(	(	PUNCT
bibechana-19674	51	31	(	(	PUNCT
bibechana-19674	51	32	)	)	PUNCT
bibechana-19674	51	33	,	,	PUNCT
bibechana-19674	51	34	(	(	PUNCT
bibechana-19674	51	35	)	)	PUNCT
bibechana-19674	51	36	(	(	PUNCT
bibechana-19674	51	37	hxxyyhxxgyx	hxxyyhxxgyx	VERB
bibechana-19674	52	1	+	+	PROPN
bibechana-19674	52	2	−+=∇	−+=∇	PROPN
bibechana-19674	52	3	ηξϕ	ηξϕ	PROPN
bibechana-19674	52	4	(	(	PUNCT
bibechana-19674	52	5	2.19	2.19	NUM
bibechana-19674	52	6	)	)	PUNCT
bibechana-19674	52	7	)	)	PUNCT
bibechana-19674	52	8	1(2	1(2	NUM
bibechana-19674	52	9	.	.	NOUN
bibechana-19674	52	10	2	2	NUM
bibechana-19674	52	11	knhtr	knhtr	NOUN
bibechana-19674	52	12	−=	−=	VERB
bibechana-19674	52	13	(	(	PUNCT
bibechana-19674	52	14	2.20	2.20	NUM
bibechana-19674	52	15	)	)	PUNCT
bibechana-19674	52	16	ϕϕϕ	ϕϕϕ	NOUN
bibechana-19674	52	17	hnqq	hnqq	PROPN
bibechana-19674	52	18	)	)	PUNCT
bibechana-19674	52	19	1(4	1(4	NUM
bibechana-19674	52	20	−=−	−=−	NOUN
bibechana-19674	52	21	(	(	PUNCT
bibechana-19674	52	22	2.21	2.21	NUM
bibechana-19674	52	23	)	)	PUNCT
bibechana-19674	52	24	)	)	PUNCT
bibechana-19674	52	25	,	,	PUNCT
bibechana-19674	52	26	(	(	PUNCT
bibechana-19674	52	27	)	)	PUNCT
bibechana-19674	52	28	1(4)()(2	1(4)()(2	NUM
bibechana-19674	52	29	)	)	PUNCT
bibechana-19674	52	30	,	,	PUNCT
bibechana-19674	52	31	(	(	PUNCT
bibechana-19674	52	32	)	)	PUNCT
bibechana-19674	52	33	,	,	PUNCT
bibechana-19674	52	34	(	(	PUNCT
bibechana-19674	52	35	yhxgnyxnkyxsyxs	yhxgnyxnkyxsyxs	NOUN
bibechana-19674	52	36	−−−=	−−−=	PROPN
bibechana-19674	52	37	ηηϕϕ	ηηϕϕ	NOUN
bibechana-19674	52	38	(	(	PUNCT
bibechana-19674	52	39	2.22	2.22	NUM
bibechana-19674	52	40	)	)	PUNCT
bibechana-19674	52	41	)	)	PUNCT
bibechana-19674	52	42	,	,	PUNCT
bibechana-19674	52	43	(	(	PUNCT
bibechana-19674	52	44	)	)	PUNCT
bibechana-19674	52	45	1(4	1(4	NUM
bibechana-19674	52	46	)	)	PUNCT
bibechana-19674	52	47	,	,	PUNCT
bibechana-19674	52	48	(	(	PUNCT
bibechana-19674	52	49	)	)	PUNCT
bibechana-19674	52	50	,	,	PUNCT
bibechana-19674	52	51	(	(	PUNCT
bibechana-19674	52	52	hyxgnyxsyxs	hyxgnyxsyxs	PROPN
bibechana-19674	52	53	ϕϕϕ	ϕϕϕ	NOUN
bibechana-19674	52	54	−=+	−=+	PROPN
bibechana-19674	52	55	(	(	PUNCT
bibechana-19674	52	56	2.23	2.23	NUM
bibechana-19674	52	57	)	)	PUNCT
bibechana-19674	52	58	)	)	PUNCT
bibechana-19674	53	1	]	]	PUNCT
bibechana-19674	53	2	(	(	PUNCT
bibechana-19674	53	3	)	)	PUNCT
bibechana-19674	53	4	,	,	PUNCT
bibechana-19674	53	5	(	(	PUNCT
bibechana-19674	53	6	)	)	PUNCT
bibechana-19674	53	7	(	(	PUNCT
bibechana-19674	53	8	)	)	PUNCT
bibechana-19674	53	9	,	,	PUNCT
bibechana-19674	53	10	(	(	PUNCT
bibechana-19674	53	11	[	[	NOUN
bibechana-19674	53	12	)	)	PUNCT
bibechana-19674	53	13	)	)	PUNCT
bibechana-19674	53	14	,	,	PUNCT
bibechana-19674	53	15	(	(	PUNCT
bibechana-19674	53	16	(	(	PUNCT
bibechana-19674	53	17	yzxgxzygkzyxr	yzxgxzygkzyxr	PROPN
bibechana-19674	53	18	ηηη	ηηη	PROPN
bibechana-19674	53	19	−=	−=	PUNCT
bibechana-19674	53	20	(	(	PUNCT
bibechana-19674	53	21	2.24	2.24	NUM
bibechana-19674	53	22	)	)	PUNCT
bibechana-19674	53	23	(	(	PUNCT
bibechana-19674	53	24	)	)	PUNCT
bibechana-19674	53	25	)	)	PUNCT
bibechana-19674	53	26	,	,	PUNCT
bibechana-19674	53	27	(	(	PUNCT
bibechana-19674	53	28	)	)	PUNCT
bibechana-19674	53	29	(	(	PUNCT
bibechana-19674	53	30	yhxxgyx	yhxxgyx	INTJ
bibechana-19674	53	31	ϕη	ϕη	ADP
bibechana-19674	53	32	+	+	NOUN
bibechana-19674	53	33	=	=	NOUN
bibechana-19674	53	34	∇	∇	X
bibechana-19674	53	35	(	(	PUNCT
bibechana-19674	53	36	2.25	2.25	NUM
bibechana-19674	53	37	)	)	PUNCT
bibechana-19674	53	38	for	for	ADP
bibechana-19674	53	39	any	any	DET
bibechana-19674	53	40	vector	vector	NOUN
bibechana-19674	53	41	fields	field	NOUN
bibechana-19674	53	42	yx	yx	NOUN
bibechana-19674	53	43	,	,	PUNCT
bibechana-19674	53	44	on	on	ADP
bibechana-19674	53	45	12	12	NUM
bibechana-19674	53	46	+	+	NOUN
bibechana-19674	53	47	nm	nm	ADJ
bibechana-19674	53	48	[	[	X
bibechana-19674	53	49	1	1	NUM
bibechana-19674	53	50	,	,	PUNCT
bibechana-19674	53	51	3	3	NUM
bibechana-19674	53	52	]	]	PUNCT
bibechana-19674	53	53	.	.	PUNCT
bibechana-19674	54	1	in	in	ADP
bibechana-19674	54	2	n	n	CCONJ
bibechana-19674	54	3	-dimensional	-dimensional	ADJ
bibechana-19674	54	4	space	space	NOUN
bibechana-19674	54	5	nv	nv	PROPN
bibechana-19674	54	6	pokhariyal	pokhariyal	NOUN
bibechana-19674	54	7	[	[	X
bibechana-19674	54	8	4	4	X
bibechana-19674	54	9	]	]	PUNCT
bibechana-19674	54	10	defined	define	VERB
bibechana-19674	54	11	the	the	DET
bibechana-19674	54	12	7w	7w	NUM
bibechana-19674	54	13	and	and	CCONJ
bibechana-19674	54	14	9w	9w	NOUN
bibechana-19674	54	15	curvature	curvature	NOUN
bibechana-19674	54	16	tensors	tensor	NOUN
bibechana-19674	54	17	as	as	SCONJ
bibechana-19674	54	18	follows	follow	VERB
bibechana-19674	54	19	)	)	PUNCT
bibechana-19674	54	20	]	]	PUNCT
bibechana-19674	54	21	,	,	PUNCT
bibechana-19674	54	22	(	(	PUNCT
bibechana-19674	54	23	)	)	PUNCT
bibechana-19674	54	24	,	,	PUNCT
bibechana-19674	54	25	(	(	PUNCT
bibechana-19674	54	26	)	)	PUNCT
bibechana-19674	54	27	,	,	PUNCT
bibechana-19674	54	28	(	(	PUNCT
bibechana-19674	54	29	)	)	PUNCT
bibechana-19674	54	30	,	,	PUNCT
bibechana-19674	54	31	(	(	PUNCT
bibechana-19674	54	32	[	[	X
bibechana-19674	54	33	11),,,(),,,(7	11),,,(),,,(7	NUM
bibechana-19674	54	34	zyrictxgtxriczygntzyxrtzyxw	zyrictxgtxriczygntzyxrtzyxw	NOUN
bibechana-19674	54	35	−	−	PROPN
bibechana-19674	55	1	−	−	PROPN
bibechana-19674	56	1	+	+	NOUN
bibechana-19674	56	2	=	=	NOUN
bibechana-19674	56	3	and	and	CCONJ
bibechana-19674	56	4	)	)	PUNCT
bibechana-19674	56	5	]	]	X
bibechana-19674	56	6	,	,	PUNCT
bibechana-19674	56	7	(	(	PUNCT
bibechana-19674	56	8	)	)	PUNCT
bibechana-19674	56	9	,	,	PUNCT
bibechana-19674	56	10	(	(	PUNCT
bibechana-19674	56	11	)	)	PUNCT
bibechana-19674	56	12	,	,	PUNCT
bibechana-19674	56	13	(	(	PUNCT
bibechana-19674	56	14	)	)	PUNCT
bibechana-19674	56	15	,	,	PUNCT
bibechana-19674	56	16	(	(	PUNCT
bibechana-19674	56	17	[	[	X
bibechana-19674	56	18	11),,,(),,,(9	11),,,(),,,(9	NUM
bibechana-19674	56	19	txriczygyxrictzgntzyxrtzyxw	txriczygyxrictzgntzyxrtzyxw	NOUN
bibechana-19674	56	20	−	−	PROPN
bibechana-19674	56	21	−	−	PROPN
bibechana-19674	57	1	+	+	NOUN
bibechana-19674	57	2	=	=	NOUN
bibechana-19674	57	3	respectively	respectively	ADV
bibechana-19674	57	4	.	.	PUNCT
bibechana-19674	58	1	in	in	ADP
bibechana-19674	58	2	)	)	PUNCT
bibechana-19674	58	3	12	12	NUM
bibechana-19674	58	4	(	(	PUNCT
bibechana-19674	58	5	+	+	NOUN
bibechana-19674	58	6	n	n	CCONJ
bibechana-19674	58	7	-dimensional	-dimensional	ADJ
bibechana-19674	58	8	)	)	PUNCT
bibechana-19674	58	9	(	(	PUNCT
bibechana-19674	58	10	kn	kn	NOUN
bibechana-19674	58	11	-contact	-contact	PROPN
bibechana-19674	58	12	metric	metric	ADJ
bibechana-19674	58	13	manifold	manifold	NOUN
bibechana-19674	58	14	above	above	ADP
bibechana-19674	58	15	two	two	NUM
bibechana-19674	58	16	tensors	tensor	NOUN
bibechana-19674	58	17	can	can	AUX
bibechana-19674	58	18	be	be	AUX
bibechana-19674	58	19	written	write	VERB
bibechana-19674	58	20	as	as	ADP
bibechana-19674	58	21	]	]	PUNCT
bibechana-19674	58	22	)	)	PUNCT
bibechana-19674	58	23	,	,	PUNCT
bibechana-19674	58	24	(	(	PUNCT
bibechana-19674	58	25	)	)	PUNCT
bibechana-19674	58	26	,	,	PUNCT
bibechana-19674	58	27	(	(	PUNCT
bibechana-19674	58	28	[	[	X
bibechana-19674	58	29	21),(),(7	21),(),(7	NUM
bibechana-19674	58	30	xzysqxzygnzyxrzyxw	xzysqxzygnzyxrzyxw	VERB
bibechana-19674	58	31	−+=	−+=	X
bibechana-19674	58	32	(	(	PUNCT
bibechana-19674	58	33	2.26	2.26	NUM
bibechana-19674	58	34	)	)	PUNCT
bibechana-19674	58	35	and	and	CCONJ
bibechana-19674	58	36	]	]	PUNCT
bibechana-19674	58	37	)	)	PUNCT
bibechana-19674	58	38	,	,	PUNCT
bibechana-19674	58	39	(	(	PUNCT
bibechana-19674	58	40	)	)	PUNCT
bibechana-19674	58	41	,	,	PUNCT
bibechana-19674	58	42	(	(	PUNCT
bibechana-19674	58	43	[	[	X
bibechana-19674	58	44	21),(),(9	21),(),(9	NUM
bibechana-19674	58	45	qxzygzyxsnzyxrzyxw	qxzygzyxsnzyxrzyxw	ADJ
bibechana-19674	58	46	−+=	−+=	X
bibechana-19674	58	47	(	(	PUNCT
bibechana-19674	58	48	2.27	2.27	NUM
bibechana-19674	58	49	)	)	PUNCT
bibechana-19674	58	50	respectively	respectively	ADV
bibechana-19674	58	51	,	,	PUNCT
bibechana-19674	58	52	where	where	SCONJ
bibechana-19674	58	53	)	)	PUNCT
bibechana-19674	58	54	,	,	PUNCT
bibechana-19674	58	55	,	,	PUNCT
bibechana-19674	58	56	,	,	PUNCT
bibechana-19674	58	57	(	(	PUNCT
bibechana-19674	58	58	)	)	PUNCT
bibechana-19674	58	59	,	,	PUNCT
bibechana-19674	58	60	)	)	PUNCT
bibechana-19674	58	61	,	,	PUNCT
bibechana-19674	58	62	(	(	PUNCT
bibechana-19674	58	63	(	(	PUNCT
bibechana-19674	58	64	tzyxrtzyxrg	tzyxrtzyxrg	NOUN
bibechana-19674	58	65	=	=	PUNCT
bibechana-19674	58	66	for	for	ADP
bibechana-19674	58	67	any	any	DET
bibechana-19674	58	68	vector	vector	NOUN
bibechana-19674	58	69	fields	field	NOUN
bibechana-19674	58	70	tzyx	tzyx	ADV
bibechana-19674	58	71	,	,	PUNCT
bibechana-19674	58	72	,	,	PUNCT
bibechana-19674	58	73	,	,	PUNCT
bibechana-19674	58	74	on	on	ADP
bibechana-19674	58	75	.12	.12	NUM
bibechana-19674	58	76	+	+	NOUN
bibechana-19674	58	77	nm	nm	ADV
bibechana-19674	58	78	now	now	ADV
bibechana-19674	58	79	,	,	PUNCT
bibechana-19674	58	80	using	use	VERB
bibechana-19674	58	81	(	(	PUNCT
bibechana-19674	58	82	2.17	2.17	NUM
bibechana-19674	58	83	)	)	PUNCT
bibechana-19674	58	84	and	and	CCONJ
bibechana-19674	58	85	(	(	PUNCT
bibechana-19674	58	86	2.18	2.18	NUM
bibechana-19674	58	87	)	)	PUNCT
bibechana-19674	58	88	in	in	ADP
bibechana-19674	58	89	(	(	PUNCT
bibechana-19674	58	90	2.26	2.26	NUM
bibechana-19674	58	91	)	)	PUNCT
bibechana-19674	58	92	and	and	CCONJ
bibechana-19674	58	93	(	(	PUNCT
bibechana-19674	58	94	2.27	2.27	NUM
bibechana-19674	58	95	)	)	PUNCT
bibechana-19674	58	96	we	we	PRON
bibechana-19674	58	97	obtain	obtain	VERB
bibechana-19674	58	98	ξηξξ	ξηξξ	NOUN
bibechana-19674	58	99	)	)	PUNCT
bibechana-19674	58	100	,	,	PUNCT
bibechana-19674	58	101	(	(	PUNCT
bibechana-19674	58	102	21])(),(2[),(7	21])(),(2[),(7	NUM
bibechana-19674	58	103	yxsnxyyxgkyxw	yxsnxyyxgkyxw	ADJ
bibechana-19674	58	104	−−=	−−=	PROPN
bibechana-19674	58	105	(	(	PUNCT
bibechana-19674	58	106	2.28	2.28	NUM
bibechana-19674	58	107	)	)	PUNCT
bibechana-19674	58	108	riddhi	riddhi	NOUN
bibechana-19674	58	109	jung	jung	PROPN
bibechana-19674	58	110	shah./	shah./	PROPN
bibechana-19674	58	111	bibechana	bibechana	PROPN
bibechana-19674	58	112	16	16	NUM
bibechana-19674	58	113	(	(	PUNCT
bibechana-19674	58	114	2019	2019	NUM
bibechana-19674	58	115	)	)	PUNCT
bibechana-19674	58	116	55	55	NUM
bibechana-19674	58	117	-	-	SYM
bibechana-19674	58	118	63	63	NUM
bibechana-19674	58	119	:	:	PUNCT
bibechana-19674	58	120	rcost	rcost	ADJ
bibechana-19674	58	121	p.58	p.58	PROPN
bibechana-19674	58	122	(	(	PUNCT
bibechana-19674	58	123	online	online	ADJ
bibechana-19674	58	124	publication	publication	NOUN
bibechana-19674	58	125	:	:	PUNCT
bibechana-19674	58	126	dec	dec	PROPN
bibechana-19674	58	127	.	.	PROPN
bibechana-19674	58	128	,	,	PUNCT
bibechana-19674	58	129	2018	2018	NUM
bibechana-19674	58	130	)	)	PUNCT
bibechana-19674	58	131	and	and	CCONJ
bibechana-19674	58	132	]	]	PUNCT
bibechana-19674	58	133	)	)	PUNCT
bibechana-19674	58	134	(	(	PUNCT
bibechana-19674	58	135	)	)	PUNCT
bibechana-19674	58	136	(	(	PUNCT
bibechana-19674	58	137	[	[	NOUN
bibechana-19674	58	138	)	)	PUNCT
bibechana-19674	58	139	,	,	PUNCT
bibechana-19674	58	140	(	(	PUNCT
bibechana-19674	58	141	9	9	NUM
bibechana-19674	58	142	xyyxkyxw	xyyxkyxw	X
bibechana-19674	58	143	ηηξ	ηηξ	PROPN
bibechana-19674	58	144	−=	−=	PROPN
bibechana-19674	58	145	(	(	PUNCT
bibechana-19674	58	146	2.29	2.29	NUM
bibechana-19674	58	147	)	)	PUNCT
bibechana-19674	58	148	respectively	respectively	ADV
bibechana-19674	58	149	.	.	PUNCT
bibechana-19674	59	1	from	from	ADP
bibechana-19674	59	2	(	(	PUNCT
bibechana-19674	59	3	2.27	2.27	NUM
bibechana-19674	59	4	)	)	PUNCT
bibechana-19674	59	5	we	we	PRON
bibechana-19674	59	6	also	also	ADV
bibechana-19674	59	7	have	have	VERB
bibechana-19674	59	8	)	)	PUNCT
bibechana-19674	59	9	(	(	PUNCT
bibechana-19674	59	10	)	)	PUNCT
bibechana-19674	59	11	,	,	PUNCT
bibechana-19674	59	12	(	(	PUNCT
bibechana-19674	59	13	)	)	PUNCT
bibechana-19674	59	14	(	(	PUNCT
bibechana-19674	59	15	)	)	PUNCT
bibechana-19674	59	16	,	,	PUNCT
bibechana-19674	59	17	(	(	PUNCT
bibechana-19674	59	18	21	21	NUM
bibechana-19674	59	19	)	)	PUNCT
bibechana-19674	59	20	)	)	PUNCT
bibechana-19674	59	21	,	,	PUNCT
bibechana-19674	59	22	(	(	PUNCT
bibechana-19674	59	23	(	(	PUNCT
bibechana-19674	59	24	9	9	NUM
bibechana-19674	59	25	yzxkgzyxsnzyxw	yzxkgzyxsnzyxw	PROPN
bibechana-19674	59	26	ηηη	ηηη	PROPN
bibechana-19674	59	27	−=	−=	PUNCT
bibechana-19674	59	28	(	(	PUNCT
bibechana-19674	59	29	2.30	2.30	NUM
bibechana-19674	59	30	)	)	PUNCT
bibechana-19674	59	31	(	(	PUNCT
bibechana-19674	59	32	)	)	PUNCT
bibechana-19674	59	33	0),(9	0),(9	PUNCT
bibechana-19674	60	1	=	=	PUNCT
bibechana-19674	60	2	yxw	yxw	X
bibechana-19674	60	3	ξη	ξη	X
bibechana-19674	60	4	(	(	PUNCT
bibechana-19674	60	5	2.31	2.31	NUM
bibechana-19674	60	6	)	)	PUNCT
bibechana-19674	60	7	(	(	PUNCT
bibechana-19674	60	8	)	)	PUNCT
bibechana-19674	60	9	)	)	PUNCT
bibechana-19674	60	10	]	]	PUNCT
bibechana-19674	60	11	,	,	PUNCT
bibechana-19674	60	12	(	(	PUNCT
bibechana-19674	60	13	)	)	PUNCT
bibechana-19674	60	14	(	(	PUNCT
bibechana-19674	60	15	)	)	PUNCT
bibechana-19674	60	16	(	(	PUNCT
bibechana-19674	60	17	[	[	NOUN
bibechana-19674	60	18	)	)	PUNCT
bibechana-19674	60	19	,	,	PUNCT
bibechana-19674	60	20	(	(	PUNCT
bibechana-19674	60	21	9	9	NUM
bibechana-19674	60	22	yxgyxkyxw	yxgyxkyxw	PROPN
bibechana-19674	60	23	−=	−=	ADJ
bibechana-19674	60	24	ηηξη	ηηξη	NOUN
bibechana-19674	60	25	(	(	PUNCT
bibechana-19674	60	26	2.32	2.32	NUM
bibechana-19674	60	27	)	)	PUNCT
bibechana-19674	60	28	(	(	PUNCT
bibechana-19674	60	29	)	)	PUNCT
bibechana-19674	60	30	)	)	PUNCT
bibechana-19674	61	1	.()(),(21),(9	.()(),(21),(9	PROPN
bibechana-19674	61	2	yxkyxsnyxw	yxkyxsnyxw	VERB
bibechana-19674	61	3	ηηξη	ηηξη	PROPN
bibechana-19674	61	4	−=	−=	X
bibechana-19674	61	5	(	(	PUNCT
bibechana-19674	61	6	2.33	2.33	NUM
bibechana-19674	61	7	)	)	PUNCT
bibechana-19674	61	8	definition	definition	NOUN
bibechana-19674	61	9	2.1	2.1	NUM
bibechana-19674	61	10	.	.	PUNCT
bibechana-19674	62	1	a	a	X
bibechana-19674	62	2	)	)	PUNCT
bibechana-19674	62	3	(	(	PUNCT
bibechana-19674	62	4	kn	kn	NOUN
bibechana-19674	62	5	-contact	-contact	PROPN
bibechana-19674	62	6	metric	metric	ADJ
bibechana-19674	62	7	manifold	manifold	NOUN
bibechana-19674	62	8	is	be	AUX
bibechana-19674	62	9	said	say	VERB
