id	sid	tid	token	lemma	pos
ejpam-3177	1	1	european	european	PROPN
ejpam-3177	1	2	journal	journal	PROPN
ejpam-3177	1	3	of	of	ADP
ejpam-3177	1	4	pure	pure	ADJ
ejpam-3177	1	5	and	and	CCONJ
ejpam-3177	1	6	applied	apply	VERB
ejpam-3177	1	7	mathematics	mathematic	NOUN
ejpam-3177	1	8	vol	vol	NOUN
ejpam-3177	1	9	.	.	PUNCT
ejpam-3177	2	1	11	11	NUM
ejpam-3177	2	2	,	,	PUNCT
ejpam-3177	2	3	no	no	INTJ
ejpam-3177	2	4	.	.	NOUN
ejpam-3177	2	5	1	1	NUM
ejpam-3177	2	6	,	,	PUNCT
ejpam-3177	2	7	2018	2018	NUM
ejpam-3177	2	8	,	,	PUNCT
ejpam-3177	2	9	150	150	NUM
ejpam-3177	2	10	-	-	SYM
ejpam-3177	2	11	159	159	NUM
ejpam-3177	2	12	issn	issn	PROPN
ejpam-3177	2	13	1307	1307	NUM
ejpam-3177	2	14	-	-	SYM
ejpam-3177	2	15	5543	5543	NUM
ejpam-3177	2	16	–	–	PUNCT
ejpam-3177	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3177	2	18	published	publish	VERB
ejpam-3177	2	19	by	by	ADP
ejpam-3177	2	20	new	new	PROPN
ejpam-3177	2	21	york	york	PROPN
ejpam-3177	2	22	business	business	PROPN
ejpam-3177	2	23	global	global	ADJ
ejpam-3177	2	24	biharmonic	biharmonic	NOUN
ejpam-3177	2	25	maps	map	NOUN
ejpam-3177	2	26	into	into	ADP
ejpam-3177	2	27	s	s	NOUN
ejpam-3177	2	28	-	-	PUNCT
ejpam-3177	2	29	space	space	NOUN
ejpam-3177	2	30	forms	form	NOUN
ejpam-3177	2	31	najma	najma	PROPN
ejpam-3177	2	32	abdul	abdul	PROPN
ejpam-3177	2	33	rehman1,∗	rehman1,∗	PROPN
ejpam-3177	2	34	,	,	PUNCT
ejpam-3177	2	35	mehwish	mehwish	PROPN
ejpam-3177	2	36	bari2	bari2	VERB
ejpam-3177	2	37	1	1	NUM
ejpam-3177	2	38	department	department	NOUN
ejpam-3177	2	39	of	of	ADP
ejpam-3177	2	40	mathematics	mathematic	NOUN
ejpam-3177	2	41	,	,	PUNCT
ejpam-3177	2	42	ciit	ciit	NOUN
ejpam-3177	2	43	,	,	PUNCT
ejpam-3177	2	44	sahiwal	sahiwal	NOUN
ejpam-3177	2	45	,	,	PUNCT
ejpam-3177	2	46	pakistan	pakistan	PROPN
ejpam-3177	2	47	2	2	NUM
ejpam-3177	2	48	department	department	NOUN
ejpam-3177	2	49	of	of	ADP
ejpam-3177	2	50	mathematics	mathematic	NOUN
ejpam-3177	2	51	,	,	PUNCT
ejpam-3177	2	52	ncba	ncba	NOUN
ejpam-3177	2	53	and	and	CCONJ
ejpam-3177	2	54	e	e	NOUN
ejpam-3177	2	55	,	,	PUNCT
ejpam-3177	2	56	bahawalpur	bahawalpur	NOUN
ejpam-3177	2	57	,	,	PUNCT
ejpam-3177	2	58	pakistan	pakistan	PROPN
ejpam-3177	2	59	abstract	abstract	NOUN
ejpam-3177	2	60	.	.	PUNCT
ejpam-3177	3	1	we	we	PRON
ejpam-3177	3	2	study	study	VERB
ejpam-3177	3	3	in	in	ADP
ejpam-3177	3	4	this	this	DET
ejpam-3177	3	5	paper	paper	NOUN
ejpam-3177	3	6	the	the	DET
ejpam-3177	3	7	condition	condition	NOUN
ejpam-3177	3	8	on	on	ADP
ejpam-3177	3	9	second	second	ADJ
ejpam-3177	3	10	fundamental	fundamental	ADJ
ejpam-3177	3	11	form	form	NOUN
ejpam-3177	3	12	for	for	ADP
ejpam-3177	3	13	biharmonicity	biharmonicity	NOUN
ejpam-3177	3	14	of	of	ADP
ejpam-3177	3	15	submanifolds	submanifold	NOUN
ejpam-3177	3	16	in	in	ADP
ejpam-3177	3	17	s	s	NOUN
ejpam-3177	3	18	-	-	PUNCT
ejpam-3177	3	19	space	space	NOUN
ejpam-3177	3	20	forms	form	NOUN
ejpam-3177	3	21	.	.	PUNCT
ejpam-3177	4	1	2010	2010	NUM
ejpam-3177	4	2	mathematics	mathematic	NOUN
ejpam-3177	4	3	subject	subject	NOUN
ejpam-3177	4	4	classifications	classification	NOUN
ejpam-3177	4	5	:	:	PUNCT
ejpam-3177	4	6	53c55	53c55	NUM
ejpam-3177	4	7	,	,	PUNCT
ejpam-3177	4	8	53c43	53c43	NUM
ejpam-3177	4	9	,	,	PUNCT
ejpam-3177	4	10	58e20	58e20	NUM
ejpam-3177	4	11	key	key	ADJ
ejpam-3177	4	12	words	word	NOUN
ejpam-3177	4	13	and	and	CCONJ
ejpam-3177	4	14	phrases	phrase	NOUN
ejpam-3177	4	15	:	:	PUNCT
ejpam-3177	4	16	s	s	NOUN
ejpam-3177	4	17	-	-	PUNCT
ejpam-3177	4	18	manifolds	manifold	NOUN
ejpam-3177	4	19	,	,	PUNCT
ejpam-3177	4	20	harmonic	harmonic	ADJ
ejpam-3177	4	21	map	map	NOUN
ejpam-3177	4	22	,	,	PUNCT
ejpam-3177	4	23	biharmonic	biharmonic	NOUN
ejpam-3177	4	24	maps	map	NOUN
ejpam-3177	4	25	1	1	NUM
ejpam-3177	4	26	.	.	PUNCT
ejpam-3177	5	1	introduction	introduction	NOUN
ejpam-3177	5	2	harmonic	harmonic	ADJ
ejpam-3177	5	3	maps	map	NOUN
ejpam-3177	5	4	between	between	ADP
ejpam-3177	5	5	riemannian	riemannian	ADJ
ejpam-3177	5	6	manifolds	manifold	NOUN
ejpam-3177	5	7	have	have	AUX
ejpam-3177	5	8	been	be	AUX
ejpam-3177	5	9	discussed	discuss	VERB
ejpam-3177	5	10	for	for	ADP
ejpam-3177	5	11	last	last	ADJ
ejpam-3177	5	12	decades	decade	NOUN
ejpam-3177	5	13	,	,	PUNCT
ejpam-3177	5	14	initiated	initiate	VERB
ejpam-3177	5	15	with	with	ADP
ejpam-3177	5	16	the	the	DET
ejpam-3177	5	17	paper	paper	NOUN
ejpam-3177	5	18	of	of	ADP
ejpam-3177	5	19	j.	j.	PROPN
ejpam-3177	5	20	eells	eells	PROPN
ejpam-3177	5	21	and	and	CCONJ
ejpam-3177	5	22	j.h	j.h	PROPN
ejpam-3177	5	23	.	.	PROPN
ejpam-3177	5	24	sampson	sampson	PROPN
ejpam-3177	6	1	[	[	X
ejpam-3177	6	2	7	7	NUM
ejpam-3177	6	3	]	]	PUNCT
ejpam-3177	6	4	.	.	PUNCT
ejpam-3177	7	1	since	since	SCONJ
ejpam-3177	7	2	harmonic	harmonic	ADJ
ejpam-3177	7	3	maps	map	NOUN
ejpam-3177	7	4	have	have	VERB
ejpam-3177	7	5	both	both	DET
ejpam-3177	7	6	properties	property	NOUN
ejpam-3177	7	7	analytic	analytic	ADJ
ejpam-3177	7	8	and	and	CCONJ
ejpam-3177	7	9	geometric	geometric	ADJ
ejpam-3177	7	10	,	,	PUNCT
ejpam-3177	7	11	they	they	PRON
ejpam-3177	7	12	have	have	AUX
ejpam-3177	7	13	become	become	VERB
ejpam-3177	7	14	an	an	DET
ejpam-3177	7	15	important	important	ADJ
ejpam-3177	7	16	and	and	CCONJ
ejpam-3177	7	17	interesting	interesting	ADJ
ejpam-3177	7	18	research	research	NOUN
ejpam-3177	7	19	field	field	NOUN
ejpam-3177	7	20	.	.	PUNCT
ejpam-3177	8	1	the	the	DET
ejpam-3177	8	2	study	study	NOUN
ejpam-3177	8	3	of	of	ADP
ejpam-3177	8	4	harmonic	harmonic	ADJ
ejpam-3177	8	5	maps	map	NOUN
ejpam-3177	8	6	on	on	ADP
ejpam-3177	8	7	riemannian	riemannian	ADJ
ejpam-3177	8	8	manifolds	manifold	NOUN
ejpam-3177	8	9	with	with	SCONJ
ejpam-3177	8	10	some	some	DET
ejpam-3177	8	11	structures	structure	NOUN
ejpam-3177	8	12	started	start	VERB
ejpam-3177	8	13	from	from	ADP
ejpam-3177	8	14	the	the	DET
ejpam-3177	8	15	paper	paper	NOUN
ejpam-3177	8	16	of	of	ADP
ejpam-3177	8	17	lichnerowicz	lichnerowicz	NOUN
ejpam-3177	8	18	[	[	X
ejpam-3177	8	19	13	13	NUM
ejpam-3177	8	20	]	]	PUNCT
ejpam-3177	8	21	.	.	PUNCT
ejpam-3177	9	1	after	after	ADP
ejpam-3177	9	2	that	that	PRON
ejpam-3177	9	3	,	,	PUNCT
ejpam-3177	9	4	rawnsley	rawnsley	VERB
ejpam-3177	9	5	[	[	X
ejpam-3177	9	6	14	14	NUM
ejpam-3177	9	7	]	]	PUNCT
ejpam-3177	9	8	studied	study	VERB
ejpam-3177	9	9	structure	structure	NOUN
ejpam-3177	9	10	preserving	preserve	VERB
ejpam-3177	9	11	harmonic	harmonic	ADJ
ejpam-3177	9	12	maps	map	NOUN
ejpam-3177	9	13	between	between	ADP
ejpam-3177	9	14	f	f	PROPN
ejpam-3177	9	15	-	-	PUNCT
ejpam-3177	9	16	manifolds	manifold	NOUN
ejpam-3177	9	17	.	.	PUNCT
ejpam-3177	10	1	later	later	ADV
ejpam-3177	10	2	on	on	ADP
ejpam-3177	10	3	many	many	ADJ
ejpam-3177	10	4	authors	author	NOUN
ejpam-3177	10	5	studied	study	VERB
ejpam-3177	10	6	harmonic	harmonic	ADJ
ejpam-3177	10	7	maps	map	NOUN
ejpam-3177	10	8	(	(	PUNCT
ejpam-3177	10	9	see	see	VERB
ejpam-3177	10	10	[	[	X
ejpam-3177	10	11	6	6	X
ejpam-3177	10	12	]	]	X
ejpam-3177	11	1	[	[	X
ejpam-3177	11	2	10	10	NUM
ejpam-3177	11	3	]	]	PUNCT
ejpam-3177	11	4	,	,	PUNCT
ejpam-3177	11	5	[	[	X
ejpam-3177	11	6	11	11	NUM
ejpam-3177	11	7	]	]	PUNCT
ejpam-3177	11	8	,	,	PUNCT
ejpam-3177	11	9	[	[	X
ejpam-3177	11	10	12	12	NUM
ejpam-3177	11	11	]	]	PUNCT
ejpam-3177	11	12	,	,	PUNCT
ejpam-3177	12	1	[	[	X
ejpam-3177	12	2	15	15	NUM
ejpam-3177	12	3	]	]	X
ejpam-3177	13	1	[	[	X
ejpam-3177	13	2	16	16	NUM
ejpam-3177	13	3	]	]	PUNCT
ejpam-3177	13	4	)	)	PUNCT
ejpam-3177	13	5	.	.	PUNCT
ejpam-3177	14	1	the	the	DET
ejpam-3177	14	2	biharmonic	biharmonic	PROPN
ejpam-3177	14	3	maps	map	NOUN
ejpam-3177	14	4	theory	theory	NOUN
ejpam-3177	14	5	is	be	AUX
ejpam-3177	14	6	an	an	DET
ejpam-3177	14	7	old	old	ADJ
ejpam-3177	14	8	and	and	CCONJ
ejpam-3177	14	9	attractive	attractive	ADJ
ejpam-3177	14	10	subject	subject	NOUN
ejpam-3177	14	11	.	.	PUNCT
ejpam-3177	15	1	they	they	PRON
ejpam-3177	15	2	have	have	AUX
ejpam-3177	15	3	been	be	AUX
ejpam-3177	15	4	studied	study	VERB
ejpam-3177	15	5	since	since	SCONJ
ejpam-3177	15	6	1862	1862	NUM
ejpam-3177	15	7	by	by	ADP
ejpam-3177	15	8	maxwell	maxwell	PROPN
ejpam-3177	15	9	and	and	CCONJ
ejpam-3177	15	10	airy	airy	ADJ
ejpam-3177	15	11	to	to	PART
ejpam-3177	15	12	describe	describe	VERB
ejpam-3177	15	13	a	a	DET
ejpam-3177	15	14	mathematical	mathematical	ADJ
ejpam-3177	15	15	model	model	NOUN
ejpam-3177	15	16	of	of	ADP
ejpam-3177	15	17	elasticity	elasticity	NOUN
ejpam-3177	15	18	.	.	PUNCT
ejpam-3177	16	1	the	the	DET
ejpam-3177	16	2	euler	euler	NOUN
ejpam-3177	16	3	-	-	PUNCT
ejpam-3177	16	4	lagrange	lagrange	NOUN
ejpam-3177	16	5	equation	equation	NOUN
ejpam-3177	16	6	for	for	ADP
ejpam-3177	16	7	bienergy	bienergy	NOUN
ejpam-3177	16	8	functional	functional	ADJ
ejpam-3177	16	9	was	be	AUX
ejpam-3177	16	10	first	first	ADV
ejpam-3177	16	11	derived	derive	VERB
ejpam-3177	16	12	by	by	ADP
ejpam-3177	16	13	jiange	jiange	NOUN
ejpam-3177	16	14	in	in	ADP
ejpam-3177	16	15	1986	1986	NUM