bibechana-19674	62	10	to	to	PART
bibechana-19674	62	11	be	be	AUX
bibechana-19674	62	12	η	η	PROPN
bibechana-19674	62	13	-einstein	-einstein	PROPN
bibechana-19674	62	14	if	if	SCONJ
bibechana-19674	62	15	its	its	PRON
bibechana-19674	62	16	ricci	ricci	PROPN
bibechana-19674	62	17	tensor	tensor	NOUN
bibechana-19674	62	18	s	s	PROPN
bibechana-19674	62	19	of	of	ADP
bibechana-19674	62	20	type	type	NOUN
bibechana-19674	62	21	(	(	PUNCT
bibechana-19674	62	22	0	0	NUM
bibechana-19674	62	23	,	,	PUNCT
bibechana-19674	62	24	2	2	NUM
bibechana-19674	62	25	)	)	PUNCT
bibechana-19674	62	26	is	be	AUX
bibechana-19674	62	27	of	of	ADP
bibechana-19674	62	28	the	the	DET
bibechana-19674	62	29	form	form	NOUN
bibechana-19674	62	30	)	)	PUNCT
bibechana-19674	62	31	(	(	PUNCT
bibechana-19674	62	32	)	)	PUNCT
bibechana-19674	62	33	(	(	PUNCT
bibechana-19674	62	34	)	)	PUNCT
bibechana-19674	62	35	,	,	PUNCT
bibechana-19674	62	36	(	(	PUNCT
bibechana-19674	62	37	)	)	PUNCT
bibechana-19674	62	38	,	,	PUNCT
bibechana-19674	62	39	(	(	PUNCT
bibechana-19674	62	40	21	21	NUM
bibechana-19674	62	41	yxyxgyxs	yxyxgyxs	ADJ
bibechana-19674	62	42	ηηµµ	ηηµµ	NOUN
bibechana-19674	63	1	+	+	PROPN
bibechana-19674	63	2	=	=	X
bibechana-19674	63	3	(	(	PUNCT
bibechana-19674	63	4	2.34	2.34	NUM
bibechana-19674	63	5	)	)	PUNCT
bibechana-19674	63	6	where	where	SCONJ
bibechana-19674	63	7	21	21	NUM
bibechana-19674	63	8	,	,	PUNCT
bibechana-19674	63	9	µµ	µµ	ADP
bibechana-19674	63	10	are	be	AUX
bibechana-19674	63	11	smooth	smooth	ADJ
bibechana-19674	63	12	functions	function	NOUN
bibechana-19674	63	13	on	on	ADP
bibechana-19674	63	14	the	the	DET
bibechana-19674	63	15	manifold	manifold	NOUN
bibechana-19674	63	16	.	.	PUNCT
bibechana-19674	64	1	definition	definition	NOUN
bibechana-19674	64	2	2.2	2.2	NUM
bibechana-19674	64	3	.	.	PUNCT
bibechana-19674	65	1	a	a	X
bibechana-19674	65	2	)	)	PUNCT
bibechana-19674	65	3	(	(	PUNCT
bibechana-19674	65	4	kn	kn	NOUN
bibechana-19674	65	5	-contact	-contact	PROPN
bibechana-19674	65	6	metric	metric	ADJ
bibechana-19674	65	7	manifold	manifold	NOUN
bibechana-19674	65	8	is	be	AUX
bibechana-19674	65	9	said	say	VERB
bibechana-19674	65	10	to	to	PART
bibechana-19674	65	11	be	be	AUX
bibechana-19674	65	12	ϕ	ϕ	NOUN
bibechana-19674	65	13	9w	9w	NOUN
bibechana-19674	65	14	flat	flat	ADJ
bibechana-19674	65	15	if	if	SCONJ
bibechana-19674	65	16	the	the	DET
bibechana-19674	65	17	condition	condition	NOUN
bibechana-19674	65	18	(	(	PUNCT
bibechana-19674	65	19	)	)	PUNCT
bibechana-19674	65	20	0,),(9	0,),(9	NOUN
bibechana-19674	66	1	=	=	NOUN
bibechana-19674	66	2	wzyxwg	wzyxwg	AUX
bibechana-19674	66	3	ϕϕϕϕ	ϕϕϕϕ	NOUN
bibechana-19674	66	4	holds	hold	VERB
bibechana-19674	66	5	for	for	ADP
bibechana-19674	66	6	any	any	DET
bibechana-19674	66	7	vector	vector	NOUN
bibechana-19674	66	8	fields	field	NOUN
bibechana-19674	66	9	)	)	PUNCT
bibechana-19674	66	10	.	.	PUNCT
bibechana-19674	67	1	(	(	PUNCT
bibechana-19674	67	2	,	,	PUNCT
bibechana-19674	67	3	,	,	PUNCT
bibechana-19674	67	4	,	,	PUNCT
bibechana-19674	67	5	mtwzyx	mtwzyx	NOUN
bibechana-19674	67	6	p∈	p∈	PROPN
bibechana-19674	67	7	3	3	NUM
bibechana-19674	67	8	.	.	NOUN
bibechana-19674	67	9	results	result	NOUN
bibechana-19674	67	10	and	and	CCONJ
bibechana-19674	67	11	discussion	discussion	NOUN
bibechana-19674	67	12	in	in	ADP
bibechana-19674	67	13	this	this	DET
bibechana-19674	67	14	section	section	NOUN
bibechana-19674	67	15	we	we	PRON
bibechana-19674	67	16	obtain	obtain	VERB
bibechana-19674	67	17	some	some	DET
bibechana-19674	67	18	results	result	NOUN
bibechana-19674	67	19	on	on	ADP
bibechana-19674	67	20	7w	7w	NUM
bibechana-19674	67	21	and	and	CCONJ
bibechana-19674	67	22	9w	9w	NOUN
bibechana-19674	67	23	curvature	curvature	NOUN
bibechana-19674	67	24	tensors	tensor	NOUN
bibechana-19674	67	25	in	in	ADP
bibechana-19674	67	26	)	)	PUNCT
bibechana-19674	67	27	(	(	PUNCT
bibechana-19674	67	28	kn	kn	NOUN
bibechana-19674	67	29	-contact	-contact	NOUN
bibechana-19674	67	30	metric	metric	ADJ
bibechana-19674	67	31	manifolds	manifold	NOUN
bibechana-19674	67	32	.	.	PUNCT
bibechana-19674	68	1	theorem	theorem	VERB
bibechana-19674	68	2	3.1	3.1	NUM
bibechana-19674	68	3	.	.	PUNCT
bibechana-19674	69	1	let	let	VERB
bibechana-19674	69	2	m	m	PRON
bibechana-19674	69	3	be	be	AUX
bibechana-19674	69	4	a	a	DET
bibechana-19674	69	5	)	)	PUNCT
bibechana-19674	69	6	12	12	NUM
bibechana-19674	69	7	(	(	PUNCT
bibechana-19674	69	8	+	+	NOUN
bibechana-19674	69	9	n	n	CCONJ
bibechana-19674	69	10	-dimensional	-dimensional	ADJ
bibechana-19674	69	11	)	)	PUNCT
bibechana-19674	69	12	(	(	PUNCT
bibechana-19674	69	13	kn	kn	NOUN
bibechana-19674	69	14	-contact	-contact	PROPN
bibechana-19674	69	15	metric	metric	ADJ
bibechana-19674	69	16	manifold	manifold	ADJ
bibechana-19674	69	17	satisfying	satisfy	VERB
bibechana-19674	69	18	the	the	DET
bibechana-19674	69	19	curvature	curvature	NOUN
bibechana-19674	69	20	condition	condition	NOUN
bibechana-19674	69	21	,	,	PUNCT
bibechana-19674	69	22	0	0	NUM
bibechana-19674	69	23	)	)	PUNCT
bibechana-19674	69	24	.	.	PUNCT
bibechana-19674	70	1	,	,	PUNCT
bibechana-19674	70	2	(	(	PUNCT
bibechana-19674	70	3	97	97	NUM
bibechana-19674	70	4	=	=	NOUN
bibechana-19674	70	5	wxw	wxw	VERB
bibechana-19674	70	6	ξ	ξ	PRON
bibechana-19674	70	7	then	then	ADV
bibechana-19674	70	8	either	either	CCONJ
bibechana-19674	70	9	m	m	NOUN
bibechana-19674	70	10	is	be	AUX
bibechana-19674	70	11	locally	locally	ADV
bibechana-19674	70	12	isometric	isometric	ADJ
bibechana-19674	70	13	to	to	ADP
bibechana-19674	70	14	the	the	DET
bibechana-19674	70	15	riemannian	riemannian	ADJ
bibechana-19674	70	16	product	product	NOUN
bibechana-19674	70	17	)	)	PUNCT
bibechana-19674	70	18	4()0(1	4()0(1	NUM
bibechana-19674	70	19	nn	nn	X
bibechana-19674	70	20	se	se	PROPN
bibechana-19674	70	21	×+	×+	PROPN
bibechana-19674	70	22	for	for	ADP
bibechana-19674	70	23	1	1	NUM
bibechana-19674	70	24	>	>	SYM
bibechana-19674	70	25	n	n	NOUN
bibechana-19674	70	26	or	or	CCONJ
bibechana-19674	70	27	m	m	VERB
bibechana-19674	70	28	is	be	AUX
bibechana-19674	70	29	η	η	PROPN
bibechana-19674	70	30	-einstein	-einstein	PROPN
bibechana-19674	70	31	manifold	manifold	ADJ
bibechana-19674	70	32	.	.	PUNCT
bibechana-19674	71	1	proof	proof	NOUN
bibechana-19674	71	2	.	.	PUNCT
bibechana-19674	72	1	let	let	VERB
bibechana-19674	72	2	us	we	PRON
bibechana-19674	72	3	consider	consider	VERB
bibechana-19674	72	4	a	a	PRON
bibechana-19674	72	5	)	)	PUNCT
bibechana-19674	72	6	12	12	NUM
bibechana-19674	72	7	(	(	PUNCT
bibechana-19674	72	8	+	+	NOUN
bibechana-19674	72	9	n	n	CCONJ
bibechana-19674	72	10	-dimensional	-dimensional	ADJ
bibechana-19674	72	11	)	)	PUNCT
bibechana-19674	72	12	(	(	PUNCT
bibechana-19674	72	13	kn	kn	NOUN
bibechana-19674	72	14	-contact	-contact	PROPN
bibechana-19674	72	15	metric	metric	ADJ
bibechana-19674	72	16	manifold	manifold	NOUN
bibechana-19674	72	17	m	m	VERB
bibechana-19674	72	18	which	which	PRON
bibechana-19674	72	19	satisfies	satisfy	VERB
bibechana-19674	72	20	the	the	DET
bibechana-19674	72	21	curvature	curvature	NOUN
bibechana-19674	72	22	condition	condition	NOUN
bibechana-19674	72	23	(	(	PUNCT
bibechana-19674	72	24	)	)	PUNCT
bibechana-19674	72	25	0	0	NUM
bibechana-19674	72	26	)	)	PUNCT
bibechana-19674	72	27	,	,	PUNCT
bibechana-19674	72	28	(	(	PUNCT
bibechana-19674	72	29	)	)	PUNCT
bibechana-19674	72	30	.	.	PUNCT
bibechana-19674	73	1	,	,	PUNCT
bibechana-19674	73	2	(	(	PUNCT
bibechana-19674	73	3	97	97	NUM
bibechana-19674	73	4	=	=	NUM
bibechana-19674	73	5	zvuwxw	zvuwxw	NOUN
bibechana-19674	73	6	ξ	ξ	PROPN
bibechana-19674	73	7	for	for	ADP
bibechana-19674	73	8	any	any	DET
bibechana-19674	73	9	vector	vector	NOUN
bibechana-19674	73	10	fields	field	NOUN
bibechana-19674	73	11	zvux	zvux	PROPN
bibechana-19674	73	12	,	,	PUNCT
bibechana-19674	73	13	,	,	PUNCT
bibechana-19674	73	14	,	,	PUNCT
bibechana-19674	73	15	on	on	ADP
bibechana-19674	73	16	.12	.12	NUM
bibechana-19674	73	17	+	+	NOUN
bibechana-19674	73	18	nm	nm	NOUN
bibechana-19674	73	19	by	by	ADP
bibechana-19674	73	20	definition	definition	NOUN
bibechana-19674	73	21	we	we	PRON
bibechana-19674	73	22	have	have	VERB
bibechana-19674	73	23	(	(	PUNCT
bibechana-19674	73	24	)	)	PUNCT
bibechana-19674	73	25	(	(	PUNCT
bibechana-19674	73	26	)	)	PUNCT
bibechana-19674	73	27	(	(	PUNCT
bibechana-19674	73	28	)	)	PUNCT
bibechana-19674	73	29	zxwvuwzvxwuw	zxwvuwzvxwuw	PROPN
bibechana-19674	73	30	zvuxwwzvuwxwzvuwxw	zvuxwwzvuwxwzvuwxw	PROPN
bibechana-19674	73	31	)	)	PUNCT
bibechana-19674	73	32	,	,	PUNCT
bibechana-19674	73	33	(	(	PUNCT
bibechana-19674	73	34	)	)	PUNCT
bibechana-19674	73	35	,	,	PUNCT
bibechana-19674	73	36	(	(	PUNCT
bibechana-19674	73	37	)	)	PUNCT
bibechana-19674	73	38	,	,	PUNCT
bibechana-19674	73	39	(	(	PUNCT
bibechana-19674	73	40	,	,	PUNCT
bibechana-19674	73	41	,	,	PUNCT
bibechana-19674	73	42	)	)	PUNCT
bibechana-19674	73	43	,	,	PUNCT
bibechana-19674	73	44	(	(	PUNCT
bibechana-19674	73	45	)	)	PUNCT
bibechana-19674	73	46	,	,	PUNCT
bibechana-19674	73	47	(	(	PUNCT
bibechana-19674	73	48	)	)	PUNCT
bibechana-19674	73	49	,	,	PUNCT
bibechana-19674	73	50	(	(	PUNCT
bibechana-19674	73	51	)	)	PUNCT
bibechana-19674	73	52	,	,	PUNCT
bibechana-19674	73	53	(	(	PUNCT
bibechana-19674	73	54	)	)	PUNCT
bibechana-19674	73	55	.	.	PUNCT
bibechana-19674	74	1	,	,	PUNCT
bibechana-19674	74	2	(	(	PUNCT
bibechana-19674	74	3	7979	7979	NUM
bibechana-19674	74	4	799797	799797	NUM
bibechana-19674	74	5	ξξ	ξξ	ADV
bibechana-19674	74	6	ξξξ	ξξξ	NOUN
bibechana-19674	74	7	−−	−−	PROPN
bibechana-19674	74	8	−=	−=	PUNCT
bibechana-19674	74	9	(	(	PUNCT
bibechana-19674	74	10	)	)	PUNCT
bibechana-19674	74	11	(	(	PUNCT
bibechana-19674	74	12	)	)	PUNCT
bibechana-19674	74	13	.	.	PUNCT
bibechana-19674	74	14	)	)	PUNCT
bibechana-19674	74	15	,	,	PUNCT
bibechana-19674	74	16	(	(	PUNCT
bibechana-19674	74	17	)	)	PUNCT
bibechana-19674	74	18	,	,	PUNCT
bibechana-19674	74	19	(	(	PUNCT
bibechana-19674	74	20	)	)	PUNCT
bibechana-19674	74	21	,	,	PUNCT
bibechana-19674	74	22	(	(	PUNCT
bibechana-19674	74	23	,	,	PUNCT
bibechana-19674	74	24	,	,	PUNCT
bibechana-19674	74	25	)	)	PUNCT
bibechana-19674	74	26	,	,	PUNCT
bibechana-19674	74	27	(	(	PUNCT
bibechana-19674	74	28	)	)	PUNCT
bibechana-19674	74	29	,	,	PUNCT
bibechana-19674	74	30	(	(	PUNCT
bibechana-19674	74	31	)	)	PUNCT
bibechana-19674	74	32	,	,	PUNCT
bibechana-19674	74	33	(	(	PUNCT
bibechana-19674	74	34	0	0	NUM
bibechana-19674	74	35	or	or	CCONJ
bibechana-19674	74	36	,	,	PUNCT
bibechana-19674	74	37	7979	7979	NUM
bibechana-19674	74	38	7997	7997	NUM
bibechana-19674	74	39	zxwvuwzvxwuw	zxwvuwzvxwuw	PROPN
bibechana-19674	74	40	zvuxwwzvuwxw	zvuxwwzvuwxw	VERB
bibechana-19674	74	41	ξξ	ξξ	ADV
bibechana-19674	74	42	ξξ	ξξ	ADP
bibechana-19674	74	43	−−	−−	NOUN
bibechana-19674	74	44	−=	−=	X
bibechana-19674	74	45	(	(	PUNCT
bibechana-19674	74	46	3.1	3.1	NUM
bibechana-19674	74	47	)	)	PUNCT
bibechana-19674	74	48	in	in	ADP
bibechana-19674	74	49	view	view	NOUN
bibechana-19674	74	50	of	of	ADP
bibechana-19674	74	51	(	(	PUNCT
bibechana-19674	74	52	2.28	2.28	NUM
bibechana-19674	74	53	)	)	PUNCT
bibechana-19674	74	54	and	and	CCONJ
bibechana-19674	74	55	(	(	PUNCT
bibechana-19674	74	56	3.1	3.1	NUM
bibechana-19674	74	57	)	)	PUNCT
bibechana-19674	74	58	we	we	PRON
bibechana-19674	74	59	get	get	VERB
bibechana-19674	74	60	(	(	PUNCT
bibechana-19674	74	61	)	)	PUNCT
bibechana-19674	74	62	(	(	PUNCT
bibechana-19674	74	63	)	)	PUNCT
bibechana-19674	74	64	(	(	PUNCT
bibechana-19674	74	65	)	)	PUNCT
bibechana-19674	74	66	.),(),(21),()(),(),(2	.),(),(21),()(),(),(2	PROPN
bibechana-19674	74	67	)	)	PUNCT
bibechana-19674	74	68	,	,	PUNCT
bibechana-19674	74	69	(	(	PUNCT
bibechana-19674	74	70	)	)	PUNCT
bibechana-19674	74	71	,	,	PUNCT
bibechana-19674	74	72	(	(	PUNCT
bibechana-19674	74	73	21),()(),(),(2	21),()(),(),(2	NUM
bibechana-19674	74	74	)	)	PUNCT
bibechana-19674	74	75	,	,	PUNCT
bibechana-19674	74	76	(	(	PUNCT
bibechana-19674	74	77	)	)	PUNCT
bibechana-19674	74	78	,	,	PUNCT
bibechana-19674	74	79	(	(	PUNCT
bibechana-19674	74	80	21),()(),(),(2	21),()(),(),(2	NUM
bibechana-19674	74	81	)	)	PUNCT
bibechana-19674	74	82	,	,	PUNCT
bibechana-19674	74	83	(	(	PUNCT
bibechana-19674	74	84	,	,	PUNCT
bibechana-19674	74	85	21),(),(,20	21),(),(,20	NUM
bibechana-19674	74	86	999	999	NUM
bibechana-19674	74	87	999	999	NUM
bibechana-19674	74	88	999	999	NUM
bibechana-19674	74	89	999	999	NUM
bibechana-19674	74	90	ξηξ	ξηξ	NOUN
bibechana-19674	74	91	ξηξ	ξηξ	NOUN
bibechana-19674	74	92	ξηξ	ξηξ	NOUN
bibechana-19674	74	93	ξηξ	ξηξ	PROPN
bibechana-19674	74	94	vuwzxsnxvuwzkvuwzxkg	vuwzxsnxvuwzkvuwzxkg	PROPN
bibechana-19674	74	95	zuwvxsnzxuwvkzuwvxkg	zuwvxsnzxuwvkzuwvxkg	PROPN
bibechana-19674	74	96	zvwuxsnzvxwukzvwuxkg	zvwuxsnzvxwukzvwuxkg	PROPN
bibechana-19674	74	97	zvuwxsnxzvuwkzvuwxkg	zvuwxsnxzvuwkzvuwxkg	PROPN
bibechana-19674	75	1	+	+	PROPN
bibechana-19674	75	2	+	+	ADJ
bibechana-19674	75	3	−	−	ADJ
bibechana-19674	76	1	+	+	ADJ
bibechana-19674	76	2	+	+	NOUN
bibechana-19674	76	3	−	−	ADJ
bibechana-19674	76	4	+	+	ADJ
bibechana-19674	76	5	+	+	NOUN
bibechana-19674	76	6	−	−	ADJ
bibechana-19674	76	7	−−=	−−=	NOUN
bibechana-19674	76	8	(	(	PUNCT
bibechana-19674	76	9	3.2	3.2	NUM
bibechana-19674	76	10	)	)	PUNCT
bibechana-19674	76	11	taking	take	VERB
bibechana-19674	76	12	inner	inner	ADJ
bibechana-19674	76	13	product	product	NOUN
bibechana-19674	76	14	on	on	ADP
bibechana-19674	76	15	both	both	DET
bibechana-19674	76	16	sides	side	NOUN
bibechana-19674	76	17	of	of	ADP
bibechana-19674	76	18	(	(	PUNCT
bibechana-19674	76	19	3.2	3.2	NUM
bibechana-19674	76	20	)	)	PUNCT
bibechana-19674	76	21	by	by	ADP
bibechana-19674	76	22	ξ	ξ	PROPN
bibechana-19674	76	23	and	and	CCONJ
bibechana-19674	76	24	using	use	VERB
bibechana-19674	76	25	(	(	PUNCT
bibechana-19674	76	26	2.1	2.1	NUM
bibechana-19674	76	27	)	)	PUNCT
bibechana-19674	76	28	and	and	CCONJ
bibechana-19674	76	29	(	(	PUNCT
bibechana-19674	76	30	2.2	2.2	NUM
bibechana-19674	76	31	)	)	PUNCT
bibechana-19674	76	32	we	we	PRON
bibechana-19674	76	33	obtain	obtain	VERB
bibechana-19674	76	34	riddhi	riddhi	ADJ
bibechana-19674	76	35	jung	jung	PROPN
bibechana-19674	76	36	shah./	shah./	PROPN
bibechana-19674	76	37	bibechana	bibechana	PROPN
bibechana-19674	76	38	16	16	NUM
bibechana-19674	76	39	(	(	PUNCT
bibechana-19674	76	40	2019	2019	NUM
bibechana-19674	76	41	)	)	PUNCT
bibechana-19674	76	42	55	55	NUM
bibechana-19674	76	43	-	-	SYM
bibechana-19674	76	44	63	63	NUM
bibechana-19674	76	45	:	:	PUNCT
bibechana-19674	76	46	rcost	rcost	NOUN
bibechana-19674	76	47	p.59	p.59	NOUN