ejpam-3177	16	16	[	[	X
ejpam-3177	16	17	8	8	NUM
ejpam-3177	16	18	]	]	PUNCT
ejpam-3177	16	19	.	.	PUNCT
ejpam-3177	17	1	after	after	SCONJ
ejpam-3177	17	2	this	this	DET
ejpam-3177	17	3	biharmonic	biharmonic	NOUN
ejpam-3177	17	4	maps	map	NOUN
ejpam-3177	17	5	were	be	AUX
ejpam-3177	17	6	studied	study	VERB
ejpam-3177	17	7	by	by	ADP
ejpam-3177	17	8	many	many	ADJ
ejpam-3177	17	9	authors	author	NOUN
ejpam-3177	17	10	see	see	VERB
ejpam-3177	17	11	[	[	X
ejpam-3177	17	12	2	2	NUM
ejpam-3177	17	13	]	]	PUNCT
ejpam-3177	17	14	,	,	PUNCT
ejpam-3177	17	15	[	[	X
ejpam-3177	17	16	3	3	NUM
ejpam-3177	17	17	]	]	PUNCT
ejpam-3177	17	18	,	,	PUNCT
ejpam-3177	17	19	[	[	X
ejpam-3177	17	20	5	5	NUM
ejpam-3177	17	21	]	]	PUNCT
ejpam-3177	17	22	.	.	PUNCT
ejpam-3177	18	1	in	in	ADP
ejpam-3177	18	2	[	[	X
ejpam-3177	18	3	5	5	NUM
ejpam-3177	18	4	]	]	PUNCT
ejpam-3177	18	5	,	,	PUNCT
ejpam-3177	18	6	authors	author	NOUN
ejpam-3177	18	7	have	have	AUX
ejpam-3177	18	8	studied	study	VERB
ejpam-3177	18	9	the	the	DET
ejpam-3177	18	10	biharmonic	biharmonic	NOUN
ejpam-3177	18	11	submanifolds	submanifold	NOUN
ejpam-3177	18	12	in	in	ADP
ejpam-3177	18	13	complex	complex	ADJ
ejpam-3177	18	14	space	space	NOUN
ejpam-3177	18	15	form	form	NOUN
ejpam-3177	18	16	.	.	PUNCT
ejpam-3177	19	1	the	the	DET
ejpam-3177	19	2	objective	objective	NOUN
ejpam-3177	19	3	of	of	ADP
ejpam-3177	19	4	this	this	DET
ejpam-3177	19	5	paper	paper	NOUN
ejpam-3177	19	6	is	be	AUX
ejpam-3177	19	7	to	to	PART
ejpam-3177	19	8	find	find	VERB
ejpam-3177	19	9	condition	condition	NOUN
ejpam-3177	19	10	on	on	ADP
ejpam-3177	19	11	second	second	ADJ
ejpam-3177	19	12	fundamental	fundamental	ADJ
ejpam-3177	19	13	form	form	NOUN
ejpam-3177	19	14	for	for	ADP
ejpam-3177	19	15	biharmonicity	biharmonicity	NOUN
ejpam-3177	19	16	of	of	ADP
ejpam-3177	19	17	a	a	DET
ejpam-3177	19	18	map	map	NOUN
ejpam-3177	19	19	from	from	ADP
ejpam-3177	19	20	submanifolds	submanifold	NOUN
ejpam-3177	19	21	of	of	ADP
ejpam-3177	19	22	s	s	NOUN
ejpam-3177	19	23	-	-	PUNCT
ejpam-3177	19	24	space	space	NOUN
ejpam-3177	19	25	form	form	NOUN
ejpam-3177	19	26	to	to	ADP
ejpam-3177	19	27	s	s	NOUN
ejpam-3177	19	28	-	-	PUNCT
ejpam-3177	19	29	space	space	NOUN
ejpam-3177	19	30	forms	form	NOUN
ejpam-3177	19	31	.	.	PUNCT
ejpam-3177	20	1	after	after	SCONJ
ejpam-3177	20	2	we	we	PRON
ejpam-3177	20	3	recall	recall	VERB
ejpam-3177	20	4	some	some	DET
ejpam-3177	20	5	well	well	ADV
ejpam-3177	20	6	known	know	VERB
ejpam-3177	20	7	facts	fact	NOUN
ejpam-3177	20	8	about	about	ADP
ejpam-3177	20	9	biharmonic	biharmonic	NOUN
ejpam-3177	20	10	maps	map	NOUN
ejpam-3177	20	11	and	and	CCONJ
ejpam-3177	20	12	s	s	NOUN
ejpam-3177	20	13	-	-	VERB
ejpam-3177	20	14	manifolds	manifold	NOUN
ejpam-3177	20	15	,	,	PUNCT
ejpam-3177	20	16	we	we	PRON
ejpam-3177	20	17	prove	prove	VERB
ejpam-3177	20	18	the	the	DET
ejpam-3177	20	19	main	main	ADJ
ejpam-3177	20	20	results	result	NOUN
ejpam-3177	20	21	in	in	ADP
ejpam-3177	20	22	third	third	ADJ
ejpam-3177	20	23	section	section	NOUN
ejpam-3177	20	24	.	.	PUNCT
ejpam-3177	21	1	∗corresponding	∗corresponde	VERB
ejpam-3177	21	2	author	author	NOUN
ejpam-3177	21	3	.	.	PUNCT
ejpam-3177	22	1	email	email	NOUN
ejpam-3177	22	2	addresses	address	NOUN
ejpam-3177	22	3	:	:	PUNCT
ejpam-3177	22	4	najma−ar@hotmail.com	najma−ar@hotmail.com	X
ejpam-3177	22	5	(	(	PUNCT
ejpam-3177	22	6	n.	n.	PROPN
ejpam-3177	22	7	a.	a.	PROPN
ejpam-3177	22	8	rehman	rehman	PROPN
ejpam-3177	22	9	)	)	PUNCT
ejpam-3177	22	10	,	,	PUNCT
ejpam-3177	22	11	mehwishbari@yahoo.com	mehwishbari@yahoo.com	X
ejpam-3177	22	12	(	(	PUNCT
ejpam-3177	22	13	m.	m.	NOUN
ejpam-3177	22	14	bari	bari	NOUN
ejpam-3177	22	15	)	)	PUNCT
ejpam-3177	22	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3177	23	1	150	150	NUM
ejpam-3177	23	2	c	c	NOUN
ejpam-3177	23	3	©	©	PROPN
ejpam-3177	23	4	2018	2018	NUM
ejpam-3177	23	5	ejpam	ejpam	VERB
ejpam-3177	23	6	all	all	DET
ejpam-3177	23	7	rights	right	NOUN
ejpam-3177	23	8	reserved	reserve	VERB
ejpam-3177	23	9	.	.	PUNCT
ejpam-3177	24	1	n.	n.	PROPN
ejpam-3177	24	2	a.	a.	PROPN
ejpam-3177	24	3	rehman	rehman	PROPN
ejpam-3177	24	4	,	,	PUNCT
ejpam-3177	24	5	m.	m.	NOUN
ejpam-3177	24	6	bari	bari	NOUN
ejpam-3177	24	7	/	/	SYM
ejpam-3177	24	8	eur	eur	PROPN
ejpam-3177	24	9	.	.	PUNCT
ejpam-3177	25	1	j.	j.	PROPN
ejpam-3177	25	2	pure	pure	PROPN
ejpam-3177	25	3	appl	appl	PROPN
ejpam-3177	25	4	.	.	PROPN
ejpam-3177	25	5	math	math	PROPN