bibechana-19674	76	48	(	(	PUNCT
bibechana-19674	76	49	online	online	ADJ
bibechana-19674	76	50	publication	publication	NOUN
bibechana-19674	76	51	:	:	PUNCT
bibechana-19674	76	52	dec	dec	PROPN
bibechana-19674	76	53	.	.	PROPN
bibechana-19674	76	54	,	,	PUNCT
bibechana-19674	76	55	2018	2018	NUM
bibechana-19674	76	56	)	)	PUNCT
bibechana-19674	76	57	(	(	PUNCT
bibechana-19674	76	58	)	)	PUNCT
bibechana-19674	76	59	(	(	PUNCT
bibechana-19674	76	60	)	)	PUNCT
bibechana-19674	76	61	(	(	PUNCT
bibechana-19674	76	62	)	)	PUNCT
bibechana-19674	76	63	(	(	PUNCT
bibechana-19674	76	64	)	)	PUNCT
bibechana-19674	76	65	(	(	PUNCT
bibechana-19674	76	66	)	)	PUNCT
bibechana-19674	76	67	(	(	PUNCT
bibechana-19674	76	68	)	)	PUNCT
bibechana-19674	76	69	(	(	PUNCT
bibechana-19674	76	70	)	)	PUNCT
bibechana-19674	76	71	(	(	PUNCT
bibechana-19674	76	72	)	)	PUNCT
bibechana-19674	76	73	(	(	PUNCT
bibechana-19674	76	74	)	)	PUNCT
bibechana-19674	76	75	(	(	PUNCT
bibechana-19674	76	76	)	)	PUNCT
bibechana-19674	76	77	(	(	PUNCT
bibechana-19674	76	78	)	)	PUNCT
bibechana-19674	76	79	(	(	PUNCT
bibechana-19674	76	80	)	)	PUNCT
bibechana-19674	76	81	.),(),(21),()(),(),(2	.),(),(21),()(),(),(2	PROPN
bibechana-19674	76	82	)	)	PUNCT
bibechana-19674	76	83	,	,	PUNCT
bibechana-19674	76	84	(	(	PUNCT
bibechana-19674	76	85	)	)	PUNCT
bibechana-19674	76	86	,	,	PUNCT
bibechana-19674	76	87	(	(	PUNCT
bibechana-19674	76	88	21),()(),(),(2	21),()(),(),(2	NUM
bibechana-19674	76	89	)	)	PUNCT
bibechana-19674	76	90	,	,	PUNCT
bibechana-19674	76	91	(	(	PUNCT
bibechana-19674	76	92	)	)	PUNCT
bibechana-19674	76	93	,	,	PUNCT
bibechana-19674	76	94	(	(	PUNCT
bibechana-19674	76	95	21),()(),(),(2	21),()(),(),(2	NUM
bibechana-19674	76	96	)	)	PUNCT
bibechana-19674	76	97	,	,	PUNCT
bibechana-19674	76	98	(	(	PUNCT
bibechana-19674	76	99	,	,	PUNCT
bibechana-19674	76	100	21)(),(),(,20	21)(),(),(,20	NUM
bibechana-19674	76	101	999	999	NUM
bibechana-19674	76	102	999	999	NUM
bibechana-19674	76	103	999	999	NUM
bibechana-19674	76	104	999	999	NUM
bibechana-19674	76	105	ξηηηξη	ξηηηξη	NOUN
bibechana-19674	76	106	ξηηηξη	ξηηηξη	NOUN
bibechana-19674	76	107	ξηηηξη	ξηηηξη	PROPN
bibechana-19674	76	108	ηη	ηη	PROPN
bibechana-19674	76	109	vuwzxsnxvuwzkvuwzxkg	vuwzxsnxvuwzkvuwzxkg	PROPN
bibechana-19674	76	110	zuwvxsnzxuwvkzuwvxkg	zuwvxsnzxuwvkzuwvxkg	PROPN
bibechana-19674	76	111	zvwuxsnzvxwukzvwuxkg	zvwuxsnzvxwukzvwuxkg	PROPN
bibechana-19674	76	112	zvuwxsnxzvuwkzvuwxkg	zvuwxsnxzvuwkzvuwxkg	PROPN
bibechana-19674	77	1	+	+	PROPN
bibechana-19674	77	2	+	+	ADJ
bibechana-19674	77	3	−	−	ADJ
bibechana-19674	78	1	+	+	ADJ
bibechana-19674	78	2	+	+	NOUN
bibechana-19674	78	3	−	−	ADJ
bibechana-19674	78	4	+	+	ADJ
bibechana-19674	78	5	+	+	NOUN
bibechana-19674	78	6	−	−	ADJ
bibechana-19674	78	7	−−=	−−=	NOUN
bibechana-19674	78	8	(	(	PUNCT
bibechana-19674	78	9	3.3	3.3	NUM
bibechana-19674	78	10	)	)	PUNCT
bibechana-19674	78	11	by	by	ADP
bibechana-19674	78	12	the	the	DET
bibechana-19674	78	13	use	use	NOUN
bibechana-19674	78	14	of	of	ADP
bibechana-19674	78	15	(	(	PUNCT
bibechana-19674	78	16	2.30	2.30	NUM
bibechana-19674	78	17	)	)	PUNCT
bibechana-19674	78	18	(	(	PUNCT
bibechana-19674	78	19	2.33	2.33	NUM
bibechana-19674	78	20	)	)	PUNCT
bibechana-19674	78	21	,	,	PUNCT
bibechana-19674	78	22	(	(	PUNCT
bibechana-19674	78	23	3.3	3.3	NUM
bibechana-19674	78	24	)	)	PUNCT
bibechana-19674	78	25	reduces	reduce	VERB
bibechana-19674	78	26	to	to	PART
bibechana-19674	78	27	)	)	PUNCT
bibechana-19674	78	28	.()(),(2),(),(41	.()(),(2),(),(41	PROPN
bibechana-19674	78	29	)	)	PUNCT
bibechana-19674	78	30	(	(	PUNCT
bibechana-19674	78	31	)	)	PUNCT
bibechana-19674	78	32	(	(	PUNCT
bibechana-19674	78	33	)	)	PUNCT
bibechana-19674	78	34	}	}	PUNCT
bibechana-19674	78	35	,	,	PUNCT
bibechana-19674	78	36	(	(	PUNCT
bibechana-19674	78	37	)	)	PUNCT
bibechana-19674	78	38	,	,	PUNCT
bibechana-19674	78	39	(	(	PUNCT
bibechana-19674	78	40	{	{	PUNCT
bibechana-19674	78	41	)	)	PUNCT
bibechana-19674	78	42	}	}	PUNCT
bibechana-19674	78	43	(	(	PUNCT
bibechana-19674	78	44	)	)	PUNCT
bibechana-19674	78	45	(	(	PUNCT
bibechana-19674	78	46	)	)	PUNCT
bibechana-19674	78	47	,	,	PUNCT
bibechana-19674	78	48	(	(	PUNCT
bibechana-19674	78	49	)	)	PUNCT
bibechana-19674	78	50	{	{	PUNCT
bibechana-19674	78	51	,	,	PUNCT
bibechana-19674	78	52	(	(	PUNCT
bibechana-19674	78	53	2	2	NUM
bibechana-19674	78	54	)	)	PUNCT
bibechana-19674	78	55	}	}	PUNCT
bibechana-19674	78	56	,	,	PUNCT
bibechana-19674	78	57	(	(	PUNCT
bibechana-19674	78	58	1	1	NUM
bibechana-19674	78	59	)	)	PUNCT
bibechana-19674	78	60	(	(	PUNCT
bibechana-19674	78	61	)	)	PUNCT
bibechana-19674	78	62	(	(	PUNCT
bibechana-19674	78	63	)	)	PUNCT
bibechana-19674	78	64	{	{	PUNCT
bibechana-19674	78	65	,	,	PUNCT
bibechana-19674	78	66	(	(	PUNCT
bibechana-19674	78	67	)	)	PUNCT
bibechana-19674	78	68	}	}	PUNCT
bibechana-19674	78	69	,	,	PUNCT
bibechana-19674	78	70	(	(	PUNCT
bibechana-19674	78	71	21	21	NUM
bibechana-19674	78	72	)	)	PUNCT
bibechana-19674	78	73	(	(	PUNCT
bibechana-19674	78	74	)	)	PUNCT
bibechana-19674	78	75	(	(	PUNCT
bibechana-19674	78	76	)	)	PUNCT
bibechana-19674	78	77	{	{	PUNCT
bibechana-19674	78	78	,	,	PUNCT
bibechana-19674	78	79	(	(	PUNCT
bibechana-19674	78	80	)	)	PUNCT
bibechana-19674	78	81	)	)	PUNCT
bibechana-19674	78	82	,	,	PUNCT
bibechana-19674	78	83	(	(	PUNCT
bibechana-19674	78	84	,	,	PUNCT
bibechana-19674	78	85	(	(	PUNCT
bibechana-19674	78	86	21)),(,(20	21)),(,(20	NUM
bibechana-19674	78	87	22	22	NUM
bibechana-19674	78	88	99	99	NUM
bibechana-19674	78	89	vuzxsnkvuszxsnzvuxkg	vuzxsnkvuszxsnzvuxkg	NOUN
bibechana-19674	78	90	uxskzuzugvxgkvusn	uxskzuzugvxgkvusn	NOUN
bibechana-19674	78	91	vukzxkgzugzuvxsnk	vukzxkgzugzuvxsnk	NOUN
bibechana-19674	78	92	zvuwxsnzvuwxkg	zvuwxsnzvuwxkg	NOUN
bibechana-19674	78	93	ηηηη	ηηηη	VERB
bibechana-19674	78	94	ηη	ηη	ADP
bibechana-19674	78	95	ηηηη	ηηηη	VERB
bibechana-19674	78	96	−+−	−+−	NOUN
bibechana-19674	78	97	+	+	CCONJ
bibechana-19674	78	98	−+−	−+−	PROPN
bibechana-19674	79	1	+	+	NOUN
bibechana-19674	79	2	−+	−+	PROPN
bibechana-19674	79	3	−=	−=	PUNCT
bibechana-19674	79	4	(	(	PUNCT
bibechana-19674	79	5	3.4	3.4	NUM
bibechana-19674	79	6	)	)	PUNCT
bibechana-19674	79	7	putting	put	VERB
bibechana-19674	79	8	ξ	ξ	NOUN
bibechana-19674	79	9	=	=	NOUN
bibechana-19674	79	10	u	u	NOUN
bibechana-19674	79	11	in	in	ADP
bibechana-19674	79	12	(	(	PUNCT
bibechana-19674	79	13	3.4	3.4	NUM
bibechana-19674	79	14	)	)	PUNCT
bibechana-19674	79	15	and	and	CCONJ
bibechana-19674	79	16	using	use	VERB
bibechana-19674	79	17	(	(	PUNCT
bibechana-19674	79	18	2.1	2.1	NUM
bibechana-19674	79	19	)	)	PUNCT
bibechana-19674	79	20	,	,	PUNCT
bibechana-19674	79	21	(	(	PUNCT
bibechana-19674	79	22	2.2	2.2	NUM
bibechana-19674	79	23	)	)	PUNCT
bibechana-19674	79	24	,	,	PUNCT
bibechana-19674	79	25	(	(	PUNCT
bibechana-19674	79	26	2.17	2.17	NUM
bibechana-19674	79	27	)	)	PUNCT
bibechana-19674	79	28	and	and	CCONJ
bibechana-19674	79	29	(	(	PUNCT
bibechana-19674	79	30	2.29	2.29	NUM
bibechana-19674	79	31	)	)	PUNCT
bibechana-19674	79	32	we	we	PRON
bibechana-19674	79	33	get	get	VERB
bibechana-19674	79	34	)	)	PUNCT
bibechana-19674	79	35	]	]	PUNCT
bibechana-19674	79	36	.()()()12()(),(1	.()()()12()(),(1	PROPN
bibechana-19674	79	37	)	)	PUNCT
bibechana-19674	79	38	(	(	PUNCT
bibechana-19674	79	39	)	)	PUNCT
bibechana-19674	79	40	,	,	PUNCT
bibechana-19674	79	41	(	(	PUNCT
bibechana-19674	79	42	21)(),(2)(),([0	21)(),(2)(),([0	NUM
bibechana-19674	79	43	zxvknzvxsn	zxvknzvxsn	ADJ
bibechana-19674	79	44	vzxsnzvxkgvzxkgk	vzxsnzvxkgvzxkgk	NOUN
bibechana-19674	79	45	ηηηη	ηηηη	NOUN
bibechana-19674	79	46	ηηη	ηηη	PRON
bibechana-19674	79	47	−++	−++	ADP
bibechana-19674	79	48	−−=	−−=	PROPN
bibechana-19674	79	49	(	(	PUNCT
bibechana-19674	79	50	3.5	3.5	NUM
bibechana-19674	79	51	)	)	PUNCT
bibechana-19674	79	52	from	from	ADP
bibechana-19674	79	53	(	(	PUNCT
bibechana-19674	79	54	3.5	3.5	NUM
bibechana-19674	79	55	)	)	PUNCT
bibechana-19674	79	56	it	it	PRON
bibechana-19674	79	57	follows	follow	VERB
bibechana-19674	79	58	that	that	SCONJ
bibechana-19674	79	59	either	either	CCONJ
bibechana-19674	79	60	0	0	NUM
bibechana-19674	79	61	=	=	SYM
bibechana-19674	79	62	k	k	PROPN
bibechana-19674	79	63	or	or	CCONJ
bibechana-19674	79	64	.0)]()()()12()(),(1	.0)]()()()12()(),(1	PROPN
bibechana-19674	79	65	)	)	PUNCT
bibechana-19674	79	66	(	(	PUNCT
bibechana-19674	79	67	)	)	PUNCT
bibechana-19674	79	68	,	,	PUNCT
bibechana-19674	79	69	(	(	PUNCT
bibechana-19674	79	70	21)(),(2	21)(),(2	NUM
bibechana-19674	79	71	)	)	PUNCT
bibechana-19674	79	72	(	(	PUNCT
bibechana-19674	79	73	)	)	PUNCT
bibechana-19674	79	74	,	,	PUNCT
bibechana-19674	79	75	(	(	PUNCT
bibechana-19674	79	76	[	[	PUNCT
bibechana-19674	79	77	=	=	NOUN
bibechana-19674	79	78	−++	−++	ADP
bibechana-19674	79	79	−−	−−	NOUN
bibechana-19674	79	80	zxvknzvxsn	zxvknzvxsn	NOUN
bibechana-19674	80	1	vzxsnzvxkgvzxkg	vzxsnzvxkgvzxkg	PRON
bibechana-19674	80	2	ηηηη	ηηηη	VERB
bibechana-19674	80	3	ηηη	ηηη	PROPN
bibechana-19674	80	4	if	if	SCONJ
bibechana-19674	80	5	,	,	PUNCT
bibechana-19674	80	6	0	0	PUNCT
bibechana-19674	80	7	=	=	SYM
bibechana-19674	80	8	k	k	PROPN
bibechana-19674	80	9	then	then	ADV
bibechana-19674	80	10	we	we	PRON
bibechana-19674	80	11	know	know	VERB
bibechana-19674	80	12	that	that	PRON
bibechana-19674	80	13	)	)	PUNCT
bibechana-19674	81	1	(	(	PUNCT
bibechana-19674	81	2	kn	kn	NOUN
bibechana-19674	81	3	-contact	-contact	PROPN
bibechana-19674	81	4	metric	metric	ADJ
bibechana-19674	81	5	manifold	manifold	NOUN
bibechana-19674	81	6	is	be	AUX
bibechana-19674	81	7	locally	locally	ADV
bibechana-19674	81	8	isometric	isometric	ADJ
bibechana-19674	81	9	to	to	ADP
bibechana-19674	81	10	the	the	DET
bibechana-19674	81	11	riemannian	riemannian	ADJ
bibechana-19674	81	12	product	product	NOUN
bibechana-19674	81	13	)	)	PUNCT
bibechana-19674	81	14	4()0(1	4()0(1	NUM
bibechana-19674	81	15	nn	nn	X
bibechana-19674	81	16	se	se	PROPN
bibechana-19674	81	17	×+	×+	PROPN
bibechana-19674	81	18	for	for	ADP
bibechana-19674	81	19	1	1	NUM
bibechana-19674	81	20	>	>	SYM
bibechana-19674	81	21	n	n	CCONJ
bibechana-19674	81	22	[	[	X
bibechana-19674	81	23	9	9	NUM
bibechana-19674	81	24	]	]	PUNCT
bibechana-19674	81	25	.	.	PUNCT
bibechana-19674	82	1	if	if	SCONJ
bibechana-19674	82	2	,	,	PUNCT
bibechana-19674	82	3	0)]()()()12()(),(1	0)]()()()12()(),(1	NUM
bibechana-19674	82	4	)	)	PUNCT
bibechana-19674	82	5	(	(	PUNCT
bibechana-19674	82	6	)	)	PUNCT
bibechana-19674	82	7	,	,	PUNCT
bibechana-19674	82	8	(	(	PUNCT
bibechana-19674	82	9	21)(),(2	21)(),(2	NUM
bibechana-19674	82	10	)	)	PUNCT
bibechana-19674	82	11	(	(	PUNCT
bibechana-19674	82	12	)	)	PUNCT
bibechana-19674	82	13	,	,	PUNCT
bibechana-19674	82	14	(	(	PUNCT
bibechana-19674	82	15	[	[	PUNCT
bibechana-19674	82	16	=	=	NOUN
bibechana-19674	82	17	−++	−++	ADP
bibechana-19674	82	18	−−	−−	NOUN
bibechana-19674	82	19	zxvknzvxsn	zxvknzvxsn	NOUN
bibechana-19674	82	20	vzxsnzvxkgvzxkg	vzxsnzvxkgvzxkg	PRON
bibechana-19674	82	21	ηηηη	ηηηη	ADJ
bibechana-19674	82	22	ηηη	ηηη	PROPN
bibechana-19674	82	23	then	then	ADV
bibechana-19674	82	24	replacing	replace	VERB
bibechana-19674	82	25	z	z	NOUN
bibechana-19674	82	26	by	by	ADP
bibechana-19674	82	27	ξ	ξ	PROPN
bibechana-19674	82	28	we	we	PRON
bibechana-19674	82	29	get	get	VERB
bibechana-19674	82	30	)	)	PUNCT
bibechana-19674	82	31	.()()12(),(2	.()()12(),(2	NUM
bibechana-19674	82	32	)	)	PUNCT
bibechana-19674	82	33	,	,	PUNCT
bibechana-19674	82	34	(	(	PUNCT
bibechana-19674	82	35	vxknnvxnkgvxs	vxknnvxnkgvxs	PROPN
bibechana-19674	82	36	ηη−−=	ηη−−=	NUM
bibechana-19674	82	37	(	(	PUNCT
bibechana-19674	82	38	3.6	3.6	NUM
bibechana-19674	82	39	)	)	PUNCT
bibechana-19674	82	40	from	from	ADP
bibechana-19674	82	41	(	(	PUNCT
bibechana-19674	82	42	3.6	3.6	NUM
bibechana-19674	82	43	)	)	PUNCT
bibechana-19674	82	44	we	we	PRON
bibechana-19674	82	45	obtain	obtain	VERB
bibechana-19674	82	46	)	)	PUNCT
bibechana-19674	82	47	.	.	PUNCT
bibechana-19674	83	1	(	(	PUNCT
bibechana-19674	83	2	)	)	PUNCT
bibechana-19674	83	3	(	(	PUNCT
bibechana-19674	83	4	)	)	PUNCT
bibechana-19674	83	5	,	,	PUNCT
bibechana-19674	83	6	(	(	PUNCT
bibechana-19674	83	7	)	)	PUNCT
bibechana-19674	83	8	,	,	PUNCT
bibechana-19674	83	9	(	(	PUNCT
bibechana-19674	83	10	21	21	NUM
bibechana-19674	83	11	vxvxgvxs	vxvxgvxs	NOUN
bibechana-19674	83	12	ηηλλ	ηηλλ	NOUN
bibechana-19674	83	13	+	+	NOUN
bibechana-19674	83	14	=	=	X
bibechana-19674	83	15	(	(	PUNCT
bibechana-19674	83	16	3.7	3.7	NUM
bibechana-19674	83	17	)	)	PUNCT
bibechana-19674	83	18	where	where	SCONJ
bibechana-19674	83	19	nk21	nk21	PROPN
bibechana-19674	83	20	=	=	PROPN
bibechana-19674	83	21	λ	λ	PROPN
bibechana-19674	83	22	and	and	CCONJ
bibechana-19674	83	23	.)12(2	.)12(2	PROPN
bibechana-19674	84	1	knn	knn	PROPN
bibechana-19674	85	1	−−=λ	−−=λ	PROPN
bibechana-19674	85	2	in	in	ADP
bibechana-19674	85	3	view	view	NOUN
bibechana-19674	85	4	of	of	ADP
bibechana-19674	85	5	(	(	PUNCT
bibechana-19674	85	6	2.34	2.34	NUM
bibechana-19674	85	7	)	)	PUNCT
bibechana-19674	85	8	and	and	CCONJ
bibechana-19674	85	9	(	(	PUNCT
bibechana-19674	85	10	3.7	3.7	NUM
bibechana-19674	85	11	)	)	PUNCT
bibechana-19674	85	12	we	we	PRON
bibechana-19674	85	13	conclude	conclude	VERB
bibechana-19674	85	14	that	that	PRON
bibechana-19674	85	15	)	)	PUNCT
bibechana-19674	86	1	(	(	PUNCT
bibechana-19674	86	2	kn	kn	NOUN
bibechana-19674	86	3	-contact	-contact	PROPN
bibechana-19674	86	4	metric	metric	ADJ
bibechana-19674	86	5	manifold	manifold	ADJ
bibechana-19674	86	6	12	12	NUM
bibechana-19674	86	7	+	+	NOUN
bibechana-19674	86	8	nm	nm	ADJ
bibechana-19674	86	9	is	be	AUX
bibechana-19674	86	10	η	η	PROPN
bibechana-19674	86	11	-einstein	-einstein	PROPN
bibechana-19674	86	12	manifold	manifold	ADJ
bibechana-19674	86	13	.	.	PUNCT
bibechana-19674	87	1	this	this	PRON
bibechana-19674	87	2	completes	complete	VERB
bibechana-19674	87	3	the	the	DET
bibechana-19674	87	4	proof	proof	NOUN
bibechana-19674	87	5	of	of	ADP
bibechana-19674	87	6	the	the	DET
bibechana-19674	87	7	theorem	theorem	PROPN
bibechana-19674	87	8	.	.	PUNCT
bibechana-19674	87	9	theorem	theorem	PROPN
bibechana-19674	87	10	3.2	3.2	NUM
bibechana-19674	87	11	.	.	PUNCT
bibechana-19674	88	1	in	in	ADP
bibechana-19674	88	2	a	a	DET
bibechana-19674	88	3	ϕ	ϕ	NOUN
bibechana-19674	88	4	9w	9w	NOUN
bibechana-19674	88	5	flat	flat	ADJ
bibechana-19674	88	6	)	)	PUNCT
bibechana-19674	88	7	(	(	PUNCT
bibechana-19674	88	8	kn	kn	NOUN
bibechana-19674	88	9	-contact	-contact	PROPN
bibechana-19674	88	10	metric	metric	ADJ