ejpam-3177	25	6	,	,	PUNCT
ejpam-3177	25	7	11	11	NUM
ejpam-3177	25	8	(	(	PUNCT
ejpam-3177	25	9	1	1	NUM
ejpam-3177	25	10	)	)	PUNCT
ejpam-3177	25	11	(	(	PUNCT
ejpam-3177	25	12	2018	2018	NUM
ejpam-3177	25	13	)	)	PUNCT
ejpam-3177	25	14	,	,	PUNCT
ejpam-3177	25	15	150	150	NUM
ejpam-3177	25	16	-	-	SYM
ejpam-3177	25	17	159	159	NUM
ejpam-3177	25	18	151	151	NUM
ejpam-3177	25	19	2	2	NUM
ejpam-3177	25	20	.	.	PUNCT
ejpam-3177	25	21	preliminaries	preliminary	NOUN
ejpam-3177	25	22	in	in	ADP
ejpam-3177	25	23	this	this	DET
ejpam-3177	25	24	section	section	NOUN
ejpam-3177	25	25	,	,	PUNCT
ejpam-3177	25	26	we	we	PRON
ejpam-3177	25	27	recall	recall	VERB
ejpam-3177	25	28	some	some	DET
ejpam-3177	25	29	well	well	ADV
ejpam-3177	25	30	known	know	VERB
ejpam-3177	25	31	facts	fact	NOUN
ejpam-3177	25	32	concerning	concern	VERB
ejpam-3177	25	33	harmonic	harmonic	ADJ
ejpam-3177	25	34	maps	map	NOUN
ejpam-3177	25	35	,	,	PUNCT
ejpam-3177	25	36	biharmonic	biharmonic	NOUN
ejpam-3177	25	37	maps	map	NOUN
ejpam-3177	25	38	and	and	CCONJ
ejpam-3177	25	39	s	s	NOUN
ejpam-3177	25	40	-	-	PUNCT
ejpam-3177	25	41	manifolds	manifold	NOUN
ejpam-3177	25	42	.	.	PUNCT
ejpam-3177	26	1	let	let	VERB
ejpam-3177	26	2	f	f	NOUN
ejpam-3177	26	3	:	:	PUNCT
ejpam-3177	26	4	(	(	PUNCT
ejpam-3177	26	5	m	m	NOUN
ejpam-3177	26	6	,	,	PUNCT
ejpam-3177	26	7	g	g	NOUN
ejpam-3177	26	8	)	)	PUNCT
ejpam-3177	26	9	−→	−→	NOUN
ejpam-3177	26	10	(	(	PUNCT
ejpam-3177	26	11	n	n	CCONJ
ejpam-3177	26	12	,	,	PUNCT
ejpam-3177	26	13	h	h	NOUN
ejpam-3177	26	14	)	)	PUNCT
ejpam-3177	26	15	be	be	VERB
ejpam-3177	26	16	a	a	DET
ejpam-3177	26	17	smooth	smooth	ADJ
ejpam-3177	26	18	map	map	NOUN
ejpam-3177	26	19	between	between	ADP
ejpam-3177	26	20	two	two	NUM
ejpam-3177	26	21	riemannian	riemannian	ADJ
ejpam-3177	26	22	manifolds	manifold	NOUN
ejpam-3177	26	23	of	of	ADP
ejpam-3177	26	24	dimensions	dimension	NOUN
ejpam-3177	26	25	m	m	VERB
ejpam-3177	26	26	and	and	CCONJ
ejpam-3177	26	27	n	n	PRON
ejpam-3177	26	28	respectively	respectively	ADV
ejpam-3177	26	29	.	.	PUNCT
ejpam-3177	27	1	the	the	DET
ejpam-3177	27	2	energy	energy	NOUN
ejpam-3177	27	3	density	density	NOUN
ejpam-3177	27	4	of	of	ADP
ejpam-3177	27	5	f	f	PROPN
ejpam-3177	27	6	is	be	AUX
ejpam-3177	27	7	a	a	DET
ejpam-3177	27	8	smooth	smooth	ADJ
ejpam-3177	27	9	function	function	NOUN
ejpam-3177	27	10	e(f	e(f	PROPN
ejpam-3177	27	11	)	)	PUNCT
ejpam-3177	27	12	:	:	PUNCT
ejpam-3177	28	1	m	m	AUX
ejpam-3177	28	2	−→	−→	ADJ
ejpam-3177	28	3	[	[	X
ejpam-3177	28	4	0,∞	0,∞	NOUN
ejpam-3177	28	5	)	)	PUNCT
ejpam-3177	28	6	given	give	VERB
ejpam-3177	28	7	by	by	ADP
ejpam-3177	28	8	[	[	PUNCT
ejpam-3177	28	9	7	7	NUM
ejpam-3177	28	10	]	]	PUNCT
ejpam-3177	28	11	,	,	PUNCT
ejpam-3177	28	12	e(f	e(f	PROPN
ejpam-3177	28	13	)	)	PUNCT
ejpam-3177	28	14	p	p	NOUN
ejpam-3177	28	15	=	=	NOUN
ejpam-3177	28	16	1	1	NUM
ejpam-3177	28	17	2	2	NUM
ejpam-3177	28	18	trg(f	trg(f	PROPN
ejpam-3177	28	19	∗h)(p	∗h)(p	NOUN
ejpam-3177	28	20	)	)	PUNCT
ejpam-3177	28	21	=	=	SYM
ejpam-3177	28	22	1	1	NUM
ejpam-3177	28	23	2	2	NUM
ejpam-3177	28	24	m∑	m∑	NOUN
ejpam-3177	28	25	i=1	i=1	PRON
ejpam-3177	28	26	h(f∗pui	h(f∗pui	NOUN
ejpam-3177	28	27	,	,	PUNCT
ejpam-3177	28	28	f∗pui	f∗pui	PROPN
ejpam-3177	28	29	)	)	PUNCT
ejpam-3177	28	30	,	,	PUNCT
ejpam-3177	28	31	for	for	ADP
ejpam-3177	28	32	any	any	DET
ejpam-3177	28	33	p	p	NOUN
ejpam-3177	28	34	∈	∈	PROPN
ejpam-3177	28	35	m	m	NOUN
ejpam-3177	28	36	and	and	CCONJ
ejpam-3177	28	37	any	any	DET
ejpam-3177	28	38	orthonormal	orthonormal	ADJ
ejpam-3177	28	39	basis	basis	NOUN
ejpam-3177	28	40	{	{	PUNCT
ejpam-3177	28	41	u1	u1	NOUN
ejpam-3177	28	42	,	,	PUNCT
ejpam-3177	28	43	.	.	PUNCT
ejpam-3177	28	44	.	.	PUNCT
ejpam-3177	28	45	.	.	PUNCT
ejpam-3177	29	1	,	,	PUNCT
ejpam-3177	29	2	um	um	INTJ
ejpam-3177	29	3	}	}	PUNCT
ejpam-3177	29	4	of	of	ADP
ejpam-3177	29	5	tpm	tpm	PROPN
ejpam-3177	29	6	.	.	PUNCT
ejpam-3177	30	1	if	if	SCONJ
ejpam-3177	30	2	m	m	NOUN
ejpam-3177	30	3	is	be	AUX
ejpam-3177	30	4	a	a	DET
ejpam-3177	30	5	compact	compact	ADJ
ejpam-3177	30	6	riemannian	riemannian	ADJ
ejpam-3177	30	7	manifold	manifold	NOUN
ejpam-3177	30	8	,	,	PUNCT
ejpam-3177	30	9	the	the	DET
ejpam-3177	30	10	energy	energy	NOUN
ejpam-3177	30	11	e(f	e(f	PROPN
ejpam-3177	30	12	)	)	PUNCT
ejpam-3177	30	13	of	of	ADP
ejpam-3177	30	14	f	f	PROPN
ejpam-3177	30	15	is	be	AUX
ejpam-3177	30	16	the	the	DET
ejpam-3177	30	17	integral	integral	ADJ
ejpam-3177	30	18	of	of	ADP
ejpam-3177	30	19	its	its	PRON
ejpam-3177	30	20	energy	energy	NOUN
ejpam-3177	30	21	density	density	NOUN
ejpam-3177	30	22	:	:	PUNCT
ejpam-3177	30	23	e(f	e(f	PROPN
ejpam-3177	30	24	)	)	PUNCT
ejpam-3177	31	1	=	=	PUNCT
ejpam-3177	32	1	∫	∫	PROPN
ejpam-3177	32	2	m	m	PROPN
ejpam-3177	32	3	e(f	e(f	PROPN
ejpam-3177	32	4	)	)	PUNCT
ejpam-3177	32	5	υg	υg	INTJ
ejpam-3177	32	6	,	,	PUNCT
ejpam-3177	32	7	where	where	SCONJ
ejpam-3177	32	8	υg	υg	PROPN
ejpam-3177	32	9	is	be	AUX
ejpam-3177	32	10	the	the	DET
ejpam-3177	32	11	volume	volume	NOUN
ejpam-3177	32	12	measure	measure	NOUN
ejpam-3177	32	13	associated	associate	VERB
ejpam-3177	32	14	with	with	ADP
ejpam-3177	32	15	the	the	DET
ejpam-3177	32	16	metric	metric	ADJ
ejpam-3177	32	17	g	g	NOUN
ejpam-3177	32	18	on	on	ADP
ejpam-3177	32	19	m.	m.	NOUN
ejpam-3177	32	20	a	a	DET
ejpam-3177	32	21	map	map	NOUN
ejpam-3177	32	22	f	f	PROPN
ejpam-3177	32	23	∈	∈	PROPN
ejpam-3177	32	24	c∞(m	c∞(m	NOUN
ejpam-3177	32	25	,	,	PUNCT
ejpam-3177	32	26	n	n	CCONJ
ejpam-3177	32	27	)	)	PUNCT
ejpam-3177	32	28	is	be	AUX
ejpam-3177	32	29	said	say	VERB
ejpam-3177	32	30	to	to	PART
ejpam-3177	32	31	be	be	AUX
ejpam-3177	32	32	harmonic	harmonic	ADJ
ejpam-3177	32	33	if	if	SCONJ
ejpam-3177	32	34	it	it	PRON
ejpam-3177	32	35	is	be	AUX
ejpam-3177	32	36	a	a	DET
ejpam-3177	32	37	cricital	cricital	ADJ
ejpam-3177	32	38	point	point	NOUN
ejpam-3177	32	39	of	of	ADP
ejpam-3177	32	40	the	the	DET
ejpam-3177	32	41	energy	energy	NOUN
ejpam-3177	32	42	functional	functional	ADJ
ejpam-3177	32	43	e	e	NOUN
ejpam-3177	32	44	on	on	ADP
ejpam-3177	32	45	the	the	DET
ejpam-3177	32	46	set	set	NOUN
ejpam-3177	32	47	of	of	ADP
ejpam-3177	32	48	all	all	DET
ejpam-3177	32	49	maps	map	NOUN
ejpam-3177	32	50	between	between	ADP
ejpam-3177	32	51	(	(	PUNCT
ejpam-3177	32	52	m	m	PROPN
ejpam-3177	32	53	,	,	PUNCT
ejpam-3177	32	54	g	g	NOUN
ejpam-3177	32	55	)	)	PUNCT
ejpam-3177	32	56	and	and	CCONJ
ejpam-3177	32	57	(	(	PUNCT
ejpam-3177	32	58	n	n	CCONJ
ejpam-3177	32	59	,	,	PUNCT
ejpam-3177	32	60	h	h	NOUN
ejpam-3177	32	61	)	)	PUNCT
ejpam-3177	32	62	.	.	PUNCT
ejpam-3177	33	1	now	now	ADV
ejpam-3177	33	2	,	,	PUNCT
ejpam-3177	33	3	let	let	VERB
ejpam-3177	33	4	(	(	PUNCT
ejpam-3177	33	5	m	m	NOUN
ejpam-3177	33	6	,	,	PUNCT
ejpam-3177	33	7	g	g	NOUN
ejpam-3177	33	8	)	)	PUNCT
ejpam-3177	33	9	be	be	AUX
ejpam-3177	33	10	a	a	DET
ejpam-3177	33	11	compact	compact	ADJ
ejpam-3177	33	12	riemannian	riemannian	ADJ
ejpam-3177	33	13	manifold	manifold	NOUN
ejpam-3177	33	14	.	.	PUNCT
ejpam-3177	34	1	if	if	SCONJ
ejpam-3177	34	2	we	we	PRON
ejpam-3177	34	3	look	look	VERB
ejpam-3177	34	4	at	at	ADP
ejpam-3177	34	5	the	the	DET
ejpam-3177	34	6	euler	euler	NOUN
ejpam-3177	34	7	-	-	PUNCT
ejpam-3177	34	8	lagrange	lagrange	NOUN
ejpam-3177	34	9	equations	equation	NOUN
ejpam-3177	34	10	for	for	ADP
ejpam-3177	34	11	the	the	DET
ejpam-3177	34	12	corresponding	corresponding	ADJ
ejpam-3177	34	13	variational	variational	ADJ
ejpam-3177	34	14	problem	problem	NOUN
ejpam-3177	34	15	,	,	PUNCT
ejpam-3177	34	16	a	a	DET
ejpam-3177	34	17	map	map	NOUN
ejpam-3177	34	18	f	f	X
ejpam-3177	34	19	:	:	PUNCT
ejpam-3177	34	20	m	m	VERB
ejpam-3177	34	21	−→	−→	ADJ
ejpam-3177	34	22	n	n	NOUN
ejpam-3177	34	23	is	be	AUX
ejpam-3177	34	24	harmonic	harmonic	ADJ
ejpam-3177	34	25	if	if	SCONJ
ejpam-3177	34	26	and	and	CCONJ
ejpam-3177	34	27	only	only	ADV
ejpam-3177	34	28	if	if	SCONJ
ejpam-3177	34	29	τ(f	τ(f	NOUN
ejpam-3177	34	30	)	)	PUNCT
ejpam-3177	34	31	≡	≡	PROPN
ejpam-3177	34	32	0	0	NUM
ejpam-3177	34	33	,	,	PUNCT
ejpam-3177	34	34	where	where	SCONJ
ejpam-3177	34	35	τ(f	τ(f	X
ejpam-3177	34	36	)	)	PUNCT
ejpam-3177	34	37	is	be	AUX
ejpam-3177	34	38	the	the	DET
ejpam-3177	34	39	tension	tension	NOUN
ejpam-3177	34	40	field	field	NOUN
ejpam-3177	34	41	which	which	PRON
ejpam-3177	34	42	is	be	AUX
ejpam-3177	34	43	defined	define	VERB
ejpam-3177	34	44	by	by	ADP
ejpam-3177	34	45	τ(f	τ(f	NOUN
ejpam-3177	34	46	)	)	PUNCT
ejpam-3177	35	1	=	=	SYM
ejpam-3177	35	2	trg∇̃df	trg∇̃df	PROPN
ejpam-3177	35	3	,	,	PUNCT
ejpam-3177	35	4	where	where	SCONJ
ejpam-3177	35	5	∇̃	∇̃	PRON
ejpam-3177	35	6	is	be	AUX
ejpam-3177	35	7	the	the	DET
ejpam-3177	35	8	connection	connection	NOUN
ejpam-3177	35	9	induced	induce	VERB
ejpam-3177	35	10	by	by	ADP
ejpam-3177	35	11	the	the	DET
ejpam-3177	35	12	levi	levi	PROPN
ejpam-3177	35	13	-	-	PUNCT
ejpam-3177	35	14	civita	civita	PROPN
ejpam-3177	35	15	connection	connection	NOUN