bibechana-19674	88	11	manifold	manifold	ADJ
bibechana-19674	88	12	12	12	NUM
bibechana-19674	88	13	+	+	NOUN
bibechana-19674	88	14	nm	nm	VERB
bibechana-19674	88	15	the	the	DET
bibechana-19674	88	16	ricci	ricci	PROPN
bibechana-19674	88	17	tensor	tensor	NOUN
bibechana-19674	88	18	s	s	PROPN
bibechana-19674	88	19	and	and	CCONJ
bibechana-19674	88	20	the	the	DET
bibechana-19674	88	21	scalar	scalar	ADJ
bibechana-19674	88	22	curvature	curvature	NOUN
bibechana-19674	88	23	r	r	NOUN
bibechana-19674	88	24	are	be	AUX
bibechana-19674	88	25	given	give	VERB
bibechana-19674	88	26	by	by	ADP
bibechana-19674	88	27	)	)	PUNCT
bibechana-19674	88	28	,	,	PUNCT
bibechana-19674	88	29	(	(	PUNCT
bibechana-19674	88	30	)	)	PUNCT
bibechana-19674	88	31	1(4)()(})12(2{),()4	1(4)()(})12(2{),()4	NUM
bibechana-19674	88	32	(	(	PUNCT
bibechana-19674	88	33	)	)	PUNCT
bibechana-19674	88	34	,	,	PUNCT
bibechana-19674	88	35	(	(	PUNCT
bibechana-19674	88	36	2	2	NUM
bibechana-19674	88	37	zhygnzyrknnzygknrzys	zhygnzyrknnzygknrzys	NOUN
bibechana-19674	88	38	−+−++−=	−+−++−=	PROPN
bibechana-19674	88	39	ηη	ηη	PROPN
bibechana-19674	88	40	riddhi	riddhi	PROPN
bibechana-19674	88	41	jung	jung	PROPN
bibechana-19674	88	42	shah./	shah./	PROPN
bibechana-19674	88	43	bibechana	bibechana	PROPN
bibechana-19674	88	44	16	16	NUM
bibechana-19674	88	45	(	(	PUNCT
bibechana-19674	88	46	2019	2019	NUM
bibechana-19674	88	47	)	)	PUNCT
bibechana-19674	88	48	55	55	NUM
bibechana-19674	88	49	-	-	SYM
bibechana-19674	88	50	63	63	NUM
bibechana-19674	88	51	:	:	PUNCT
bibechana-19674	88	52	rcost	rcost	NOUN
bibechana-19674	88	53	p.60	p.60	PROPN
bibechana-19674	88	54	(	(	PUNCT
bibechana-19674	88	55	online	online	ADJ
bibechana-19674	88	56	publication	publication	NOUN
bibechana-19674	88	57	:	:	PUNCT
bibechana-19674	89	1	dec	dec	PROPN
bibechana-19674	89	2	.	.	PROPN
bibechana-19674	89	3	,	,	PUNCT
bibechana-19674	89	4	2018	2018	NUM
bibechana-19674	89	5	)	)	PUNCT
bibechana-19674	89	6	and	and	CCONJ
bibechana-19674	89	7	knnr	knnr	NOUN
bibechana-19674	89	8	)	)	PUNCT
bibechana-19674	89	9	12(2	12(2	NOUN
bibechana-19674	90	1	+	+	PUNCT
bibechana-19674	90	2	=	=	SYM
bibechana-19674	90	3	respectively	respectively	ADV
bibechana-19674	90	4	.	.	PUNCT
bibechana-19674	91	1	proof	proof	NOUN
bibechana-19674	91	2	.	.	PUNCT
bibechana-19674	92	1	let	let	VERB
bibechana-19674	92	2	us	we	PRON
bibechana-19674	92	3	consider	consider	VERB
bibechana-19674	92	4	a	a	PRON
bibechana-19674	92	5	)	)	PUNCT
bibechana-19674	92	6	12	12	NUM
bibechana-19674	92	7	(	(	PUNCT
bibechana-19674	92	8	+	+	NOUN
bibechana-19674	92	9	n	n	CCONJ
bibechana-19674	92	10	-dimensional	-dimensional	ADJ
bibechana-19674	92	11	)	)	PUNCT
bibechana-19674	92	12	(	(	PUNCT
bibechana-19674	92	13	kn	kn	NOUN
bibechana-19674	92	14	-contact	-contact	PROPN
bibechana-19674	92	15	metric	metric	ADJ
bibechana-19674	92	16	manifold	manifold	NOUN
bibechana-19674	92	17	m	m	VERB
bibechana-19674	92	18	which	which	PRON
bibechana-19674	92	19	is	be	AUX
bibechana-19674	92	20	ϕ	ϕ	NOUN
bibechana-19674	92	21	9wflat	9wflat	NUM
bibechana-19674	92	22	.	.	PUNCT
bibechana-19674	93	1	then	then	ADV
bibechana-19674	93	2	we	we	PRON
bibechana-19674	93	3	have	have	VERB
bibechana-19674	93	4	(	(	PUNCT
bibechana-19674	93	5	)	)	PUNCT
bibechana-19674	93	6	0,),(9	0,),(9	NOUN
bibechana-19674	94	1	=	=	NOUN
bibechana-19674	94	2	wzyxwg	wzyxwg	VERB
bibechana-19674	94	3	ϕϕϕϕ	ϕϕϕϕ	NOUN
bibechana-19674	94	4	(	(	PUNCT
bibechana-19674	94	5	3.8	3.8	NUM
bibechana-19674	94	6	)	)	PUNCT
bibechana-19674	94	7	for	for	ADP
bibechana-19674	94	8	any	any	DET
bibechana-19674	94	9	vector	vector	NOUN
bibechana-19674	94	10	fields	field	NOUN
bibechana-19674	94	11	)	)	PUNCT
bibechana-19674	94	12	.	.	PUNCT
bibechana-19674	95	1	(	(	PUNCT
bibechana-19674	95	2	,	,	PUNCT
bibechana-19674	95	3	,	,	PUNCT
bibechana-19674	95	4	,	,	PUNCT
bibechana-19674	95	5	mtwzyx	mtwzyx	ADJ
bibechana-19674	95	6	p∈	p∈	PROPN
bibechana-19674	95	7	in	in	ADP
bibechana-19674	95	8	view	view	NOUN
bibechana-19674	95	9	of	of	ADP
bibechana-19674	95	10	(	(	PUNCT
bibechana-19674	95	11	2.27	2.27	NUM
bibechana-19674	95	12	)	)	PUNCT
bibechana-19674	95	13	we	we	PRON
bibechana-19674	95	14	have	have	VERB
bibechana-19674	95	15	(	(	PUNCT
bibechana-19674	95	16	)	)	PUNCT
bibechana-19674	95	17	(	(	PUNCT
bibechana-19674	95	18	)	)	PUNCT
bibechana-19674	95	19	)	)	PUNCT
bibechana-19674	95	20	]	]	PUNCT
bibechana-19674	95	21	.	.	PUNCT
bibechana-19674	95	22	,	,	PUNCT
bibechana-19674	95	23	(	(	PUNCT
bibechana-19674	95	24	)	)	PUNCT
bibechana-19674	95	25	,	,	PUNCT
bibechana-19674	95	26	(	(	PUNCT
bibechana-19674	95	27	)	)	PUNCT
bibechana-19674	95	28	,	,	PUNCT
bibechana-19674	95	29	(	(	PUNCT
bibechana-19674	95	30	)	)	PUNCT
bibechana-19674	95	31	,	,	PUNCT
bibechana-19674	95	32	(	(	PUNCT
bibechana-19674	95	33	[	[	X
bibechana-19674	95	34	21,),(,),(9	21,),(,),(9	NUM
bibechana-19674	95	35	zygwxs	zygwxs	NOUN
bibechana-19674	95	36	wzgyxsnwzyxrgwzyxwg	wzgyxsnwzyxrgwzyxwg	VERB
bibechana-19674	95	37	ϕϕϕϕ	ϕϕϕϕ	PROPN
bibechana-19674	95	38	ϕϕϕϕϕϕϕϕϕϕϕϕ	ϕϕϕϕϕϕϕϕϕϕϕϕ	PROPN
bibechana-19674	95	39	−	−	PROPN
bibechana-19674	96	1	+	+	NOUN
bibechana-19674	96	2	=	=	X
bibechana-19674	96	3	(	(	PUNCT
bibechana-19674	96	4	3.9	3.9	NUM
bibechana-19674	96	5	)	)	PUNCT
bibechana-19674	96	6	using	use	VERB
bibechana-19674	96	7	(	(	PUNCT
bibechana-19674	96	8	2.3	2.3	NUM
bibechana-19674	96	9	)	)	PUNCT
bibechana-19674	96	10	,	,	PUNCT
bibechana-19674	96	11	(	(	PUNCT
bibechana-19674	96	12	2.14	2.14	NUM
bibechana-19674	96	13	)	)	PUNCT
bibechana-19674	96	14	,	,	PUNCT
bibechana-19674	96	15	(	(	PUNCT
bibechana-19674	96	16	2.22	2.22	NUM
bibechana-19674	96	17	)	)	PUNCT
bibechana-19674	96	18	and	and	CCONJ
bibechana-19674	96	19	(	(	PUNCT
bibechana-19674	96	20	3.8	3.8	NUM
bibechana-19674	96	21	)	)	PUNCT
bibechana-19674	96	22	in	in	ADP
bibechana-19674	96	23	(	(	PUNCT
bibechana-19674	96	24	3.9	3.9	NUM
bibechana-19674	96	25	)	)	PUNCT
bibechana-19674	96	26	we	we	PRON
bibechana-19674	96	27	obtain	obtain	VERB
bibechana-19674	96	28	)	)	PUNCT
bibechana-19674	96	29	}	}	PUNCT
bibechana-19674	96	30	]	]	PUNCT
bibechana-19674	96	31	(	(	PUNCT
bibechana-19674	96	32	)	)	PUNCT
bibechana-19674	96	33	(	(	PUNCT
bibechana-19674	96	34	)	)	PUNCT
bibechana-19674	96	35	,	,	PUNCT
bibechana-19674	96	36	(	(	PUNCT
bibechana-19674	96	37	)	)	PUNCT
bibechana-19674	96	38	}	}	PUNCT
bibechana-19674	96	39	{	{	PUNCT
bibechana-19674	96	40	,	,	PUNCT
bibechana-19674	96	41	(	(	PUNCT
bibechana-19674	96	42	)	)	PUNCT
bibechana-19674	96	43	1(4)()(2	1(4)()(2	NUM
bibechana-19674	96	44	)	)	PUNCT
bibechana-19674	96	45	,	,	PUNCT
bibechana-19674	96	46	(	(	PUNCT
bibechana-19674	96	47	{	{	PUNCT
bibechana-19674	96	48	)	)	PUNCT
bibechana-19674	96	49	}	}	PUNCT
bibechana-19674	96	50	(	(	PUNCT
bibechana-19674	96	51	)	)	PUNCT
bibechana-19674	96	52	(	(	PUNCT
bibechana-19674	96	53	)	)	PUNCT
bibechana-19674	96	54	,	,	PUNCT
bibechana-19674	96	55	(	(	PUNCT
bibechana-19674	96	56	)	)	PUNCT
bibechana-19674	96	57	}	}	PUNCT
bibechana-19674	96	58	{	{	PUNCT
bibechana-19674	96	59	,	,	PUNCT
bibechana-19674	96	60	(	(	PUNCT
bibechana-19674	96	61	)	)	PUNCT
bibechana-19674	96	62	1(4)()(2),([{21	1(4)()(2),([{21	NUM
bibechana-19674	96	63	)	)	PUNCT
bibechana-19674	96	64	,	,	PUNCT
bibechana-19674	96	65	(	(	PUNCT
bibechana-19674	96	66	)	)	PUNCT
bibechana-19674	96	67	,	,	PUNCT
bibechana-19674	96	68	(	(	PUNCT
bibechana-19674	96	69	)	)	PUNCT
bibechana-19674	96	70	,	,	PUNCT
bibechana-19674	96	71	(	(	PUNCT
bibechana-19674	96	72	)	)	PUNCT
bibechana-19674	96	73	,	,	PUNCT
bibechana-19674	96	74	(	(	PUNCT
bibechana-19674	96	75	0	0	NUM
bibechana-19674	96	76	zyzygwhxgnwxnkwxs	zyzygwhxgnwxnkwxs	PROPN
bibechana-19674	96	77	zwzwgyhxgnyxnkyxsn	zwzwgyhxgnyxnkyxsn	PROPN
bibechana-19674	96	78	wygzxkgwxgzykg	wygzxkgwxgzykg	PROPN
bibechana-19674	96	79	ηηηη	ηηηη	PROPN
bibechana-19674	96	80	ηηηη	ηηηη	PROPN
bibechana-19674	96	81	ϕϕϕϕϕϕϕϕ	ϕϕϕϕϕϕϕϕ	PROPN
bibechana-19674	96	82	−−−−−	−−−−−	X
bibechana-19674	96	83	−−−−+	−−−−+	ADP
bibechana-19674	96	84	−=	−=	VERB
bibechana-19674	96	85	)	)	PUNCT
bibechana-19674	96	86	,	,	PUNCT
bibechana-19674	96	87	(	(	PUNCT
bibechana-19674	96	88	)	)	PUNCT
bibechana-19674	96	89	,	,	PUNCT
bibechana-19674	96	90	(	(	PUNCT
bibechana-19674	96	91	)	)	PUNCT
bibechana-19674	96	92	1(2),(),(21	1(2),(),(21	NUM
bibechana-19674	96	93	)	)	PUNCT
bibechana-19674	96	94	(	(	PUNCT
bibechana-19674	96	95	)	)	PUNCT
bibechana-19674	96	96	(	(	PUNCT
bibechana-19674	96	97	)	)	PUNCT
bibechana-19674	96	98	,	,	PUNCT
bibechana-19674	96	99	(	(	PUNCT
bibechana-19674	96	100	)	)	PUNCT
bibechana-19674	96	101	1(2)()(),(21	1(2)()(),(21	NUM
bibechana-19674	96	102	)	)	PUNCT
bibechana-19674	96	103	,	,	PUNCT
bibechana-19674	96	104	(	(	PUNCT
bibechana-19674	96	105	)	)	PUNCT
bibechana-19674	96	106	,	,	PUNCT
bibechana-19674	96	107	(	(	PUNCT
bibechana-19674	96	108	)	)	PUNCT
bibechana-19674	96	109	1(2	1(2	NUM
bibechana-19674	96	110	)	)	PUNCT
bibechana-19674	96	111	(	(	PUNCT
bibechana-19674	96	112	)	)	PUNCT
bibechana-19674	96	113	(	(	PUNCT
bibechana-19674	96	114	)	)	PUNCT
bibechana-19674	96	115	,	,	PUNCT
bibechana-19674	96	116	(	(	PUNCT
bibechana-19674	96	117	)	)	PUNCT
bibechana-19674	96	118	,	,	PUNCT
bibechana-19674	96	119	(	(	PUNCT
bibechana-19674	96	120	)	)	PUNCT
bibechana-19674	96	121	,	,	PUNCT
bibechana-19674	96	122	(	(	PUNCT
bibechana-19674	96	123	21	21	NUM
bibechana-19674	96	124	)	)	PUNCT
bibechana-19674	96	125	(	(	PUNCT
bibechana-19674	96	126	)	)	PUNCT
bibechana-19674	96	127	(	(	PUNCT
bibechana-19674	96	128	)	)	PUNCT
bibechana-19674	96	129	,	,	PUNCT
bibechana-19674	96	130	(	(	PUNCT
bibechana-19674	96	131	)	)	PUNCT
bibechana-19674	96	132	(	(	PUNCT
bibechana-19674	96	133	)	)	PUNCT
bibechana-19674	96	134	(	(	PUNCT
bibechana-19674	96	135	)	)	PUNCT
bibechana-19674	96	136	,	,	PUNCT
bibechana-19674	96	137	(	(	PUNCT
bibechana-19674	96	138	)	)	PUNCT
bibechana-19674	96	139	,	,	PUNCT
bibechana-19674	96	140	(	(	PUNCT
bibechana-19674	96	141	)	)	PUNCT
bibechana-19674	96	142	,	,	PUNCT
bibechana-19674	96	143	(	(	PUNCT
bibechana-19674	96	144	)	)	PUNCT
bibechana-19674	96	145	(	(	PUNCT
bibechana-19674	96	146	)	)	PUNCT
bibechana-19674	96	147	(	(	PUNCT
bibechana-19674	96	148	)	)	PUNCT
bibechana-19674	96	149	,	,	PUNCT
bibechana-19674	96	150	(	(	PUNCT
bibechana-19674	96	151	)	)	PUNCT
bibechana-19674	96	152	,	,	PUNCT
bibechana-19674	96	153	(	(	PUNCT
bibechana-19674	96	154	)	)	PUNCT
bibechana-19674	96	155	,	,	PUNCT
bibechana-19674	96	156	(	(	PUNCT
bibechana-19674	96	157	0	0	NUM
bibechana-19674	96	158	or	or	CCONJ
bibechana-19674	96	159	,	,	PUNCT
bibechana-19674	96	160	whxgzygnnzygwxsn	whxgzygnnzygwxsn	VERB
bibechana-19674	96	161	zwyhxgnnzwyxsn	zwyhxgnnzwyxsn	PROPN
bibechana-19674	96	162	yhxgzwgnnyxzwkg	yhxgzwgnnyxzwkg	PROPN
bibechana-19674	96	163	zwgyxsnwyzxkgzxwykg	zwgyxsnwyzxkgzxwykg	PROPN
bibechana-19674	96	164	wygzxkgzywxkgwxgzykg	wygzxkgzywxkgwxgzykg	PROPN
bibechana-19674	96	165	−	−	PROPN
bibechana-19674	97	1	+	+	NOUN
bibechana-19674	97	2	−	−	NOUN
bibechana-19674	97	3	−	−	PROPN
bibechana-19674	98	1	+	+	NOUN
bibechana-19674	98	2	−	−	NOUN
bibechana-19674	98	3	−	−	PROPN
bibechana-19674	98	4	−−	−−	NOUN
bibechana-19674	98	5	+	+	NOUN
bibechana-19674	98	6	+	+	ADJ
bibechana-19674	98	7	+	+	ADJ
bibechana-19674	98	8	−−=	−−=	PROPN
bibechana-19674	98	9	ηηηη	ηηηη	NOUN
bibechana-19674	98	10	ηη	ηη	ADP
bibechana-19674	98	11	ηηηη	ηηηη	VERB
bibechana-19674	98	12	ηη	ηη	PROPN
bibechana-19674	98	13	(	(	PUNCT
bibechana-19674	98	14	3.10	3.10	NUM
bibechana-19674	98	15	)	)	PUNCT
bibechana-19674	98	16	)	)	PUNCT
bibechana-19674	99	1	.()(),()1(2)()(),(21	.()(),()1(2)()(),(21	PROPN
bibechana-19674	99	2	zywhxgnnzywxsn	zywhxgnnzywxsn	VERB
bibechana-19674	99	3	ηηηη	ηηηη	PROPN
bibechana-19674	100	1	−	−	PROPN
bibechana-19674	100	2	−+	−+	PROPN
bibechana-19674	100	3	let	let	VERB
bibechana-19674	100	4	12,	12,	NUM
bibechana-19674	100	5	...	...	PUNCT
bibechana-19674	100	6	,2,1	,2,1	PROPN
bibechana-19674	100	7	}	}	PUNCT
bibechana-19674	100	8	,	,	PUNCT
bibechana-19674	100	9	{	{	PUNCT
bibechana-19674	100	10	+	+	NOUN
bibechana-19674	100	11	=	=	NOUN
bibechana-19674	100	12	niei	niei	PROPN
bibechana-19674	100	13	be	be	VERB
bibechana-19674	100	14	an	an	DET
bibechana-19674	100	15	orthonormal	orthonormal	ADJ
bibechana-19674	100	16	basis	basis	NOUN
bibechana-19674	100	17	of	of	ADP
bibechana-19674	100	18	the	the	DET
bibechana-19674	100	19	tangent	tangent	ADJ
bibechana-19674	100	20	space	space	NOUN
bibechana-19674	100	21	at	at	ADP
bibechana-19674	100	22	any	any	DET
bibechana-19674	100	23	point	point	NOUN
bibechana-19674	100	24	of	of	ADP
bibechana-19674	100	25	the	the	DET
bibechana-19674	100	26	manifold	manifold	NOUN
bibechana-19674	100	27	.	.	PUNCT
bibechana-19674	101	1	putting	put	VERB
bibechana-19674	101	2	iewx	iewx	NOUN
bibechana-19674	101	3	=	=	NOUN
bibechana-19674	101	4	=	=	SYM
bibechana-19674	101	5	in	in	ADP
bibechana-19674	101	6	(	(	PUNCT
bibechana-19674	101	7	3.10	3.10	NUM
bibechana-19674	101	8	)	)	PUNCT
bibechana-19674	101	9	and	and	CCONJ
bibechana-19674	101	10	taking	take	VERB
bibechana-19674	101	11	summation	summation	NOUN
bibechana-19674	101	12	over	over	ADP
bibechana-19674	101	13	,	,	PUNCT
bibechana-19674	101	14	121	121	NUM
bibechana-19674	101	15	,	,	PUNCT
bibechana-19674	101	16	+	+	ADP
bibechana-19674	101	17	≤≤	≤≤	X
bibechana-19674	101	18	nii	nii	NOUN
bibechana-19674	101	19	we	we	PRON
bibechana-19674	101	20	get	get	VERB
bibechana-19674	101	21	)	)	PUNCT
bibechana-19674	101	22	,	,	PUNCT
bibechana-19674	101	23	(	(	PUNCT
bibechana-19674	101	24	)	)	PUNCT
bibechana-19674	101	25	1(4)()(})12(2{),()4	1(4)()(})12(2{),()4	NUM
bibechana-19674	101	26	(	(	PUNCT
bibechana-19674	101	27	)	)	PUNCT
bibechana-19674	101	28	,	,	PUNCT
bibechana-19674	101	29	(	(	PUNCT
bibechana-19674	101	30	2	2	NUM
bibechana-19674	101	31	zhygnzyrknnzygknrzys	zhygnzyrknnzygknrzys	NOUN
bibechana-19674	101	32	−+−++−=	−+−++−=	NOUN
bibechana-19674	101	33	ηη	ηη	X
bibechana-19674	101	34	(	(	PUNCT
bibechana-19674	101	35	3.11	3.11	NUM
bibechana-19674	101	36	)	)	PUNCT
bibechana-19674	101	37	by	by	ADP
bibechana-19674	101	38	the	the	DET
bibechana-19674	101	39	use	use	NOUN
bibechana-19674	101	40	of	of	ADP
bibechana-19674	101	41	(	(	PUNCT
bibechana-19674	101	42	2.5	2.5	NUM
bibechana-19674	101	43	)	)	PUNCT
bibechana-19674	101	44	and	and	CCONJ
bibechana-19674	101	45	symmetry	symmetry	NOUN
bibechana-19674	101	46	property	property	NOUN
bibechana-19674	101	47	of	of	ADP
bibechana-19674	101	48	.h	.h	NOUN