ejpam-3177	35	16	on	on	ADP
ejpam-3177	35	17	m	m	PROPN
ejpam-3177	35	18	and	and	CCONJ
ejpam-3177	35	19	the	the	DET
ejpam-3177	35	20	f	f	NOUN
ejpam-3177	35	21	-	-	PUNCT
ejpam-3177	35	22	pullback	pullback	NOUN
ejpam-3177	35	23	connection	connection	NOUN
ejpam-3177	35	24	of	of	ADP
ejpam-3177	35	25	the	the	DET
ejpam-3177	35	26	levi	levi	PROPN
ejpam-3177	35	27	civita	civita	PROPN
ejpam-3177	35	28	connection	connection	NOUN
ejpam-3177	35	29	on	on	ADP
ejpam-3177	35	30	n.	n.	NOUN
ejpam-3177	35	31	we	we	PRON
ejpam-3177	35	32	take	take	VERB
ejpam-3177	35	33	now	now	ADV
ejpam-3177	35	34	a	a	DET
ejpam-3177	35	35	smooth	smooth	ADJ
ejpam-3177	35	36	variation	variation	NOUN
ejpam-3177	35	37	fs	f	NOUN
ejpam-3177	35	38	,	,	PUNCT
ejpam-3177	35	39	t	t	NOUN
ejpam-3177	35	40	with	with	ADP
ejpam-3177	35	41	two	two	NUM
ejpam-3177	35	42	parameters	parameter	NOUN
ejpam-3177	35	43	s	s	PART
ejpam-3177	35	44	,	,	PUNCT
ejpam-3177	35	45	t	t	PROPN
ejpam-3177	35	46	∈	∈	PROPN
ejpam-3177	35	47	(	(	PUNCT
ejpam-3177	35	48	−ε	−ε	NOUN
ejpam-3177	35	49	,	,	PUNCT
ejpam-3177	35	50	ε	ε	PROPN
ejpam-3177	35	51	)	)	PUNCT
ejpam-3177	35	52	such	such	ADJ
ejpam-3177	35	53	that	that	SCONJ
ejpam-3177	35	54	f0,0	f0,0	NOUN
ejpam-3177	35	55	=	=	SYM
ejpam-3177	35	56	f	f	PROPN
ejpam-3177	35	57	.	.	PUNCT
ejpam-3177	36	1	the	the	DET
ejpam-3177	36	2	corresponding	corresponding	ADJ
ejpam-3177	36	3	variation	variation	NOUN
ejpam-3177	36	4	vector	vector	NOUN
ejpam-3177	36	5	fields	field	NOUN
ejpam-3177	36	6	are	be	AUX
ejpam-3177	36	7	denoted	denote	VERB
ejpam-3177	36	8	by	by	ADP
ejpam-3177	36	9	v	v	NOUN
ejpam-3177	36	10	and	and	CCONJ
ejpam-3177	36	11	w.	w.	NOUN
ejpam-3177	36	12	the	the	DET
ejpam-3177	36	13	second	second	ADJ
ejpam-3177	36	14	variation	variation	NOUN
ejpam-3177	36	15	formula	formula	NOUN
ejpam-3177	36	16	of	of	ADP
ejpam-3177	36	17	e	e	NOUN
ejpam-3177	36	18	is	be	AUX
ejpam-3177	36	19	:	:	PUNCT
ejpam-3177	36	20	hf	hf	INTJ
ejpam-3177	36	21	(	(	PUNCT
ejpam-3177	36	22	v	v	NOUN
ejpam-3177	36	23	,	,	PUNCT
ejpam-3177	36	24	w	w	NOUN
ejpam-3177	36	25	)	)	PUNCT
ejpam-3177	36	26	=	=	SYM
ejpam-3177	36	27	∂2	∂2	NOUN
ejpam-3177	36	28	∂s∂t	∂s∂t	NOUN
ejpam-3177	36	29	(	(	PUNCT
ejpam-3177	36	30	e(fs	e(fs	PROPN
ejpam-3177	36	31	,	,	PUNCT
ejpam-3177	36	32	t	t	PROPN
ejpam-3177	36	33	)	)	PUNCT
ejpam-3177	36	34	)	)	PUNCT
ejpam-3177	37	1	∣∣	∣∣	PUNCT
ejpam-3177	37	2	(	(	PUNCT
ejpam-3177	37	3	s	s	X
ejpam-3177	37	4	,	,	PUNCT
ejpam-3177	37	5	t)=(0,0	t)=(0,0	NOUN
ejpam-3177	37	6	)	)	PUNCT
ejpam-3177	38	1	=	=	SYM
ejpam-3177	39	1	∫	∫	PROPN
ejpam-3177	39	2	m	m	VERB
ejpam-3177	39	3	h(jf	h(jf	PROPN
ejpam-3177	39	4	(	(	PUNCT
ejpam-3177	39	5	v	v	NOUN
ejpam-3177	39	6	)	)	PUNCT
ejpam-3177	39	7	,	,	PUNCT
ejpam-3177	39	8	w	w	PROPN
ejpam-3177	39	9	)	)	PUNCT
ejpam-3177	39	10	υg	υg	PROPN
ejpam-3177	39	11	,	,	PUNCT
ejpam-3177	39	12	where	where	SCONJ
ejpam-3177	39	13	jf	jf	PROPN
ejpam-3177	39	14	is	be	AUX
ejpam-3177	39	15	a	a	DET
ejpam-3177	39	16	second	second	ADJ
ejpam-3177	39	17	order	order	NOUN
ejpam-3177	39	18	self	self	NOUN
ejpam-3177	39	19	-	-	PUNCT
ejpam-3177	39	20	adjoint	adjoint	NOUN
ejpam-3177	39	21	elliptic	elliptic	ADJ
ejpam-3177	39	22	operator	operator	NOUN
ejpam-3177	39	23	acting	act	VERB
ejpam-3177	39	24	on	on	ADP
ejpam-3177	39	25	the	the	DET
ejpam-3177	39	26	space	space	NOUN
ejpam-3177	39	27	of	of	ADP
ejpam-3177	39	28	variation	variation	NOUN
ejpam-3177	39	29	vector	vector	NOUN
ejpam-3177	39	30	fields	field	NOUN
ejpam-3177	39	31	along	along	ADP
ejpam-3177	39	32	f	f	PROPN
ejpam-3177	39	33	(	(	PUNCT
ejpam-3177	39	34	which	which	PRON
ejpam-3177	39	35	can	can	AUX
ejpam-3177	39	36	be	be	AUX
ejpam-3177	39	37	identified	identify	VERB
ejpam-3177	39	38	with	with	ADP
ejpam-3177	39	39	γ(f−1(tn	γ(f−1(tn	ADJ
ejpam-3177	39	40	)	)	PUNCT
ejpam-3177	39	41	)	)	PUNCT
ejpam-3177	39	42	)	)	PUNCT
ejpam-3177	40	1	and	and	CCONJ
ejpam-3177	40	2	is	be	AUX
ejpam-3177	40	3	defined	define	VERB
ejpam-3177	40	4	by	by	ADP
ejpam-3177	40	5	jf	jf	PROPN
ejpam-3177	40	6	(	(	PUNCT
ejpam-3177	40	7	v	v	NOUN
ejpam-3177	40	8	)	)	PUNCT
ejpam-3177	41	1	=	=	SYM
ejpam-3177	41	2	−	−	PROPN
ejpam-3177	41	3	m∑	m∑	INTJ
ejpam-3177	41	4	i=1	i=1	PROPN
ejpam-3177	41	5	(	(	PUNCT
ejpam-3177	41	6	∇̃ui∇̃ui	∇̃ui∇̃ui	PROPN
ejpam-3177	41	7	−	−	X
ejpam-3177	41	8	∇̃∇uiui	∇̃∇uiui	NOUN
ejpam-3177	41	9	)	)	PUNCT
ejpam-3177	41	10	v	v	ADP
ejpam-3177	41	11	−	−	NOUN
ejpam-3177	41	12	m∑	m∑	INTJ
ejpam-3177	41	13	i=1	i=1	PROPN