bibechana-19674	101	49	again	again	ADV
bibechana-19674	101	50	,	,	PUNCT
bibechana-19674	101	51	taking	take	VERB
bibechana-19674	101	52	an	an	DET
bibechana-19674	101	53	orthonormal	orthonormal	ADJ
bibechana-19674	101	54	frame	frame	NOUN
bibechana-19674	101	55	field	field	NOUN
bibechana-19674	101	56	at	at	ADP
bibechana-19674	101	57	any	any	DET
bibechana-19674	101	58	point	point	NOUN
bibechana-19674	101	59	of	of	ADP
bibechana-19674	101	60	the	the	DET
bibechana-19674	101	61	manifold	manifold	ADJ
bibechana-19674	101	62	and	and	CCONJ
bibechana-19674	101	63	contracting	contracting	NOUN
bibechana-19674	101	64	over	over	ADP
bibechana-19674	101	65	y	y	PROPN
bibechana-19674	101	66	and	and	CCONJ
bibechana-19674	101	67	z	z	PROPN
bibechana-19674	101	68	in	in	SCONJ
bibechana-19674	101	69	(	(	PUNCT
bibechana-19674	101	70	3.11	3.11	NUM
bibechana-19674	101	71	)	)	PUNCT
bibechana-19674	101	72	we	we	PRON
bibechana-19674	101	73	obtain	obtain	VERB
bibechana-19674	101	74	.)12(2	.)12(2	PUNCT
bibechana-19674	102	1	knnr	knnr	NOUN
bibechana-19674	102	2	+	+	PROPN
bibechana-19674	102	3	=	=	SYM
bibechana-19674	102	4	(	(	PUNCT
bibechana-19674	102	5	3.12	3.12	NUM
bibechana-19674	102	6	)	)	PUNCT
bibechana-19674	102	7	in	in	ADP
bibechana-19674	102	8	view	view	NOUN
bibechana-19674	102	9	of	of	ADP
bibechana-19674	102	10	(	(	PUNCT
bibechana-19674	102	11	3.11	3.11	NUM
bibechana-19674	102	12	)	)	PUNCT
bibechana-19674	102	13	and	and	CCONJ
bibechana-19674	102	14	(	(	PUNCT
bibechana-19674	102	15	3.12	3.12	NUM
bibechana-19674	102	16	)	)	PUNCT
bibechana-19674	102	17	,	,	PUNCT
bibechana-19674	102	18	the	the	DET
bibechana-19674	102	19	theorem	theorem	NOUN
bibechana-19674	102	20	is	be	AUX
bibechana-19674	102	21	proved	prove	VERB
bibechana-19674	102	22	.	.	PUNCT
bibechana-19674	103	1	theorem	theorem	VERB
bibechana-19674	103	2	3.3	3.3	NUM
bibechana-19674	103	3	.	.	PUNCT
bibechana-19674	104	1	if	if	SCONJ
bibechana-19674	104	2	a	a	DET
bibechana-19674	104	3	)	)	PUNCT
bibechana-19674	104	4	12	12	NUM
bibechana-19674	104	5	(	(	PUNCT
bibechana-19674	104	6	+	+	NOUN
bibechana-19674	104	7	n	n	CCONJ
bibechana-19674	104	8	-dimensional	-dimensional	ADJ
bibechana-19674	104	9	)	)	PUNCT
bibechana-19674	104	10	(	(	PUNCT
bibechana-19674	104	11	kn	kn	NOUN
bibechana-19674	104	12	-contact	-contact	PROPN
bibechana-19674	104	13	metric	metric	ADJ
bibechana-19674	104	14	manifold	manifold	NOUN
bibechana-19674	104	15	m	m	VERB
bibechana-19674	104	16	satisfies	satisfy	VERB
bibechana-19674	104	17	the	the	DET
bibechana-19674	104	18	condition	condition	NOUN
bibechana-19674	104	19	,	,	PUNCT
bibechana-19674	104	20	09	09	NUM
bibechana-19674	104	21	=	=	NUM
bibechana-19674	104	22	divw	divw	NOUN
bibechana-19674	104	23	then	then	ADV
bibechana-19674	104	24	the	the	DET
bibechana-19674	104	25	ricci	ricci	PROPN
bibechana-19674	104	26	tensor	tensor	NOUN
bibechana-19674	104	27	s	s	NOUN
bibechana-19674	104	28	is	be	AUX
bibechana-19674	104	29	of	of	ADP
bibechana-19674	104	30	the	the	DET
bibechana-19674	104	31	form	form	NOUN
bibechana-19674	104	32	)	)	PUNCT
bibechana-19674	104	33	.,(),(12	.,(),(12	PUNCT
bibechana-19674	104	34	)	)	PUNCT
bibechana-19674	104	35	12(2),(2	12(2),(2	PROPN
bibechana-19674	104	36	)	)	PUNCT
bibechana-19674	104	37	,	,	PUNCT
bibechana-19674	104	38	(	(	PUNCT
bibechana-19674	104	39	yhzshzygn	yhzshzygn	PROPN
bibechana-19674	104	40	knnzynkgzys	knnzynkgzys	X
bibechana-19674	105	1	+	+	X
bibechana-19674	106	1	+	+	CCONJ
bibechana-19674	107	1	−	−	X
bibechana-19674	107	2	+	+	ADJ
bibechana-19674	107	3	=	=	NOUN
bibechana-19674	107	4	proof	proof	NOUN
bibechana-19674	107	5	.	.	PUNCT
bibechana-19674	108	1	let	let	VERB
bibechana-19674	108	2	us	we	PRON
bibechana-19674	108	3	consider	consider	VERB
bibechana-19674	108	4	a	a	PRON
bibechana-19674	108	5	)	)	PUNCT
bibechana-19674	108	6	12	12	NUM
bibechana-19674	108	7	(	(	PUNCT
bibechana-19674	108	8	+	+	NOUN
bibechana-19674	108	9	n	n	CCONJ
bibechana-19674	108	10	-dimensional	-dimensional	ADJ
bibechana-19674	108	11	)	)	PUNCT
bibechana-19674	108	12	(	(	PUNCT
bibechana-19674	108	13	kn	kn	NOUN
bibechana-19674	108	14	-contact	-contact	PROPN
bibechana-19674	108	15	metric	metric	ADJ
bibechana-19674	108	16	manifold	manifold	NOUN
bibechana-19674	108	17	m	m	VERB
bibechana-19674	108	18	which	which	PRON
bibechana-19674	108	19	satisfies	satisfy	VERB
bibechana-19674	108	20	the	the	DET
bibechana-19674	108	21	condition	condition	NOUN
bibechana-19674	108	22	0	0	NUM
bibechana-19674	108	23	)	)	PUNCT
bibechana-19674	108	24	,	,	PUNCT
bibechana-19674	108	25	)	)	PUNCT
bibechana-19674	108	26	(	(	PUNCT
bibechana-19674	108	27	(	(	PUNCT
bibechana-19674	108	28	9	9	NUM
bibechana-19674	108	29	=	=	PROPN
bibechana-19674	108	30	zyxdivw	zyxdivw	X
bibechana-19674	108	31	(	(	PUNCT
bibechana-19674	108	32	3.13	3.13	NUM
bibechana-19674	108	33	)	)	PUNCT
bibechana-19674	108	34	where	where	SCONJ
bibechana-19674	108	35	'	'	PUNCT
bibechana-19674	108	36	div	div	PROPN
bibechana-19674	108	37	'	'	PART
bibechana-19674	108	38	denotes	denote	NOUN
bibechana-19674	108	39	the	the	DET
bibechana-19674	108	40	divergence	divergence	NOUN
bibechana-19674	108	41	.	.	PUNCT
bibechana-19674	109	1	taking	take	VERB
bibechana-19674	109	2	inner	inner	ADJ
bibechana-19674	109	3	product	product	NOUN
bibechana-19674	109	4	on	on	ADP
bibechana-19674	109	5	both	both	DET
bibechana-19674	109	6	sides	side	NOUN
bibechana-19674	109	7	of	of	ADP
bibechana-19674	109	8	(	(	PUNCT
bibechana-19674	109	9	2.27	2.27	NUM
bibechana-19674	109	10	)	)	PUNCT
bibechana-19674	109	11	with	with	ADP
bibechana-19674	109	12	v	v	NOUN
bibechana-19674	109	13	we	we	PRON
bibechana-19674	109	14	get	get	VERB
bibechana-19674	109	15	riddhi	riddhi	ADJ
bibechana-19674	109	16	jung	jung	PROPN
bibechana-19674	109	17	shah./	shah./	PROPN
bibechana-19674	109	18	bibechana	bibechana	PROPN
bibechana-19674	109	19	16	16	NUM
bibechana-19674	109	20	(	(	PUNCT
bibechana-19674	109	21	2019	2019	NUM
bibechana-19674	109	22	)	)	PUNCT
bibechana-19674	109	23	55	55	NUM
bibechana-19674	109	24	-	-	SYM
bibechana-19674	109	25	63	63	NUM
bibechana-19674	109	26	:	:	PUNCT
bibechana-19674	109	27	rcost	rcost	NOUN
bibechana-19674	109	28	p.61	p.61	NOUN
bibechana-19674	109	29	(	(	PUNCT
bibechana-19674	109	30	online	online	ADJ
bibechana-19674	109	31	publication	publication	NOUN
bibechana-19674	109	32	:	:	PUNCT
bibechana-19674	109	33	dec	dec	PROPN
bibechana-19674	109	34	.	.	PROPN
bibechana-19674	109	35	,	,	PUNCT
bibechana-19674	109	36	2018	2018	NUM
bibechana-19674	109	37	)	)	PUNCT
bibechana-19674	109	38	(	(	PUNCT
bibechana-19674	109	39	)	)	PUNCT
bibechana-19674	109	40	(	(	PUNCT
bibechana-19674	109	41	)	)	PUNCT
bibechana-19674	109	42	)	)	PUNCT
bibechana-19674	110	1	]	]	PUNCT
bibechana-19674	110	2	.,(),(),(),([21,),(,),(9	.,(),(),(),([21,),(,),(9	PRON
bibechana-19674	110	3	zygvxsvzgyxsnvzyxrgvzyxwg	zygvxsvzgyxsnvzyxrgvzyxwg	NOUN
bibechana-19674	110	4	−+=	−+=	X
bibechana-19674	110	5	(	(	PUNCT
bibechana-19674	110	6	3.14	3.14	NUM
bibechana-19674	110	7	)	)	PUNCT
bibechana-19674	110	8	differentiating	differentiating	NOUN
bibechana-19674	110	9	(	(	PUNCT
bibechana-19674	110	10	3.14	3.14	NUM
bibechana-19674	110	11	)	)	PUNCT
bibechana-19674	110	12	covariantly	covariantly	ADV
bibechana-19674	110	13	along	along	ADP
bibechana-19674	110	14	u	u	NOUN
bibechana-19674	110	15	we	we	PRON
bibechana-19674	110	16	have	have	VERB
bibechana-19674	110	17	)	)	PUNCT
bibechana-19674	110	18	]	]	PUNCT
bibechana-19674	110	19	,	,	PUNCT
bibechana-19674	110	20	(	(	PUNCT
bibechana-19674	110	21	)	)	PUNCT
bibechana-19674	110	22	,	,	PUNCT
bibechana-19674	110	23	)	)	PUNCT
bibechana-19674	110	24	(	(	PUNCT
bibechana-19674	110	25	(	(	PUNCT
bibechana-19674	110	26	)	)	PUNCT
bibechana-19674	110	27	,	,	PUNCT
bibechana-19674	110	28	(	(	PUNCT
bibechana-19674	110	29	)	)	PUNCT
bibechana-19674	110	30	,	,	PUNCT
bibechana-19674	110	31	)	)	PUNCT
bibechana-19674	110	32	(	(	PUNCT
bibechana-19674	110	33	[	[	X
bibechana-19674	110	34	(	(	PUNCT
bibechana-19674	110	35	21),,,)(~	21),,,)(~	NOUN
bibechana-19674	110	36	(	(	PUNCT
bibechana-19674	110	37	)	)	PUNCT
bibechana-19674	110	38	,	,	PUNCT
bibechana-19674	110	39	,	,	PUNCT
bibechana-19674	110	40	,	,	PUNCT
bibechana-19674	110	41	)	)	PUNCT
bibechana-19674	110	42	(	(	PUNCT
bibechana-19674	110	43	~	~	X
bibechana-19674	110	44	(	(	PUNCT
bibechana-19674	110	45	9	9	NUM
bibechana-19674	110	46	zygvxsvzgyxsnvzyxr	zygvxsvzgyxsnvzyxr	PROPN
bibechana-19674	110	47	vzyxw	vzyxw	PROPN
bibechana-19674	110	48	uuuu	uuuu	PROPN
bibechana-19674	110	49	∇−∇+∇=	∇−∇+∇=	PROPN
bibechana-19674	110	50	∇	∇	X
bibechana-19674	110	51	(	(	PUNCT
bibechana-19674	110	52	3.15	3.15	NUM
bibechana-19674	110	53	)	)	PUNCT
bibechana-19674	110	54	where	where	SCONJ
bibechana-19674	110	55	)	)	PUNCT
bibechana-19674	110	56	,	,	PUNCT
bibechana-19674	110	57	,	,	PUNCT
bibechana-19674	110	58	,	,	PUNCT
bibechana-19674	110	59	(	(	PUNCT
bibechana-19674	110	60	~	~	NOUN
bibechana-19674	110	61	)	)	PUNCT
bibechana-19674	110	62	,	,	PUNCT
bibechana-19674	110	63	)	)	PUNCT
bibechana-19674	110	64	,	,	PUNCT
bibechana-19674	110	65	(	(	PUNCT
bibechana-19674	110	66	(	(	PUNCT
bibechana-19674	110	67	vzyxrvzyxrg	vzyxrvzyxrg	ADV
bibechana-19674	110	68	=	=	PUNCT
bibechana-19674	110	69	for	for	ADP
bibechana-19674	110	70	all	all	PRON
bibechana-19674	110	71	.	.	PUNCT
bibechana-19674	110	72	,	,	PUNCT
bibechana-19674	110	73	,	,	PUNCT
bibechana-19674	110	74	,	,	PUNCT
bibechana-19674	110	75	vzyx	vzyx	ADV
bibechana-19674	110	76	let	let	VERB
bibechana-19674	110	77	12,	12,	NUM
bibechana-19674	110	78	...	...	PUNCT
bibechana-19674	110	79	,2,1	,2,1	PROPN
bibechana-19674	110	80	}	}	PUNCT
bibechana-19674	110	81	,	,	PUNCT
bibechana-19674	110	82	{	{	PUNCT
bibechana-19674	110	83	+	+	NOUN
bibechana-19674	110	84	=	=	NOUN
bibechana-19674	110	85	niei	niei	PROPN
bibechana-19674	110	86	be	be	VERB
bibechana-19674	110	87	an	an	DET
bibechana-19674	110	88	orthonormal	orthonormal	ADJ
bibechana-19674	110	89	basis	basis	NOUN
bibechana-19674	110	90	of	of	ADP
bibechana-19674	110	91	the	the	DET
bibechana-19674	110	92	tangent	tangent	ADJ
bibechana-19674	110	93	space	space	NOUN
bibechana-19674	110	94	at	at	ADP
bibechana-19674	110	95	any	any	DET
bibechana-19674	110	96	point	point	NOUN
bibechana-19674	110	97	of	of	ADP
bibechana-19674	110	98	the	the	DET
bibechana-19674	110	99	manifold	manifold	NOUN
bibechana-19674	110	100	.	.	PUNCT
bibechana-19674	111	1	putting	put	VERB
bibechana-19674	111	2	ievu	ievu	NOUN
bibechana-19674	111	3	=	=	NOUN
bibechana-19674	111	4	=	=	SYM
bibechana-19674	111	5	in	in	ADP
bibechana-19674	111	6	(	(	PUNCT
bibechana-19674	111	7	3.15	3.15	NUM
bibechana-19674	111	8	)	)	PUNCT
bibechana-19674	111	9	and	and	CCONJ
bibechana-19674	111	10	taking	take	VERB
bibechana-19674	111	11	summation	summation	NOUN
bibechana-19674	111	12	over	over	ADP
bibechana-19674	111	13	,	,	PUNCT
bibechana-19674	111	14	121	121	NUM
bibechana-19674	111	15	,	,	PUNCT
bibechana-19674	111	16	+	+	ADP
bibechana-19674	111	17	≤≤	≤≤	X
bibechana-19674	111	18	nii	nii	NOUN
bibechana-19674	111	19	we	we	PRON
bibechana-19674	111	20	get	get	VERB
bibechana-19674	111	21	)	)	PUNCT
bibechana-19674	111	22	]	]	X
bibechana-19674	111	23	.,(2	.,(2	PUNCT
bibechana-19674	111	24	)	)	PUNCT
bibechana-19674	111	25	(	(	PUNCT
bibechana-19674	111	26	)	)	PUNCT
bibechana-19674	111	27	,	,	PUNCT
bibechana-19674	111	28	)	)	PUNCT
bibechana-19674	111	29	(	(	PUNCT
bibechana-19674	111	30	[	[	X
bibechana-19674	111	31	(	(	PUNCT
bibechana-19674	111	32	21	21	NUM
bibechana-19674	111	33	)	)	PUNCT
bibechana-19674	111	34	,	,	PUNCT
bibechana-19674	111	35	)	)	PUNCT
bibechana-19674	111	36	(	(	PUNCT
bibechana-19674	111	37	(	(	PUNCT
bibechana-19674	111	38	)	)	PUNCT
bibechana-19674	111	39	,	,	PUNCT
bibechana-19674	111	40	)	)	PUNCT
bibechana-19674	111	41	(	(	PUNCT
bibechana-19674	111	42	(	(	PUNCT
bibechana-19674	111	43	9	9	NUM
bibechana-19674	111	44	zygxdryxsnzyxdivrzyxdivw	zygxdryxsnzyxdivrzyxdivw	NOUN
bibechana-19674	111	45	z	z	PROPN
bibechana-19674	111	46	−∇+=	−∇+=	X
bibechana-19674	111	47	(	(	PUNCT
bibechana-19674	111	48	3.16	3.16	NUM
bibechana-19674	111	49	)	)	PUNCT
bibechana-19674	111	50	from	from	ADP
bibechana-19674	111	51	bianchi	bianchi	NOUN
bibechana-19674	111	52	second	second	ADJ
bibechana-19674	111	53	identity	identity	NOUN
bibechana-19674	111	54	we	we	PRON
bibechana-19674	111	55	also	also	ADV
bibechana-19674	111	56	know	know	VERB
bibechana-19674	111	57	that	that	PRON
bibechana-19674	111	58	)	)	PUNCT
bibechana-19674	111	59	.	.	PUNCT
bibechana-19674	111	60	,	,	PUNCT
bibechana-19674	111	61	)	)	PUNCT
bibechana-19674	111	62	(	(	PUNCT
bibechana-19674	111	63	(	(	PUNCT
bibechana-19674	111	64	)	)	PUNCT
bibechana-19674	111	65	,	,	PUNCT
bibechana-19674	111	66	)	)	PUNCT
bibechana-19674	111	67	(	(	PUNCT
bibechana-19674	111	68	(	(	PUNCT
bibechana-19674	111	69	)	)	PUNCT
bibechana-19674	111	70	,	,	PUNCT
bibechana-19674	111	71	)	)	PUNCT
bibechana-19674	111	72	(	(	PUNCT
bibechana-19674	111	73	(	(	PUNCT
bibechana-19674	111	74	zxszyszyxdivr	zxszyszyxdivr	PROPN
bibechana-19674	111	75	yx	yx	NOUN
bibechana-19674	111	76	∇−∇=	∇−∇=	PROPN
bibechana-19674	111	77	(	(	PUNCT
bibechana-19674	111	78	3.17	3.17	NUM
bibechana-19674	111	79	)	)	PUNCT
bibechana-19674	111	80	in	in	ADP
bibechana-19674	111	81	view	view	NOUN
bibechana-19674	111	82	of	of	ADP
bibechana-19674	111	83	(	(	PUNCT
bibechana-19674	111	84	3.13	3.13	NUM
bibechana-19674	111	85	)	)	PUNCT
bibechana-19674	111	86	,	,	PUNCT
bibechana-19674	111	87	(	(	PUNCT
bibechana-19674	111	88	3.16	3.16	NUM
bibechana-19674	111	89	)	)	PUNCT
bibechana-19674	111	90	and	and	CCONJ
bibechana-19674	111	91	(	(	PUNCT
bibechana-19674	111	92	3.17	3.17	NUM
bibechana-19674	111	93	)	)	PUNCT
bibechana-19674	111	94	we	we	PRON
bibechana-19674	111	95	have	have	VERB
bibechana-19674	111	96	)	)	PUNCT
bibechana-19674	111	97	.(),(41),)((21),)((),)((0	.(),(41),)((21),)((),)((0	PROPN
bibechana-19674	112	1	xdrzygnyxsnzxszys	xdrzygnyxsnzxszys	PROPN
bibechana-19674	112	2	zyx	zyx	PROPN
bibechana-19674	112	3	−∇+∇−∇=	−∇+∇−∇=	PROPN
bibechana-19674	112	4	(	(	PUNCT
bibechana-19674	112	5	3.18	3.18	NUM
bibechana-19674	112	6	)	)	PUNCT
bibechana-19674	112	7	replacing	replace	VERB
bibechana-19674	112	8	x	x	PUNCT
bibechana-19674	112	9	by	by	ADP
bibechana-19674	112	10	ξ	ξ	PROPN
bibechana-19674	112	11	in	in	ADP
bibechana-19674	112	12	(	(	PUNCT
bibechana-19674	112	13	3.18	3.18	NUM
bibechana-19674	112	14	)	)	PUNCT
bibechana-19674	112	15	we	we	PRON
bibechana-19674	112	16	obtain	obtain	VERB