ejpam-3177	41	14	rn	rn	PROPN
ejpam-3177	41	15	(	(	PUNCT
ejpam-3177	41	16	v	v	PROPN
ejpam-3177	41	17	,	,	PUNCT
ejpam-3177	41	18	df	df	PROPN
ejpam-3177	41	19	(	(	PUNCT
ejpam-3177	41	20	ui))df	ui))df	PROPN
ejpam-3177	41	21	(	(	PUNCT
ejpam-3177	41	22	ui	ui	NOUN
ejpam-3177	41	23	)	)	PUNCT
ejpam-3177	41	24	,	,	PUNCT
ejpam-3177	41	25	(	(	PUNCT
ejpam-3177	41	26	1	1	X
ejpam-3177	41	27	)	)	PUNCT
ejpam-3177	41	28	for	for	ADP
ejpam-3177	41	29	any	any	DET
ejpam-3177	41	30	v	v	NUM
ejpam-3177	41	31	∈	∈	PROPN
ejpam-3177	41	32	γ(f−1(tn	γ(f−1(tn	NOUN
ejpam-3177	41	33	)	)	PUNCT
ejpam-3177	41	34	)	)	PUNCT
ejpam-3177	41	35	and	and	CCONJ
ejpam-3177	41	36	any	any	DET
ejpam-3177	41	37	local	local	ADJ
ejpam-3177	41	38	orthonormal	orthonormal	ADJ
ejpam-3177	41	39	frame	frame	NOUN
ejpam-3177	41	40	{	{	PUNCT
ejpam-3177	41	41	u1	u1	NOUN
ejpam-3177	41	42	,	,	PUNCT
ejpam-3177	41	43	.	.	PUNCT
ejpam-3177	41	44	.	.	PUNCT
ejpam-3177	42	1	.	.	PUNCT
ejpam-3177	43	1	,	,	PUNCT
ejpam-3177	43	2	um	um	INTJ
ejpam-3177	43	3	}	}	PUNCT
ejpam-3177	43	4	on	on	ADP
ejpam-3177	43	5	m.	m.	NOUN
ejpam-3177	43	6	here	here	ADV
ejpam-3177	43	7	rn	rn	PROPN
ejpam-3177	43	8	is	be	AUX
ejpam-3177	43	9	the	the	DET
ejpam-3177	43	10	curvature	curvature	NOUN
ejpam-3177	43	11	tensor	tensor	NOUN
ejpam-3177	43	12	of	of	ADP
ejpam-3177	43	13	(	(	PUNCT
ejpam-3177	43	14	n	n	CCONJ
ejpam-3177	43	15	,	,	PUNCT
ejpam-3177	43	16	h	h	NOUN
ejpam-3177	43	17	)	)	PUNCT
ejpam-3177	43	18	(	(	PUNCT
ejpam-3177	43	19	see	see	VERB
ejpam-3177	43	20	[	[	X
ejpam-3177	43	21	9	9	X
ejpam-3177	43	22	]	]	PUNCT
ejpam-3177	43	23	for	for	ADP
ejpam-3177	43	24	more	more	ADJ
ejpam-3177	43	25	details	detail	NOUN
ejpam-3177	43	26	on	on	ADP
ejpam-3177	43	27	harmonic	harmonic	ADJ
ejpam-3177	43	28	maps	map	NOUN
ejpam-3177	43	29	)	)	PUNCT
ejpam-3177	43	30	.	.	PUNCT
ejpam-3177	44	1	j.	j.	PROPN
ejpam-3177	44	2	eells	eells	PROPN
ejpam-3177	44	3	and	and	CCONJ
ejpam-3177	44	4	l.	l.	PROPN
ejpam-3177	44	5	lemaire	lemaire	PROPN
ejpam-3177	45	1	[	[	X
ejpam-3177	45	2	9	9	X
ejpam-3177	45	3	]	]	PUNCT
ejpam-3177	45	4	proposed	propose	VERB
ejpam-3177	45	5	polyharmonic	polyharmonic	ADJ
ejpam-3177	45	6	(	(	PUNCT
ejpam-3177	45	7	k	k	NOUN
ejpam-3177	45	8	-	-	ADJ
ejpam-3177	45	9	harmonic	harmonic	ADJ
ejpam-3177	45	10	)	)	PUNCT
ejpam-3177	45	11	maps	map	NOUN
ejpam-3177	45	12	,	,	PUNCT
ejpam-3177	45	13	and	and	CCONJ
ejpam-3177	45	14	jiang	jiang	X
ejpam-3177	46	1	[	[	X
ejpam-3177	46	2	8	8	NUM
ejpam-3177	46	3	]	]	X
ejpam-3177	46	4	n.	n.	PROPN
ejpam-3177	46	5	a.	a.	PROPN
ejpam-3177	46	6	rehman	rehman	PROPN
ejpam-3177	46	7	,	,	PUNCT
ejpam-3177	46	8	m.	m.	NOUN
ejpam-3177	46	9	bari	bari	NOUN
ejpam-3177	46	10	/	/	SYM
ejpam-3177	46	11	eur	eur	PROPN
ejpam-3177	46	12	.	.	PUNCT
ejpam-3177	47	1	j.	j.	PROPN
ejpam-3177	47	2	pure	pure	PROPN
ejpam-3177	47	3	appl	appl	PROPN
ejpam-3177	47	4	.	.	PROPN
ejpam-3177	47	5	math	math	PROPN
ejpam-3177	47	6	,	,	PUNCT
ejpam-3177	47	7	11	11	NUM
ejpam-3177	47	8	(	(	PUNCT
ejpam-3177	47	9	1	1	NUM
ejpam-3177	47	10	)	)	PUNCT
ejpam-3177	47	11	(	(	PUNCT
ejpam-3177	47	12	2018	2018	NUM
ejpam-3177	47	13	)	)	PUNCT
ejpam-3177	47	14	,	,	PUNCT
ejpam-3177	47	15	150	150	NUM
ejpam-3177	47	16	-	-	SYM
ejpam-3177	47	17	159	159	NUM
ejpam-3177	47	18	152	152	NUM
ejpam-3177	47	19	studied	study	VERB
ejpam-3177	47	20	the	the	DET
ejpam-3177	47	21	first	first	ADJ
ejpam-3177	47	22	and	and	CCONJ
ejpam-3177	47	23	second	second	ADJ
ejpam-3177	47	24	variation	variation	NOUN
ejpam-3177	47	25	formulas	formula	NOUN
ejpam-3177	47	26	of	of	ADP
ejpam-3177	47	27	biharmonic	biharmonic	NOUN
ejpam-3177	47	28	maps	map	NOUN
ejpam-3177	47	29	.	.	PUNCT
ejpam-3177	48	1	let	let	VERB
ejpam-3177	48	2	us	we	PRON
ejpam-3177	48	3	consider	consider	VERB
ejpam-3177	48	4	the	the	DET
ejpam-3177	48	5	bienergy	bienergy	NOUN
ejpam-3177	48	6	functional	functional	ADJ
ejpam-3177	48	7	defined	define	VERB
ejpam-3177	48	8	by	by	ADP
ejpam-3177	48	9	:	:	PUNCT
ejpam-3177	48	10	e2(f	e2(f	ADJ
ejpam-3177	48	11	)	)	PUNCT
ejpam-3177	48	12	=	=	SYM
ejpam-3177	48	13	1	1	NUM
ejpam-3177	48	14	2	2	NUM
ejpam-3177	48	15	∫	∫	NOUN
ejpam-3177	48	16	m	m	NOUN
ejpam-3177	48	17	|	|	ADV
ejpam-3177	48	18	τ(f	τ(f	NOUN
ejpam-3177	48	19	)	)	PUNCT
ejpam-3177	48	20	|2	|2	NUM
ejpam-3177	49	1	νg	νg	NOUN
ejpam-3177	49	2	,	,	PUNCT
ejpam-3177	49	3	(	(	PUNCT
ejpam-3177	49	4	2	2	X
ejpam-3177	49	5	)	)	PUNCT
ejpam-3177	49	6	where	where	SCONJ