bibechana-19674	112	17	0),)((21	0),)((21	NUM
bibechana-19674	112	18	)	)	PUNCT
bibechana-19674	112	19	,	,	PUNCT
bibechana-19674	112	20	)	)	PUNCT
bibechana-19674	112	21	(	(	PUNCT
bibechana-19674	112	22	(	(	PUNCT
bibechana-19674	112	23	)	)	PUNCT
bibechana-19674	112	24	,	,	PUNCT
bibechana-19674	112	25	)	)	PUNCT
bibechana-19674	112	26	(	(	PUNCT
bibechana-19674	112	27	(	(	PUNCT
bibechana-19674	112	28	=	=	NOUN
bibechana-19674	112	29	∇+∇−∇	∇+∇−∇	PROPN
bibechana-19674	112	30	ysnzszys	ysnzszys	NOUN
bibechana-19674	112	31	zy	zy	PROPN
bibechana-19674	112	32	ξξξ	ξξξ	NOUN
bibechana-19674	112	33	(	(	PUNCT
bibechana-19674	112	34	3.19	3.19	NUM
bibechana-19674	112	35	)	)	PUNCT
bibechana-19674	112	36	since	since	SCONJ
bibechana-19674	112	37	.0	.0	NUM
bibechana-19674	112	38	)	)	PUNCT
bibechana-19674	112	39	(	(	PUNCT
bibechana-19674	113	1	=	=	NOUN
bibechana-19674	113	2	ξdr	ξdr	NOUN
bibechana-19674	113	3	from	from	ADP
bibechana-19674	113	4	ëξ	ëξ	PROPN
bibechana-19674	113	5	0	0	NUM
bibechana-19674	114	1	=	=	SYM
bibechana-19674	114	2	s	s	X
bibechana-19674	114	3	we	we	PRON
bibechana-19674	114	4	get	get	VERB
bibechana-19674	114	5	)	)	PUNCT
bibechana-19674	114	6	,	,	PUNCT
bibechana-19674	114	7	(	(	PUNCT
bibechana-19674	114	8	)	)	PUNCT
bibechana-19674	114	9	,	,	PUNCT
bibechana-19674	114	10	(	(	PUNCT
bibechana-19674	114	11	)	)	PUNCT
bibechana-19674	114	12	,	,	PUNCT
bibechana-19674	114	13	(	(	PUNCT
bibechana-19674	114	14	)	)	PUNCT
bibechana-19674	114	15	1(4	1(4	NUM
bibechana-19674	114	16	)	)	PUNCT
bibechana-19674	114	17	,	,	PUNCT
bibechana-19674	114	18	(	(	PUNCT
bibechana-19674	114	19	)	)	PUNCT
bibechana-19674	114	20	,	,	PUNCT
bibechana-19674	114	21	(	(	PUNCT
bibechana-19674	114	22	)	)	PUNCT
bibechana-19674	114	23	,	,	PUNCT
bibechana-19674	114	24	)	)	PUNCT
bibechana-19674	114	25	(	(	PUNCT
bibechana-19674	114	26	(	(	PUNCT
bibechana-19674	114	27	yhzszhyshzygn	yhzszhyshzygn	PROPN
bibechana-19674	114	28	yszszys	yszszys	PROPN
bibechana-19674	114	29	zy	zy	PROPN
bibechana-19674	114	30	ϕϕϕ	ϕϕϕ	PROPN
bibechana-19674	114	31	ξξ	ξξ	ADP
bibechana-19674	114	32	ξ	ξ	X
bibechana-19674	115	1	+	+	NOUN
bibechana-19674	115	2	+	+	ADJ
bibechana-19674	115	3	−=	−=	ADJ
bibechana-19674	115	4	∇−∇−=∇	∇−∇−=∇	NOUN
bibechana-19674	115	5	by	by	ADP
bibechana-19674	115	6	the	the	DET
bibechana-19674	115	7	use	use	NOUN
bibechana-19674	115	8	of	of	ADP
bibechana-19674	115	9	(	(	PUNCT
bibechana-19674	115	10	2.6	2.6	NUM
bibechana-19674	115	11	)	)	PUNCT
bibechana-19674	115	12	and	and	CCONJ
bibechana-19674	115	13	(	(	PUNCT
bibechana-19674	115	14	2.23	2.23	NUM
bibechana-19674	115	15	)	)	PUNCT
bibechana-19674	115	16	.	.	PUNCT
bibechana-19674	116	1	again	again	ADV
bibechana-19674	116	2	,	,	PUNCT
bibechana-19674	116	3	(	(	PUNCT
bibechana-19674	116	4	)	)	PUNCT
bibechana-19674	116	5	)	)	PUNCT
bibechana-19674	117	1	.,(),(),(2),(2	.,(),(),(2),(2	X
bibechana-19674	117	2	)	)	PUNCT
bibechana-19674	117	3	,	,	PUNCT
bibechana-19674	117	4	(	(	PUNCT
bibechana-19674	117	5	)	)	PUNCT
bibechana-19674	117	6	,	,	PUNCT
bibechana-19674	117	7	(	(	PUNCT
bibechana-19674	117	8	)	)	PUNCT
bibechana-19674	117	9	(	(	PUNCT
bibechana-19674	117	10	2	2	NUM
bibechana-19674	117	11	)	)	PUNCT
bibechana-19674	117	12	,	,	PUNCT
bibechana-19674	117	13	(	(	PUNCT
bibechana-19674	117	14	)	)	PUNCT
bibechana-19674	117	15	,	,	PUNCT
bibechana-19674	117	16	(	(	PUNCT
bibechana-19674	117	17	)	)	PUNCT
bibechana-19674	117	18	,	,	PUNCT
bibechana-19674	117	19	(	(	PUNCT
bibechana-19674	117	20	)	)	PUNCT
bibechana-19674	117	21	,	,	PUNCT
bibechana-19674	117	22	)	)	PUNCT
bibechana-19674	117	23	(	(	PUNCT
bibechana-19674	117	24	(	(	PUNCT
bibechana-19674	117	25	zhyszyszhynkgzynkg	zhyszyszhynkgzynkg	NOUN
bibechana-19674	117	26	zhyszysznk	zhyszysznk	NOUN
bibechana-19674	117	27	zszszszs	zszszszs	NOUN
bibechana-19674	117	28	y	y	PROPN
bibechana-19674	117	29	yyyy	yyyy	PROPN
bibechana-19674	117	30	ϕϕϕϕ	ϕϕϕϕ	PROPN
bibechana-19674	117	31	ϕϕη	ϕϕη	PROPN
bibechana-19674	117	32	ξξξξ	ξξξξ	VERB
bibechana-19674	118	1	+	+	PROPN
bibechana-19674	119	1	+	+	ADJ
bibechana-19674	119	2	+	+	NOUN
bibechana-19674	119	3	=	=	ADJ
bibechana-19674	119	4	+	+	ADJ
bibechana-19674	119	5	+	+	ADJ
bibechana-19674	119	6	∇=	∇=	ADJ
bibechana-19674	119	7	∇−∇−∇=∇	∇−∇−∇=∇	NOUN
bibechana-19674	119	8	by	by	ADP
bibechana-19674	119	9	the	the	DET
bibechana-19674	119	10	use	use	NOUN
bibechana-19674	119	11	of	of	ADP
bibechana-19674	119	12	(	(	PUNCT
bibechana-19674	119	13	2.6	2.6	NUM
bibechana-19674	119	14	)	)	PUNCT
bibechana-19674	119	15	,	,	PUNCT
bibechana-19674	119	16	(	(	PUNCT
bibechana-19674	119	17	2.17	2.17	NUM
bibechana-19674	119	18	)	)	PUNCT
bibechana-19674	119	19	and	and	CCONJ
bibechana-19674	119	20	(	(	PUNCT
bibechana-19674	119	21	2.25	2.25	NUM
bibechana-19674	119	22	)	)	PUNCT
bibechana-19674	119	23	.	.	PUNCT
bibechana-19674	120	1	similarly	similarly	ADV
bibechana-19674	120	2	,	,	PUNCT
bibechana-19674	120	3	)	)	PUNCT
bibechana-19674	120	4	.,(),(),(2),(2	.,(),(),(2),(2	X
bibechana-19674	120	5	)	)	PUNCT
bibechana-19674	120	6	,	,	PUNCT
bibechana-19674	120	7	)	)	PUNCT
bibechana-19674	120	8	(	(	PUNCT
bibechana-19674	120	9	(	(	PUNCT
bibechana-19674	120	10	yhzsyzsyhznkgyznkgysz	yhzsyzsyhznkgyznkgysz	NOUN
bibechana-19674	120	11	ϕϕϕϕξ	ϕϕϕϕξ	NOUN
bibechana-19674	121	1	+	+	PROPN
bibechana-19674	121	2	+	+	ADJ
bibechana-19674	121	3	+	+	ADJ
bibechana-19674	121	4	=	=	NOUN
bibechana-19674	121	5	∇	∇	X
bibechana-19674	121	6	using	use	VERB
bibechana-19674	121	7	above	above	ADP
bibechana-19674	121	8	relations	relation	NOUN
bibechana-19674	121	9	in	in	ADP
bibechana-19674	121	10	(	(	PUNCT
bibechana-19674	121	11	3.19	3.19	NUM
bibechana-19674	121	12	)	)	PUNCT
bibechana-19674	121	13	we	we	PRON
bibechana-19674	121	14	get	get	VERB
bibechana-19674	121	15	)	)	PUNCT
bibechana-19674	121	16	.,(21),(),(),(2	.,(21),(),(),(2	PROPN
bibechana-19674	121	17	)	)	PUNCT
bibechana-19674	121	18	,	,	PUNCT
bibechana-19674	121	19	(	(	PUNCT
bibechana-19674	121	20	2),(2	2),(2	NUM
bibechana-19674	121	21	)	)	PUNCT
bibechana-19674	121	22	12(),(})1(4{0	12(),(})1(4{0	NUM
bibechana-19674	121	23	yzsnyzkgzyszhynkg	yzsnyzkgzyszhynkg	NOUN
bibechana-19674	121	24	zynkgyhzsnnhzygkn	zynkgyhzsnnhzygkn	PROPN
bibechana-19674	121	25	ϕϕϕϕ	ϕϕϕϕ	PROPN
bibechana-19674	121	26	ϕϕϕ	ϕϕϕ	PROPN
bibechana-19674	122	1	+	+	PROPN
bibechana-19674	122	2	+	+	PROPN
bibechana-19674	122	3	−−	−−	NOUN
bibechana-19674	122	4	−	−	VERB
bibechana-19674	123	1	+	+	CCONJ
bibechana-19674	124	1	+	+	ADJ
bibechana-19674	124	2	+	+	ADJ
bibechana-19674	124	3	−=	−=	PUNCT
bibechana-19674	124	4	(	(	PUNCT
bibechana-19674	124	5	3.20	3.20	NUM
bibechana-19674	124	6	)	)	PUNCT
bibechana-19674	124	7	replacing	replace	VERB
bibechana-19674	124	8	z	z	NOUN
bibechana-19674	124	9	by	by	ADP
bibechana-19674	124	10	zϕ	zϕ	PROPN
bibechana-19674	124	11	in	in	ADP
bibechana-19674	124	12	(	(	PUNCT
bibechana-19674	124	13	3.20	3.20	NUM
bibechana-19674	124	14	)	)	PUNCT
bibechana-19674	124	15	and	and	CCONJ
bibechana-19674	124	16	using	use	VERB
bibechana-19674	124	17	(	(	PUNCT
bibechana-19674	124	18	2.2	2.2	NUM
bibechana-19674	124	19	)	)	PUNCT
bibechana-19674	124	20	,	,	PUNCT
bibechana-19674	124	21	(	(	PUNCT
bibechana-19674	124	22	2.3	2.3	NUM
bibechana-19674	124	23	)	)	PUNCT
bibechana-19674	124	24	,	,	PUNCT
bibechana-19674	124	25	(	(	PUNCT
bibechana-19674	124	26	2.5	2.5	NUM
bibechana-19674	124	27	)	)	PUNCT
bibechana-19674	124	28	,	,	PUNCT
bibechana-19674	124	29	(	(	PUNCT
bibechana-19674	124	30	2.17	2.17	NUM
bibechana-19674	124	31	)	)	PUNCT
bibechana-19674	124	32	,	,	PUNCT
bibechana-19674	124	33	(	(	PUNCT
bibechana-19674	124	34	2.22	2.22	NUM
bibechana-19674	124	35	)	)	PUNCT
bibechana-19674	124	36	and	and	CCONJ
bibechana-19674	124	37	symmetry	symmetry	NOUN
bibechana-19674	124	38	property	property	NOUN
bibechana-19674	124	39	of	of	ADP
bibechana-19674	124	40	h	h	NOUN
bibechana-19674	124	41	we	we	PRON
bibechana-19674	124	42	obtain	obtain	VERB
bibechana-19674	124	43	)	)	PUNCT
bibechana-19674	124	44	,	,	PUNCT
bibechana-19674	124	45	(	(	PUNCT
bibechana-19674	124	46	21),(),(),(2	21),(),(),(2	NUM
bibechana-19674	124	47	)	)	PUNCT
bibechana-19674	124	48	,	,	PUNCT
bibechana-19674	124	49	(	(	PUNCT
bibechana-19674	124	50	2),(2	2),(2	X
bibechana-19674	124	51	)	)	PUNCT
bibechana-19674	124	52	12(),(})1(4{0	12(),(})1(4{0	NUM
bibechana-19674	124	53	22	22	NUM
bibechana-19674	125	1	2yzsnzykgzyszhynkg	2yzsnzykgzyszhynkg	NUM
bibechana-19674	125	2	zynkgyzhsnnzhygkn	zynkgyzhsnnzhygkn	NOUN
bibechana-19674	125	3	ϕϕϕϕϕϕ	ϕϕϕϕϕϕ	PROPN
bibechana-19674	125	4	ϕϕϕϕϕ	ϕϕϕϕϕ	PROPN
bibechana-19674	126	1	+	+	PROPN
bibechana-19674	126	2	+	+	ADJ
bibechana-19674	126	3	−−	−−	NOUN
bibechana-19674	126	4	−	−	VERB
bibechana-19674	127	1	+	+	CCONJ
bibechana-19674	128	1	+	+	ADJ
bibechana-19674	128	2	+	+	ADJ
bibechana-19674	128	3	−=	−=	NOUN
bibechana-19674	128	4	or	or	CCONJ
bibechana-19674	128	5	,	,	PUNCT
bibechana-19674	128	6	)	)	PUNCT
bibechana-19674	129	1	.,(),(12	.,(),(12	PUNCT
bibechana-19674	129	2	)	)	PUNCT
bibechana-19674	129	3	12(2),(2	12(2),(2	PROPN
bibechana-19674	129	4	)	)	PUNCT
bibechana-19674	129	5	,	,	PUNCT
bibechana-19674	129	6	(	(	PUNCT
bibechana-19674	129	7	yhzshzygn	yhzshzygn	PROPN
bibechana-19674	129	8	knnzynkgzys	knnzynkgzys	X
bibechana-19674	130	1	+	+	X
bibechana-19674	131	1	+	+	CCONJ
bibechana-19674	131	2	−	−	X
bibechana-19674	132	1	+	+	NOUN
bibechana-19674	132	2	=	=	X
bibechana-19674	132	3	(	(	PUNCT
bibechana-19674	132	4	3.21	3.21	NUM
bibechana-19674	132	5	)	)	PUNCT
bibechana-19674	132	6	riddhi	riddhi	NOUN
bibechana-19674	132	7	jung	jung	PROPN
bibechana-19674	132	8	shah./	shah./	PROPN
bibechana-19674	132	9	bibechana	bibechana	PROPN
bibechana-19674	132	10	16	16	NUM
bibechana-19674	132	11	(	(	PUNCT
bibechana-19674	132	12	2019	2019	NUM
bibechana-19674	132	13	)	)	PUNCT
bibechana-19674	132	14	55	55	NUM
bibechana-19674	132	15	-	-	SYM
bibechana-19674	132	16	63	63	NUM
bibechana-19674	132	17	:	:	PUNCT
bibechana-19674	132	18	rcost	rcost	NOUN
bibechana-19674	132	19	p.62	p.62	PROPN
bibechana-19674	132	20	(	(	PUNCT
bibechana-19674	132	21	online	online	ADJ
bibechana-19674	132	22	publication	publication	NOUN
bibechana-19674	132	23	:	:	PUNCT
bibechana-19674	132	24	dec	dec	PROPN
bibechana-19674	132	25	.	.	PROPN
bibechana-19674	132	26	,	,	PUNCT
bibechana-19674	132	27	2018	2018	NUM
bibechana-19674	132	28	)	)	PUNCT
bibechana-19674	132	29	this	this	PRON
bibechana-19674	132	30	completes	complete	VERB
bibechana-19674	132	31	the	the	DET
bibechana-19674	132	32	proof	proof	NOUN
bibechana-19674	132	33	of	of	ADP
bibechana-19674	132	34	the	the	DET
bibechana-19674	132	35	theorem	theorem	NOUN
bibechana-19674	132	36	.	.	PROPN
bibechana-19674	132	37	4	4	NUM
bibechana-19674	132	38	.	.	NOUN
bibechana-19674	132	39	example	example	NOUN
bibechana-19674	132	40	of	of	ADP
bibechana-19674	132	41	3	3	NUM
bibechana-19674	132	42	-	-	PUNCT
bibechana-19674	132	43	dimensional	dimensional	ADJ
bibechana-19674	132	44	)	)	PUNCT
bibechana-19674	132	45	(	(	PUNCT
bibechana-19674	132	46	kn	kn	NOUN
bibechana-19674	132	47	-contact	-contact	PROPN
bibechana-19674	132	48	metric	metric	ADJ
bibechana-19674	132	49	manifold	manifold	NOUN
bibechana-19674	132	50	consider	consider	VERB
bibechana-19674	132	51	a	a	DET
bibechana-19674	132	52	3	3	NUM
bibechana-19674	132	53	-	-	PUNCT
bibechana-19674	132	54	dimensional	dimensional	ADJ
bibechana-19674	132	55	manifold	manifold	ADJ
bibechana-19674	132	56	}	}	PUNCT
bibechana-19674	132	57	0	0	NUM
bibechana-19674	132	58	:)	:)	NOUN
bibechana-19674	132	59	,	,	PUNCT
bibechana-19674	132	60	,	,	PUNCT
bibechana-19674	132	61	{	{	PUNCT
bibechana-19674	132	62	(	(	PUNCT
bibechana-19674	132	63	3	3	NUM
bibechana-19674	132	64	≠∈=	≠∈=	NOUN
bibechana-19674	132	65	xrzyxm	xrzyxm	NOUN
bibechana-19674	132	66	where	where	SCONJ
bibechana-19674	132	67	)	)	PUNCT
bibechana-19674	132	68	,	,	PUNCT
bibechana-19674	132	69	,	,	PUNCT
bibechana-19674	132	70	(	(	PUNCT
bibechana-19674	132	71	zyx	zyx	PROPN
bibechana-19674	132	72	are	be	AUX
bibechana-19674	132	73	the	the	DET
bibechana-19674	132	74	standard	standard	ADJ
bibechana-19674	132	75	coordinates	coordinate	NOUN
bibechana-19674	132	76	in	in	ADP
bibechana-19674	132	77	.3r	.3r	PROPN
bibechana-19674	132	78	let	let	VERB
bibechana-19674	132	79	}	}	PUNCT
bibechana-19674	132	80	,	,	PUNCT
bibechana-19674	132	81	,	,	PUNCT
bibechana-19674	132	82	{	{	PUNCT
bibechana-19674	132	83	321	321	NUM
bibechana-19674	132	84	eee	eee	NOUN
bibechana-19674	132	85	be	be	AUX
bibechana-19674	132	86	linearly	linearly	ADV
bibechana-19674	132	87	independent	independent	ADJ
bibechana-19674	132	88	global	global	ADJ
bibechana-19674	132	89	frame	frame	NOUN
bibechana-19674	132	90	on	on	ADP
bibechana-19674	132	91	m	m	VERB
bibechana-19674	132	92	defined	define	VERB
bibechana-19674	132	93	by	by	ADP
bibechana-19674	132	94	zxyyxzxeyxe	zxyyxzxeyxe	PROPN
bibechana-19674	132	95	∂	∂	NUM
bibechana-19674	132	96	∂	∂	NUM
bibechana-19674	132	97	+	+	NUM
bibechana-19674	132	98	∂	∂	NUM
bibechana-19674	132	99	∂	∂	NUM
bibechana-19674	132	100	−	−	PROPN
bibechana-19674	132	101	∂	∂	NUM
bibechana-19674	132	102	∂	∂	NUM
bibechana-19674	132	103	=	=	SYM
bibechana-19674	132	104	∂	∂	NOUN
bibechana-19674	132	105	∂	∂	NOUN
bibechana-19674	132	106	=	=	SYM
bibechana-19674	132	107	42	42	NUM
bibechana-19674	132	108	,	,	PUNCT
bibechana-19674	132	109	2	2	NUM
bibechana-19674	132	110	21	21	NUM
bibechana-19674	132	111	and	and	CCONJ
bibechana-19674	132	112	.3	.3	NUM
bibechana-19674	132	113	ze	ze	PROPN
bibechana-19674	132	114	∂	∂	NOUN
bibechana-19674	132	115	∂	∂	NOUN
bibechana-19674	132	116	=	=	PUNCT
bibechana-19674	132	117	let	let	VERB
bibechana-19674	132	118	g	g	NOUN
bibechana-19674	132	119	be	be	AUX
bibechana-19674	132	120	the	the	DET
bibechana-19674	132	121	riemannian	riemannian	ADJ
bibechana-19674	132	122	metric	metric	NOUN
bibechana-19674	132	123	defined	define	VERB
bibechana-19674	132	124	by	by	ADP
bibechana-19674	132	125	,	,	PUNCT
bibechana-19674	132	126	0	0	NUM
bibechana-19674	132	127	)	)	PUNCT
bibechana-19674	132	128	,	,	PUNCT
bibechana-19674	132	129	(	(	PUNCT
bibechana-19674	132	130	)	)	PUNCT
bibechana-19674	132	131	,	,	PUNCT
bibechana-19674	132	132	(	(	PUNCT
bibechana-19674	132	133	)	)	PUNCT
bibechana-19674	132	134	,	,	PUNCT
bibechana-19674	132	135	(	(	PUNCT
bibechana-19674	132	136	213231	213231	NUM
bibechana-19674	132	137	=	=	SYM
bibechana-19674	132	138	=	=	SYM
bibechana-19674	132	139	=	=	X
bibechana-19674	132	140	eegeegeeg	eegeegeeg	PROPN
bibechana-19674	132	141	.1	.1	NUM
bibechana-19674	132	142	)	)	PUNCT
bibechana-19674	132	143	,	,	PUNCT
bibechana-19674	132	144	(	(	PUNCT
bibechana-19674	132	145	)	)	PUNCT
bibechana-19674	132	146	,	,	PUNCT
bibechana-19674	132	147	(	(	PUNCT
bibechana-19674	132	148	)	)	PUNCT
bibechana-19674	132	149	,	,	PUNCT
bibechana-19674	132	150	(	(	PUNCT
bibechana-19674	132	151	332211	332211	NUM
bibechana-19674	132	152	=	=	SYM
bibechana-19674	132	153	=	=	SYM
bibechana-19674	132	154	=	=	NOUN
bibechana-19674	132	155	eegeegeeg	eegeegeeg	NOUN
bibechana-19674	132	156	let	let	VERB
bibechana-19674	132	157	η	η	PROPN
bibechana-19674	132	158	be	be	AUX
bibechana-19674	132	159	the	the	DET
bibechana-19674	132	160	1	1	NUM
bibechana-19674	132	161	-	-	PUNCT
bibechana-19674	132	162	form	form	NOUN
bibechana-19674	132	163	defined	define	VERB
bibechana-19674	132	164	by	by	ADP
bibechana-19674	132	165	)	)	PUNCT
bibechana-19674	132	166	,	,	PUNCT
bibechana-19674	132	167	(	(	PUNCT
bibechana-19674	132	168	)	)	PUNCT
bibechana-19674	132	169	(	(	PUNCT
bibechana-19674	132	170	3evgv	3evgv	NUM
bibechana-19674	132	171	=	=	SYM
bibechana-19674	132	172	η	η	PROPN
bibechana-19674	132	173	for	for	ADP
bibechana-19674	132	174	any	any	PRON
bibechana-19674	132	175	)	)	PUNCT
bibechana-19674	132	176	,	,	PUNCT
bibechana-19674	132	177	(	(	PUNCT
bibechana-19674	132	178	mv	mv	PROPN
bibechana-19674	132	179	χ∈	χ∈	VERB
bibechana-19674	132	180	the	the	DET
bibechana-19674	132	181	set	set	NOUN
bibechana-19674	132	182	of	of	ADP
bibechana-19674	132	183	vector	vector	NOUN
bibechana-19674	132	184	fields	field	NOUN
bibechana-19674	132	185	.	.	PUNCT
bibechana-19674	133	1	let	let	VERB
bibechana-19674	133	2	ϕ	ϕ	NOUN
bibechana-19674	133	3	be	be	AUX
bibechana-19674	133	4	the	the	DET
bibechana-19674	133	5	(	(	PUNCT
bibechana-19674	133	6	1	1	NUM
bibechana-19674	133	7	,	,	PUNCT
bibechana-19674	133	8	1	1	X
bibechana-19674	133	9	)	)	PUNCT
bibechana-19674	133	10	tensor	tensor	NOUN
bibechana-19674	133	11	field	field	NOUN
bibechana-19674	133	12	defined	define	VERB
bibechana-19674	133	13	by	by	ADP
bibechana-19674	133	14	.0	.0	PROPN
bibechana-19674	133	15	,	,	PUNCT
bibechana-19674	133	16	,	,	PUNCT
bibechana-19674	133	17	31221	31221	NUM
bibechana-19674	133	18	=	=	SYM
bibechana-19674	133	19	−==	−==	PROPN
bibechana-19674	133	20	eeeee	eeeee	PROPN
bibechana-19674	133	21	ϕϕϕ	ϕϕϕ	PROPN
bibechana-19674	133	22	then	then	ADV
bibechana-19674	133	23	using	use	VERB
bibechana-19674	133	24	the	the	DET
bibechana-19674	133	25	linearity	linearity	NOUN
bibechana-19674	133	26	of	of	ADP
bibechana-19674	133	27	ϕ	ϕ	PROPN
bibechana-19674	133	28	and	and	CCONJ
bibechana-19674	133	29	g	g	NOUN
bibechana-19674	133	30	we	we	PRON
bibechana-19674	133	31	have	have	VERB
bibechana-19674	133	32	323	323	NUM
bibechana-19674	133	33	)	)	PUNCT
bibechana-19674	133	34	(	(	PUNCT
bibechana-19674	133	35	,	,	PUNCT
bibechana-19674	133	36	1	1	X
bibechana-19674	133	37	)	)	PUNCT
bibechana-19674	133	38	(	(	PUNCT
bibechana-19674	133	39	evvve	evvve	ADJ
bibechana-19674	133	40	ηϕη	ηϕη	X
bibechana-19674	134	1	+	+	ADJ
bibechana-19674	134	2	−==	−==	ADJ
bibechana-19674	134	3	and	and	CCONJ
bibechana-19674	134	4	)	)	PUNCT
bibechana-19674	134	5	(	(	PUNCT
bibechana-19674	134	6	)	)	PUNCT
bibechana-19674	134	7	(	(	PUNCT
bibechana-19674	134	8	)	)	PUNCT
bibechana-19674	134	9	,	,	PUNCT
bibechana-19674	134	10	(	(	PUNCT
bibechana-19674	134	11	)	)	PUNCT
bibechana-19674	134	12	,	,	PUNCT
bibechana-19674	134	13	(	(	PUNCT
bibechana-19674	134	14	vuvugvug	vuvugvug	ADJ
bibechana-19674	134	15	ηηϕϕ	ηηϕϕ	NOUN
bibechana-19674	134	16	−=	−=	VERB
bibechana-19674	134	17	for	for	ADP
bibechana-19674	134	18	any	any	PRON
bibechana-19674	134	19	)	)	PUNCT
bibechana-19674	134	20	.	.	PUNCT
bibechana-19674	135	1	(	(	PUNCT
bibechana-19674	135	2	,	,	PUNCT
bibechana-19674	135	3	mvu	mvu	PROPN
bibechana-19674	135	4	χ∈	χ∈	VERB
bibechana-19674	135	5	moreover	moreover	ADV
bibechana-19674	135	6	,	,	PUNCT
bibechana-19674	135	7	.0	.0	NUM
bibechana-19674	135	8	,	,	PUNCT
bibechana-19674	135	9	,	,	PUNCT
bibechana-19674	135	10	32211	32211	NUM
bibechana-19674	136	1	=	=	SYM
bibechana-19674	136	2	=	=	NOUN
bibechana-19674	136	3	−=	−=	X
bibechana-19674	136	4	heeheehe	heeheehe	ADV
bibechana-19674	136	5	thus	thus	ADV
bibechana-19674	136	6	for	for	ADP
bibechana-19674	136	7	,	,	PUNCT
bibechana-19674	136	8	3	3	NUM
bibechana-19674	136	9	ξ	ξ	X
bibechana-19674	136	10	=	=	SYM
bibechana-19674	136	11	e	e	X
bibechana-19674	136	12	the	the	DET
bibechana-19674	136	13	structure	structure	NOUN
bibechana-19674	136	14	)	)	PUNCT
bibechana-19674	136	15	,	,	PUNCT
bibechana-19674	136	16	,	,	PUNCT
bibechana-19674	136	17	,	,	PUNCT
bibechana-19674	136	18	(	(	PUNCT
bibechana-19674	136	19	gηξϕ	gηξϕ	PROPN
bibechana-19674	136	20	defines	define	VERB
bibechana-19674	136	21	a	a	DET
bibechana-19674	136	22	contact	contact	NOUN
bibechana-19674	136	23	metric	metric	ADJ
bibechana-19674	136	24	structure	structure	NOUN
bibechana-19674	136	25	on	on	ADP
bibechana-19674	136	26	.m	.m	NOUN
bibechana-19674	136	27	now	now	ADV
bibechana-19674	136	28	,	,	PUNCT
bibechana-19674	136	29	from	from	ADP
bibechana-19674	136	30	definition	definition	NOUN
bibechana-19674	136	31	of	of	ADP
bibechana-19674	136	32	lie	lie	NOUN
bibechana-19674	136	33	bracket	bracket	NOUN
bibechana-19674	136	34	we	we	PRON
bibechana-19674	136	35	have	have	VERB
bibechana-19674	136	36	.22	.22	NUM
bibechana-19674	136	37	24	24	NUM
bibechana-19674	136	38	242422	242422	NUM
bibechana-19674	136	39	]	]	PUNCT
bibechana-19674	136	40	,	,	PUNCT
bibechana-19674	136	41	[	[	PUNCT
bibechana-19674	136	42	31221	31221	NUM
bibechana-19674	136	43	eex	eex	NOUN
bibechana-19674	136	44	zyx	zyx	PROPN
bibechana-19674	136	45	yxzxyyxzxzxyyxzxyxee	yxzxyyxzxzxyyxzxyxee	PROPN
bibechana-19674	136	46	+	+	PROPN
bibechana-19674	136	47	=	=	PROPN
bibechana-19674	136	48	∂	∂	NUM
bibechana-19674	136	49	∂	∂	NUM
bibechana-19674	136	50	+	+	NUM
bibechana-19674	136	51	∂	∂	NUM
bibechana-19674	136	52	∂	∂	NOUN
bibechana-19674	136	53	=	=	SYM
bibechana-19674	136	54			NOUN
bibechana-19674	136	55			PUNCT
bibechana-19674	137	1			PROPN
bibechana-19674	138	1			INTJ
bibechana-19674	138	2			NOUN
bibechana-19674	138	3			VERB
bibechana-19674	138	4	∂	∂	NUM
bibechana-19674	138	5	∂	∂	NUM
bibechana-19674	138	6			NOUN
bibechana-19674	138	7			PUNCT
bibechana-19674	139	1			PROPN
bibechana-19674	140	1			INTJ
bibechana-19674	140	2			NOUN
bibechana-19674	140	3			VERB
bibechana-19674	140	4	∂	∂	NUM
bibechana-19674	140	5	∂	∂	NUM
bibechana-19674	140	6	+	+	NUM
bibechana-19674	140	7	∂	∂	NUM
bibechana-19674	140	8	∂	∂	NUM
bibechana-19674	140	9	−	−	PROPN
bibechana-19674	140	10	∂	∂	NUM
bibechana-19674	140	11	∂	∂	NOUN
bibechana-19674	140	12	−	−	NOUN
bibechana-19674	140	13			PUNCT
bibechana-19674	141	1			PROPN
bibechana-19674	142	1			INTJ
bibechana-19674	142	2			NOUN
bibechana-19674	142	3			VERB
bibechana-19674	142	4	∂	∂	NUM
bibechana-19674	142	5	∂	∂	NUM
bibechana-19674	142	6	+	+	NUM
bibechana-19674	142	7	∂	∂	NUM
bibechana-19674	142	8	∂	∂	NUM
bibechana-19674	142	9	−	−	PROPN
bibechana-19674	142	10	∂	∂	NUM
bibechana-19674	142	11	∂	∂	NUM
bibechana-19674	142	12	∂	∂	NUM
bibechana-19674	142	13	∂	∂	NOUN
bibechana-19674	142	14	=	=	PUNCT
bibechana-19674	142	15	similarly	similarly	ADV
bibechana-19674	142	16	,	,	PUNCT
bibechana-19674	142	17	we	we	PRON
bibechana-19674	142	18	obtain	obtain	VERB
bibechana-19674	142	19	0	0	NUM
bibechana-19674	142	20	]	]	PUNCT
bibechana-19674	142	21	,	,	PUNCT
bibechana-19674	142	22	[	[	PUNCT
bibechana-19674	142	23	31	31	NUM
bibechana-19674	142	24	=	=	SYM
bibechana-19674	142	25	ee	ee	NOUN
bibechana-19674	142	26	and	and	CCONJ
bibechana-19674	142	27	.2	.2	NUM
bibechana-19674	142	28	]	]	X
bibechana-19674	142	29	,	,	PUNCT
bibechana-19674	142	30	[	[	PUNCT
bibechana-19674	142	31	132	132	NUM
bibechana-19674	142	32	eee	eee	NOUN
bibechana-19674	142	33	=	=	PUNCT
bibechana-19674	142	34	now	now	ADV
bibechana-19674	142	35	,	,	PUNCT
bibechana-19674	142	36	we	we	PRON
bibechana-19674	142	37	have	have	VERB
bibechana-19674	142	38	koszul	koszul	PROPN
bibechana-19674	142	39	's	's	PART
bibechana-19674	142	40	formula	formula	NOUN
bibechana-19674	142	41	(	(	PUNCT
bibechana-19674	142	42	)	)	PUNCT
bibechana-19674	142	43	(	(	PUNCT
bibechana-19674	142	44	)	)	PUNCT
bibechana-19674	142	45	(	(	PUNCT
bibechana-19674	142	46	)	)	PUNCT
bibechana-19674	142	47	(	(	PUNCT
bibechana-19674	142	48	)	)	PUNCT
bibechana-19674	142	49	.	.	PUNCT
bibechana-19674	143	1	]	]	X
bibechana-19674	143	2	,	,	PUNCT
bibechana-19674	144	1	[	[	X
bibechana-19674	144	2	,	,	PUNCT
bibechana-19674	144	3	]	]	X
bibechana-19674	144	4	,	,	PUNCT
bibechana-19674	144	5	[	[	X
bibechana-19674	144	6	,	,	PUNCT
bibechana-19674	144	7	]	]	X
bibechana-19674	144	8	,	,	PUNCT
bibechana-19674	144	9	[	[	X
bibechana-19674	144	10	,	,	PUNCT
bibechana-19674	144	11	)	)	PUNCT
bibechana-19674	144	12	,	,	PUNCT
bibechana-19674	144	13	(	(	PUNCT
bibechana-19674	144	14	)	)	PUNCT
bibechana-19674	144	15	,	,	PUNCT
bibechana-19674	144	16	(	(	PUNCT
bibechana-19674	144	17	)	)	PUNCT
bibechana-19674	144	18	,	,	PUNCT
bibechana-19674	144	19	(	(	PUNCT
bibechana-19674	144	20	,	,	PUNCT
bibechana-19674	144	21	2	2	NUM
bibechana-19674	144	22	yxzgzxyg	yxzgzxyg	NOUN
bibechana-19674	144	23	zyxgyxzgxzygzyxgzyg	zyxgyxzgxzygzyxgzyg	NOUN
bibechana-19674	144	24	x	x	PUNCT
bibechana-19674	145	1	+	+	NOUN
bibechana-19674	145	2	−	−	NOUN
bibechana-19674	145	3	−−+=∇	−−+=∇	VERB
bibechana-19674	145	4	taking	take	VERB
bibechana-19674	145	5	ξ=3e	ξ=3e	NOUN
bibechana-19674	145	6	and	and	CCONJ
bibechana-19674	145	7	using	use	VERB
bibechana-19674	145	8	koszul	koszul	ADJ
bibechana-19674	145	9	formula	formula	NOUN
bibechana-19674	145	10	we	we	PRON
bibechana-19674	145	11	obtain	obtain	VERB
bibechana-19674	145	12	(	(	PUNCT
bibechana-19674	145	13	)	)	PUNCT
bibechana-19674	145	14	)	)	PUNCT
bibechana-19674	145	15	,	,	PUNCT
bibechana-19674	145	16	,	,	PUNCT
bibechana-19674	145	17	(	(	PUNCT
bibechana-19674	145	18	4,2	4,2	NUM
bibechana-19674	145	19	11121	11121	NUM
bibechana-19674	145	20	eegxeeg	eegxeeg	X
bibechana-19674	145	21	e	e	NOUN
bibechana-19674	145	22	=	=	NOUN
bibechana-19674	145	23	∇	∇	X
bibechana-19674	145	24	(	(	PUNCT
bibechana-19674	145	25	)	)	PUNCT
bibechana-19674	145	26	)	)	PUNCT
bibechana-19674	145	27	,	,	PUNCT
bibechana-19674	145	28	(	(	PUNCT
bibechana-19674	145	29	40,2	40,2	NOUN
bibechana-19674	145	30	21221	21221	NUM
bibechana-19674	145	31	eegxeeg	eegxeeg	X
bibechana-19674	145	32	e	e	NOUN
bibechana-19674	145	33	=	=	PUNCT
bibechana-19674	145	34	=	=	NOUN
bibechana-19674	145	35	∇	∇	X
bibechana-19674	145	36	and	and	CCONJ
bibechana-19674	145	37	(	(	PUNCT
bibechana-19674	145	38	)	)	PUNCT
bibechana-19674	145	39	)	)	PUNCT
bibechana-19674	145	40	.,(40,2	.,(40,2	PROPN
bibechana-19674	145	41	31321	31321	NUM
bibechana-19674	145	42	eegxeeg	eegxeeg	X
bibechana-19674	145	43	e	e	NOUN
bibechana-19674	145	44	=	=	PUNCT
bibechana-19674	145	45	=	=	NOUN
bibechana-19674	145	46	∇	∇	X
bibechana-19674	145	47	from	from	ADP
bibechana-19674	145	48	above	above	ADP
bibechana-19674	145	49	it	it	PRON
bibechana-19674	145	50	follows	follow	VERB
bibechana-19674	145	51	that	that	PRON
bibechana-19674	145	52	(	(	PUNCT
bibechana-19674	145	53	)	)	PUNCT
bibechana-19674	145	54	)	)	PUNCT
bibechana-19674	145	55	.,(2	.,(2	PROPN
bibechana-19674	145	56	,	,	PUNCT
bibechana-19674	145	57	121	121	NUM
bibechana-19674	145	58	xegxxeg	xegxxeg	NOUN
bibechana-19674	145	59	e	e	X
bibechana-19674	146	1	=	=	NOUN
bibechana-19674	146	2	∇	∇	X
bibechana-19674	146	3	hence	hence	ADV
bibechana-19674	146	4	.2	.2	NUM
bibechana-19674	146	5	121	121	NUM
bibechana-19674	146	6	exee	exee	NOUN
bibechana-19674	146	7	=	=	NOUN
bibechana-19674	146	8	∇	∇	VERB
bibechana-19674	146	9	similarly	similarly	ADV
bibechana-19674	146	10	we	we	PRON
bibechana-19674	146	11	obtain	obtain	VERB
bibechana-19674	146	12	other	other	ADJ
bibechana-19674	146	13	results	result	NOUN
bibechana-19674	146	14	and	and	CCONJ
bibechana-19674	146	15	finally	finally	ADV
bibechana-19674	146	16	we	we	PRON
bibechana-19674	146	17	have	have	VERB
bibechana-19674	146	18	,	,	PUNCT
bibechana-19674	146	19	2	2	NUM
bibechana-19674	146	20	211	211	NUM
bibechana-19674	146	21	exee	exee	NOUN
bibechana-19674	146	22	−=∇	−=∇	NUM
bibechana-19674	146	23	,	,	PUNCT
bibechana-19674	146	24	2	2	NUM
bibechana-19674	146	25	121	121	NUM
bibechana-19674	146	26	exee	exee	NOUN
bibechana-19674	146	27	=	=	NOUN
bibechana-19674	146	28	∇	∇	X
bibechana-19674	146	29	,	,	PUNCT
bibechana-19674	146	30	2	2	NUM
bibechana-19674	146	31	312	312	NUM
bibechana-19674	146	32	eee	eee	NOUN
bibechana-19674	146	33	−=∇	−=∇	NOUN
bibechana-19674	146	34	,	,	PUNCT
bibechana-19674	146	35	2	2	NUM
bibechana-19674	146	36	132	132	NUM
bibechana-19674	146	37	eee	eee	NOUN
bibechana-19674	146	38	=	=	NOUN
bibechana-19674	146	39	∇	∇	X
bibechana-19674	146	40	.03323132231	.03323132231	PUNCT
bibechana-19674	147	1	=	=	AUX
bibechana-19674	147	2	∇=∇=∇=∇=∇	∇=∇=∇=∇=∇	PROPN
bibechana-19674	147	3	eeeee	eeeee	PROPN
bibechana-19674	147	4	eeeee	eeeee	PROPN
bibechana-19674	147	5	from	from	ADP
bibechana-19674	147	6	above	above	ADP
bibechana-19674	147	7	one	one	NUM
bibechana-19674	147	8	can	can	AUX
bibechana-19674	147	9	easily	easily	ADV
bibechana-19674	147	10	seen	see	VERB
bibechana-19674	147	11	that	that	SCONJ
bibechana-19674	147	12	the	the	DET
bibechana-19674	147	13	conditions	condition	NOUN
bibechana-19674	147	14	for	for	ADP
bibechana-19674	147	15	)	)	PUNCT
bibechana-19674	147	16	(	(	PUNCT
bibechana-19674	147	17	kn	kn	NOUN
bibechana-19674	147	18	-contact	-contact	PROPN
bibechana-19674	147	19	metric	metric	ADJ
bibechana-19674	147	20	manifold	manifold	NOUN
bibechana-19674	147	21	are	be	AUX
bibechana-19674	147	22	satisfied	satisfied	ADJ
bibechana-19674	147	23	for	for	ADP
bibechana-19674	147	24	ξ=3e	ξ=3e	NOUN
bibechana-19674	147	25	and	and	CCONJ
bibechana-19674	147	26	.0,4	.0,4	X
bibechana-19674	147	27	≠−=	≠−=	PROPN
bibechana-19674	147	28	xxk	xxk	PROPN
bibechana-19674	147	29	riddhi	riddhi	PROPN
bibechana-19674	147	30	jung	jung	PROPN
bibechana-19674	147	31	shah./	shah./	PROPN
bibechana-19674	147	32	bibechana	bibechana	PROPN
bibechana-19674	147	33	16	16	NUM
bibechana-19674	147	34	(	(	PUNCT
bibechana-19674	147	35	2019	2019	NUM
bibechana-19674	147	36	)	)	PUNCT
bibechana-19674	147	37	55	55	NUM
bibechana-19674	147	38	-	-	SYM
bibechana-19674	147	39	63	63	NUM
bibechana-19674	147	40	:	:	PUNCT
bibechana-19674	147	41	rcost	rcost	NOUN
bibechana-19674	147	42	p.63	p.63	X
bibechana-19674	147	43	(	(	PUNCT
bibechana-19674	147	44	online	online	ADJ
bibechana-19674	147	45	publication	publication	NOUN
bibechana-19674	147	46	:	:	PUNCT
bibechana-19674	147	47	dec	dec	PROPN
bibechana-19674	147	48	.	.	PROPN
bibechana-19674	147	49	,	,	PUNCT
bibechana-19674	147	50	2018	2018	NUM
bibechana-19674	147	51	)	)	PUNCT
bibechana-19674	147	52	5	5	NUM
bibechana-19674	147	53	.	.	X
bibechana-19674	147	54	conclusion	conclusion	NOUN
bibechana-19674	147	55	in	in	ADP
bibechana-19674	147	56	this	this	DET
bibechana-19674	147	57	paper	paper	NOUN
bibechana-19674	147	58	we	we	PRON
bibechana-19674	147	59	have	have	AUX
bibechana-19674	147	60	studied	study	VERB
bibechana-19674	147	61	7w	7w	NOUN
bibechana-19674	147	62	and	and	CCONJ
bibechana-19674	147	63	9w	9w	NOUN
bibechana-19674	147	64	curvature	curvature	NOUN
bibechana-19674	147	65	tensors	tensor	NOUN
bibechana-19674	147	66	on	on	ADP
bibechana-19674	147	67	)	)	PUNCT
bibechana-19674	147	68	(	(	PUNCT
bibechana-19674	147	69	kn	kn	NOUN
bibechana-19674	147	70	-contact	-contact	NOUN
bibechana-19674	147	71	metric	metric	ADJ
bibechana-19674	147	72	manifolds	manifold	NOUN
bibechana-19674	147	73	.	.	PUNCT
bibechana-19674	148	1	it	it	PRON
bibechana-19674	148	2	is	be	AUX
bibechana-19674	148	3	proved	prove	VERB
bibechana-19674	148	4	that	that	SCONJ
bibechana-19674	148	5	a	a	X
bibechana-19674	148	6	)	)	PUNCT
bibechana-19674	148	7	12	12	NUM
bibechana-19674	148	8	(	(	PUNCT
bibechana-19674	148	9	+	+	NOUN
bibechana-19674	148	10	n	n	CCONJ
bibechana-19674	148	11	-dimensional	-dimensional	ADJ
bibechana-19674	148	12	)	)	PUNCT
bibechana-19674	148	13	(	(	PUNCT
bibechana-19674	148	14	kn	kn	NOUN
bibechana-19674	148	15	-contact	-contact	PROPN
bibechana-19674	148	16	metric	metric	ADJ
bibechana-19674	148	17	manifold	manifold	NOUN
bibechana-19674	148	18	satisfying	satisfy	VERB
bibechana-19674	148	19	the	the	DET
bibechana-19674	148	20	condition	condition	NOUN
bibechana-19674	148	21	0	0	NUM
bibechana-19674	148	22	)	)	PUNCT
bibechana-19674	148	23	.	.	PUNCT
bibechana-19674	149	1	,	,	PUNCT
bibechana-19674	149	2	(	(	PUNCT
bibechana-19674	149	3	97	97	NUM
bibechana-19674	149	4	=	=	NOUN
bibechana-19674	149	5	wxw	wxw	NOUN
bibechana-19674	149	6	ξ	ξ	PROPN
bibechana-19674	149	7	is	be	AUX
bibechana-19674	149	8	either	either	CCONJ
bibechana-19674	149	9	locally	locally	ADV
bibechana-19674	149	10	isometric	isometric	ADJ
bibechana-19674	149	11	to	to	ADP
bibechana-19674	149	12	the	the	DET
bibechana-19674	149	13	riemannian	riemannian	ADJ
bibechana-19674	149	14	product	product	NOUN
bibechana-19674	149	15	)	)	PUNCT
bibechana-19674	149	16	4()0(1	4()0(1	NUM
bibechana-19674	149	17	nn	nn	X
bibechana-19674	149	18	se	se	PROPN
bibechana-19674	149	19	×+	×+	PROPN
bibechana-19674	149	20	or	or	CCONJ
bibechana-19674	149	21	is	be	AUX
bibechana-19674	149	22	η	η	NOUN
bibechana-19674	149	23	-einstein	-einstein	PROPN
bibechana-19674	149	24	.	.	PUNCT
bibechana-19674	150	1	it	it	PRON
bibechana-19674	150	2	is	be	AUX
bibechana-19674	150	3	also	also	ADV
bibechana-19674	150	4	investigated	investigate	VERB
bibechana-19674	150	5	that	that	SCONJ
bibechana-19674	150	6	a	a	X
bibechana-19674	150	7	)	)	PUNCT
bibechana-19674	150	8	(	(	PUNCT
bibechana-19674	150	9	kn	kn	NOUN
bibechana-19674	150	10	-contact	-contact	PROPN
bibechana-19674	150	11	metric	metric	ADJ
bibechana-19674	150	12	manifold	manifold	NOUN
bibechana-19674	150	13	satisfying	satisfy	VERB
bibechana-19674	150	14	the	the	DET
bibechana-19674	150	15	conditions	condition	NOUN
bibechana-19674	150	16	9w−ϕ	9w−ϕ	NOUN
bibechana-19674	150	17	flat	flat	ADJ
bibechana-19674	150	18	and	and	CCONJ
bibechana-19674	150	19	09	09	NUM
bibechana-19674	150	20	=	=	NOUN
bibechana-19674	150	21	divw	divw	NOUN
bibechana-19674	150	22	has	have	VERB
bibechana-19674	150	23	the	the	DET
bibechana-19674	150	24	ricci	ricci	PROPN
bibechana-19674	150	25	tensor	tensor	NOUN
bibechana-19674	150	26	s	s	PROPN
bibechana-19674	150	27	of	of	ADP
bibechana-19674	150	28	different	different	ADJ
bibechana-19674	150	29	forms	form	NOUN
bibechana-19674	150	30	.	.	PUNCT
bibechana-19674	151	1	references	reference	NOUN
bibechana-19674	151	2	[	[	X
bibechana-19674	151	3	1	1	X
bibechana-19674	151	4	]	]	PUNCT
bibechana-19674	151	5	s.	s.	PROPN
bibechana-19674	151	6	tanno	tanno	PROPN
bibechana-19674	151	7	,	,	PUNCT
bibechana-19674	151	8	ricci	ricci	NOUN
bibechana-19674	151	9	curvatures	curvature	NOUN
bibechana-19674	151	10	of	of	ADP
bibechana-19674	151	11	contact	contact	NOUN
bibechana-19674	151	12	riemannian	riemannian	NOUN
bibechana-19674	151	13	manifolds	manifold	NOUN
bibechana-19674	151	14	,	,	PUNCT
bibechana-19674	151	15	tohoku	tohoku	PROPN
bibechana-19674	151	16	math	math	NOUN
bibechana-19674	151	17	.	.	PUNCT
bibechana-19674	152	1	j.	j.	PROPN
bibechana-19674	152	2	40	40	NUM
bibechana-19674	152	3	(	(	PUNCT
bibechana-19674	152	4	1988	1988	NUM
bibechana-19674	152	5	)	)	PUNCT
bibechana-19674	152	6	441	441	NUM
bibechana-19674	152	7	-	-	SYM
bibechana-19674	152	8	448	448	NUM
bibechana-19674	152	9	.	.	PUNCT
bibechana-19674	153	1	[	[	X
bibechana-19674	153	2	2	2	NUM
bibechana-19674	153	3	]	]	X
bibechana-19674	153	4	g.	g.	PROPN
bibechana-19674	153	5	reeb	reeb	PROPN
bibechana-19674	153	6	,	,	PUNCT
bibechana-19674	153	7	sur	sur	PROPN
bibechana-19674	153	8	certaines	certaines	PROPN
bibechana-19674	153	9	proprietes	propriete	VERB
bibechana-19674	153	10	topologiques	topologiques	PROPN
bibechana-19674	153	11	des	des	PROPN
bibechana-19674	153	12	trajectoires	trajectoires	PROPN
bibechana-19674	153	13	des	des	PROPN
bibechana-19674	153	14	systemes	systemes	PROPN
bibechana-19674	153	15	dynamiques	dynamiques	PROPN
bibechana-19674	153	16	,	,	PUNCT
bibechana-19674	153	17	memoires	memoire	NOUN
bibechana-19674	153	18	de	de	ADP
bibechana-19674	153	19	1acad	1acad	NUM
bibechana-19674	153	20	.	.	PUNCT
bibechana-19674	154	1	roy	roy	PROPN
bibechana-19674	154	2	.	.	PROPN
bibechana-19674	154	3	de	de	PROPN
bibechana-19674	154	4	beligique	beligique	PROPN
bibechana-19674	154	5	,	,	PUNCT
bibechana-19674	154	6	sci	sci	PROPN
bibechana-19674	154	7	.	.	PROPN
bibechana-19674	154	8	ser	ser	PROPN
bibechana-19674	154	9	.	.	PROPN
bibechana-19674	154	10	2	2	NUM
bibechana-19674	154	11	(	(	PUNCT
bibechana-19674	154	12	1952	1952	NUM
bibechana-19674	154	13	)	)	PUNCT
bibechana-19674	154	14	1	1	NUM
bibechana-19674	154	15	-	-	SYM
bibechana-19674	154	16	62	62	NUM
bibechana-19674	154	17	.	.	PUNCT
bibechana-19674	155	1	[	[	X
bibechana-19674	155	2	3	3	X
bibechana-19674	155	3	]	]	X
bibechana-19674	155	4	d.	d.	PROPN
bibechana-19674	155	5	e.	e.	PROPN
bibechana-19674	155	6	blair	blair	PROPN
bibechana-19674	155	7	,	,	PUNCT
bibechana-19674	155	8	t.	t.	PROPN
bibechana-19674	155	9	koufogiorgos	koufogiorgos	PROPN
bibechana-19674	155	10	,	,	PUNCT
bibechana-19674	155	11	b.	b.	PROPN
bibechana-19674	155	12	j.	j.	PROPN
bibechana-19674	155	13	papantoniou	papantoniou	PROPN
bibechana-19674	155	14	,	,	PUNCT
bibechana-19674	155	15	contact	contact	NOUN
bibechana-19674	155	16	metric	metric	ADJ
bibechana-19674	155	17	manifolds	manifold	NOUN
bibechana-19674	155	18	satisfying	satisfy	VERB
bibechana-19674	155	19	a	a	DET
bibechana-19674	155	20	nullity	nullity	NOUN
bibechana-19674	155	21	condition	condition	NOUN
bibechana-19674	155	22	,	,	PUNCT
bibechana-19674	155	23	israel	israel	PROPN
bibechana-19674	155	24	j.	j.	PROPN
bibechana-19674	155	25	of	of	ADP
bibechana-19674	155	26	math	math	PROPN
bibechana-19674	155	27	.	.	PUNCT
bibechana-19674	156	1	19	19	NUM
bibechana-19674	156	2	(	(	PUNCT
bibechana-19674	156	3	1995	1995	NUM
bibechana-19674	156	4	)	)	PUNCT
bibechana-19674	156	5	189	189	NUM
bibechana-19674	156	6	-	-	SYM
bibechana-19674	156	7	214	214	NUM
bibechana-19674	156	8	.	.	PUNCT
bibechana-19674	157	1	[	[	X
bibechana-19674	157	2	4	4	X
bibechana-19674	157	3	]	]	X
bibechana-19674	157	4	g.	g.	PROPN
bibechana-19674	157	5	p.	p.	PROPN
bibechana-19674	157	6	pokhariyal	pokhariyal	PROPN
bibechana-19674	157	7	,	,	PUNCT
bibechana-19674	157	8	relativistic	relativistic	ADJ
bibechana-19674	157	9	significance	significance	NOUN
bibechana-19674	157	10	of	of	ADP
bibechana-19674	157	11	curvature	curvature	NOUN
bibechana-19674	157	12	tensors	tensor	NOUN
bibechana-19674	157	13	,	,	PUNCT
bibechana-19674	157	14	internat	internat	NOUN
bibechana-19674	157	15	.	.	PUNCT
bibechana-19674	158	1	j.	j.	PROPN
bibechana-19674	158	2	math	math	PROPN
bibechana-19674	158	3	.	.	PUNCT
bibechana-19674	159	1	and	and	CCONJ
bibechana-19674	159	2	math	math	NOUN
bibechana-19674	159	3	.	.	PUNCT
bibechana-19674	160	1	sci	sci	PROPN
bibechana-19674	160	2	.	.	PROPN
bibechana-19674	160	3	5(1	5(1	NUM
bibechana-19674	160	4	)	)	PUNCT
bibechana-19674	160	5	(	(	PUNCT
bibechana-19674	160	6	1982	1982	NUM
bibechana-19674	160	7	)	)	PUNCT
bibechana-19674	160	8	133	133	NUM
bibechana-19674	160	9	-	-	SYM
bibechana-19674	160	10	139	139	NUM
bibechana-19674	160	11	.	.	PUNCT
bibechana-19674	161	1	[	[	X
bibechana-19674	161	2	5	5	X
bibechana-19674	161	3	]	]	PUNCT
bibechana-19674	161	4	l.	l.	PROPN
bibechana-19674	161	5	p.	p.	PROPN
bibechana-19674	161	6	eisenhart	eisenhart	PROPN
bibechana-19674	161	7	,	,	PUNCT
bibechana-19674	161	8	riemannian	riemannian	ADJ
bibechana-19674	161	9	geometry	geometry	NOUN
bibechana-19674	161	10	,	,	PUNCT
bibechana-19674	161	11	princeton	princeton	PROPN
bibechana-19674	161	12	university	university	PROPN
bibechana-19674	161	13	press	press	NOUN
bibechana-19674	161	14	,	,	PUNCT
bibechana-19674	161	15	1950	1950	NUM
bibechana-19674	161	16	.	.	PUNCT
bibechana-19674	162	1	[	[	X
bibechana-19674	162	2	6	6	NUM
bibechana-19674	162	3	]	]	PUNCT
bibechana-19674	162	4	d.	d.	PROPN
bibechana-19674	162	5	e.	e.	PROPN
bibechana-19674	162	6	blair	blair	PROPN
bibechana-19674	162	7	,	,	PUNCT
bibechana-19674	162	8	contact	contact	NOUN
bibechana-19674	162	9	manifolds	manifold	NOUN
bibechana-19674	162	10	in	in	ADP
bibechana-19674	162	11	riemannian	riemannian	ADJ
bibechana-19674	162	12	geometry	geometry	NOUN
bibechana-19674	162	13	,	,	PUNCT
bibechana-19674	162	14	lecture	lecture	NOUN
bibechana-19674	162	15	notes	note	NOUN
bibechana-19674	162	16	in	in	ADP
bibechana-19674	162	17	mathematics	mathematic	NOUN
bibechana-19674	162	18	,	,	PUNCT
bibechana-19674	162	19	509	509	NUM
bibechana-19674	162	20	,	,	PUNCT
bibechana-19674	162	21	springer	springer	NOUN
bibechana-19674	162	22	-	-	PUNCT
bibechana-19674	162	23	verlag	verlag	PROPN
bibechana-19674	162	24	,	,	PUNCT
bibechana-19674	162	25	berlin	berlin	PROPN
bibechana-19674	162	26	,	,	PUNCT
bibechana-19674	162	27	1976	1976	NUM
bibechana-19674	162	28	.	.	PUNCT
bibechana-19674	163	1	[	[	X
bibechana-19674	163	2	7	7	X
bibechana-19674	163	3	]	]	X
bibechana-19674	163	4	d.	d.	PROPN
bibechana-19674	163	5	e.	e.	PROPN
bibechana-19674	163	6	blair	blair	PROPN
bibechana-19674	163	7	,	,	PUNCT
bibechana-19674	163	8	j.	j.	PROPN
bibechana-19674	163	9	n.	n.	PROPN
bibechana-19674	163	10	patnaik	patnaik	PROPN
bibechana-19674	163	11	,	,	PUNCT
bibechana-19674	163	12	contact	contact	NOUN
bibechana-19674	163	13	manifolds	manifold	NOUN
bibechana-19674	163	14	with	with	ADP
bibechana-19674	163	15	characteristic	characteristic	ADJ
bibechana-19674	163	16	vector	vector	NOUN
bibechana-19674	163	17	field	field	NOUN
bibechana-19674	163	18	annihilated	annihilate	VERB
bibechana-19674	163	19	by	by	ADP
bibechana-19674	163	20	the	the	DET
bibechana-19674	163	21	curvature	curvature	NOUN
bibechana-19674	163	22	,	,	PUNCT
bibechana-19674	163	23	bull	bull	NOUN
bibechana-19674	163	24	.	.	PUNCT
bibechana-19674	163	25	inst	inst	PROPN
bibechana-19674	163	26	.	.	PUNCT
bibechana-19674	163	27	math	math	NOUN
bibechana-19674	163	28	.	.	PUNCT
bibechana-19674	164	1	acad	acad	PROPN
bibechana-19674	164	2	.	.	PUNCT
bibechana-19674	165	1	sinica	sinica	PROPN
bibechana-19674	165	2	9	9	NUM
bibechana-19674	165	3	(	(	PUNCT
bibechana-19674	165	4	1981	1981	NUM
bibechana-19674	165	5	)	)	PUNCT
bibechana-19674	165	6	533	533	NUM
bibechana-19674	165	7	-	-	SYM
bibechana-19674	165	8	545	545	NUM
bibechana-19674	165	9	.	.	PUNCT
bibechana-19674	166	1	[	[	X
bibechana-19674	166	2	8	8	NUM
bibechana-19674	166	3	]	]	X
bibechana-19674	166	4	s.	s.	PROPN
bibechana-19674	166	5	sasaki	sasaki	PROPN
bibechana-19674	166	6	,	,	PUNCT
bibechana-19674	166	7	y.	y.	PROPN
bibechana-19674	166	8	hatakeyama	hatakeyama	PROPN
bibechana-19674	166	9	,	,	PUNCT
bibechana-19674	166	10	on	on	ADP
bibechana-19674	166	11	differentiable	differentiable	ADJ
bibechana-19674	166	12	manifolds	manifold	NOUN
bibechana-19674	166	13	with	with	ADP
bibechana-19674	166	14	certain	certain	ADJ
bibechana-19674	166	15	structures	structure	NOUN
bibechana-19674	166	16	which	which	PRON
bibechana-19674	166	17	are	be	AUX
bibechana-19674	166	18	closely	closely	ADV
bibechana-19674	166	19	related	relate	VERB
bibechana-19674	166	20	to	to	ADP
bibechana-19674	166	21	almost	almost	ADV
bibechana-19674	166	22	contact	contact	VERB
bibechana-19674	166	23	structure	structure	PROPN
bibechana-19674	166	24	ii	ii	PROPN
bibechana-19674	166	25	,	,	PUNCT
bibechana-19674	166	26	tohoku	tohoku	PROPN
bibechana-19674	166	27	math	math	PROPN
bibechana-19674	166	28	.	.	PUNCT
bibechana-19674	167	1	j.	j.	PROPN
bibechana-19674	167	2	13	13	NUM
bibechana-19674	167	3	(	(	PUNCT
bibechana-19674	167	4	1961	1961	NUM
bibechana-19674	167	5	)	)	PUNCT
bibechana-19674	167	6	281	281	NUM
bibechana-19674	167	7	-	-	SYM
bibechana-19674	167	8	294	294	NUM
bibechana-19674	167	9	.	.	PUNCT
bibechana-19674	168	1	[	[	X
bibechana-19674	168	2	9	9	NUM
bibechana-19674	168	3	]	]	PUNCT
bibechana-19674	168	4	c.	c.	NOUN
bibechana-19674	168	5	baikoussis	baikoussis	PROPN
bibechana-19674	168	6	,	,	PUNCT
bibechana-19674	168	7	t.	t.	PROPN
bibechana-19674	168	8	koufogiorgos	koufogiorgos	PROPN
bibechana-19674	168	9	,	,	PUNCT
bibechana-19674	168	10	on	on	ADP
bibechana-19674	168	11	a	a	DET
bibechana-19674	168	12	type	type	NOUN
bibechana-19674	168	13	of	of	ADP
bibechana-19674	168	14	contact	contact	NOUN
bibechana-19674	168	15	manifolds	manifold	NOUN
bibechana-19674	168	16	,	,	PUNCT
bibechana-19674	168	17	j.	j.	PROPN
bibechana-19674	168	18	of	of	ADP
bibechana-19674	168	19	geometry	geometry	NOUN
bibechana-19674	168	20	46	46	NUM
bibechana-19674	168	21	(	(	PUNCT
bibechana-19674	168	22	1993	1993	NUM
bibechana-19674	168	23	)	)	PUNCT
bibechana-19674	168	24	1	1	NUM
bibechana-19674	168	25	-	-	SYM
bibechana-19674	168	26	9	9	NUM
bibechana-19674	168	27	.	.	PUNCT