ejpam-3177	49	7	|	|	ADV
ejpam-3177	49	8	v	v	ADP
ejpam-3177	49	9	|2=	|2=	NOUN
ejpam-3177	49	10	h(v	h(v	PROPN
ejpam-3177	49	11	,	,	PUNCT
ejpam-3177	49	12	v	v	NOUN
ejpam-3177	49	13	)	)	PUNCT
ejpam-3177	49	14	,	,	PUNCT
ejpam-3177	49	15	v	v	ADP
ejpam-3177	49	16	∈	∈	PROPN
ejpam-3177	49	17	γ(f−1tn	γ(f−1tn	NOUN
ejpam-3177	49	18	)	)	PUNCT
ejpam-3177	49	19	.	.	PUNCT
ejpam-3177	50	1	then	then	ADV
ejpam-3177	50	2	,	,	PUNCT
ejpam-3177	50	3	the	the	DET
ejpam-3177	50	4	first	first	ADJ
ejpam-3177	50	5	variation	variation	NOUN
ejpam-3177	50	6	formula	formula	NOUN
ejpam-3177	50	7	of	of	ADP
ejpam-3177	50	8	the	the	DET
ejpam-3177	50	9	bienergy	bienergy	NOUN
ejpam-3177	50	10	functional	functional	ADJ
ejpam-3177	50	11	is	be	AUX
ejpam-3177	50	12	given	give	VERB
ejpam-3177	50	13	by	by	ADP
ejpam-3177	50	14	:	:	PUNCT
ejpam-3177	50	15	d	d	X
ejpam-3177	50	16	dt	dt	X
ejpam-3177	50	17	|t=0	|t=0	PROPN
ejpam-3177	50	18	e2(ft	e2(ft	PROPN
ejpam-3177	50	19	)	)	PUNCT
ejpam-3177	50	20	=	=	PUNCT
ejpam-3177	51	1	−	−	PROPN
ejpam-3177	51	2	∫	∫	PROPN
ejpam-3177	51	3	m	m	NOUN
ejpam-3177	51	4	h(τ2(f	h(τ2(f	PROPN
ejpam-3177	51	5	)	)	PUNCT
ejpam-3177	51	6	,	,	PUNCT
ejpam-3177	51	7	v	v	NOUN
ejpam-3177	51	8	)	)	PUNCT
ejpam-3177	51	9	νg	νg	NOUN
ejpam-3177	51	10	,	,	PUNCT
ejpam-3177	51	11	(	(	PUNCT
ejpam-3177	51	12	3	3	X
ejpam-3177	51	13	)	)	PUNCT
ejpam-3177	51	14	here	here	ADV
ejpam-3177	51	15	τ2(f	τ2(f	X
ejpam-3177	51	16	)	)	PUNCT
ejpam-3177	51	17	:	:	PUNCT
ejpam-3177	51	18	=	=	PUNCT
ejpam-3177	51	19	j(τ(f	j(τ(f	PROPN
ejpam-3177	51	20	)	)	PUNCT
ejpam-3177	51	21	)	)	PUNCT
ejpam-3177	52	1	=	=	SYM
ejpam-3177	52	2	4̄(τ(f	4̄(τ(f	NUM
ejpam-3177	52	3	)	)	PUNCT
ejpam-3177	52	4	)	)	PUNCT
ejpam-3177	52	5	−r(τ(f	−r(τ(f	NUM
ejpam-3177	52	6	)	)	PUNCT
ejpam-3177	52	7	)	)	PUNCT
ejpam-3177	52	8	,	,	PUNCT
ejpam-3177	52	9	(	(	PUNCT
ejpam-3177	52	10	4	4	X
ejpam-3177	52	11	)	)	PUNCT
ejpam-3177	52	12	which	which	PRON
ejpam-3177	52	13	is	be	AUX
ejpam-3177	52	14	called	call	VERB
ejpam-3177	52	15	the	the	DET
ejpam-3177	52	16	bitension	bitension	NOUN
ejpam-3177	52	17	field	field	NOUN
ejpam-3177	52	18	of	of	ADP
ejpam-3177	52	19	f	f	PROPN
ejpam-3177	52	20	and	and	CCONJ
ejpam-3177	52	21	j	j	PROPN
ejpam-3177	52	22	is	be	AUX
ejpam-3177	52	23	given	give	VERB
ejpam-3177	52	24	by	by	ADP
ejpam-3177	52	25	(	(	PUNCT
ejpam-3177	52	26	1	1	NUM
ejpam-3177	52	27	)	)	PUNCT
ejpam-3177	52	28	.	.	PUNCT
ejpam-3177	53	1	a	a	DET
ejpam-3177	53	2	smooth	smooth	ADJ
ejpam-3177	53	3	map	map	NOUN
ejpam-3177	53	4	f	f	PROPN
ejpam-3177	53	5	of	of	ADP
ejpam-3177	53	6	(	(	PUNCT
ejpam-3177	53	7	m	m	PROPN
ejpam-3177	53	8	,	,	PUNCT
ejpam-3177	53	9	g	g	NOUN
ejpam-3177	53	10	)	)	PUNCT
ejpam-3177	53	11	into	into	ADP
ejpam-3177	53	12	(	(	PUNCT
ejpam-3177	53	13	n	n	CCONJ
ejpam-3177	53	14	,	,	PUNCT
ejpam-3177	53	15	h	h	NOUN
ejpam-3177	53	16	)	)	PUNCT
ejpam-3177	53	17	is	be	AUX
ejpam-3177	53	18	said	say	VERB
ejpam-3177	53	19	to	to	PART
ejpam-3177	53	20	be	be	AUX
ejpam-3177	53	21	biharmonic	biharmonic	ADJ
ejpam-3177	53	22	if	if	SCONJ
ejpam-3177	53	23	τ2(f	τ2(f	PROPN
ejpam-3177	53	24	)	)	PUNCT
ejpam-3177	53	25	=	=	SYM
ejpam-3177	54	1	0	0	X
ejpam-3177	54	2	.	.	PUNCT
ejpam-3177	55	1	as	as	ADP
ejpam-3177	55	2	a	a	DET
ejpam-3177	55	3	generalization	generalization	NOUN
ejpam-3177	55	4	of	of	ADP
ejpam-3177	55	5	both	both	DET
ejpam-3177	55	6	almost	almost	ADV
ejpam-3177	55	7	complex	complex	ADJ
ejpam-3177	55	8	(	(	PUNCT
ejpam-3177	55	9	in	in	ADP
ejpam-3177	55	10	even	even	ADV
ejpam-3177	55	11	dimension	dimension	NOUN
ejpam-3177	55	12	)	)	PUNCT
ejpam-3177	55	13	and	and	CCONJ
ejpam-3177	55	14	almost	almost	ADV
ejpam-3177	55	15	contact	contact	NOUN
ejpam-3177	55	16	(	(	PUNCT
ejpam-3177	55	17	in	in	ADP
ejpam-3177	55	18	odd	odd	ADJ
ejpam-3177	55	19	dimension	dimension	NOUN
ejpam-3177	55	20	)	)	PUNCT
ejpam-3177	55	21	structures	structure	NOUN
ejpam-3177	55	22	,	,	PUNCT
ejpam-3177	55	23	yano	yano	PROPN
ejpam-3177	55	24	introduced	introduce	VERB
ejpam-3177	55	25	in	in	ADP
ejpam-3177	55	26	[	[	X
ejpam-3177	55	27	17	17	NUM
ejpam-3177	55	28	]	]	PUNCT
ejpam-3177	55	29	the	the	DET
ejpam-3177	55	30	notion	notion	NOUN
ejpam-3177	55	31	of	of	ADP
ejpam-3177	55	32	f	f	PROPN
ejpam-3177	55	33	-structure	-structure	NOUN
ejpam-3177	55	34	on	on	ADP
ejpam-3177	55	35	a	a	DET
ejpam-3177	55	36	smooth	smooth	ADJ
ejpam-3177	55	37	manifold	manifold	NOUN
ejpam-3177	55	38	of	of	ADP
ejpam-3177	55	39	dimension	dimension	NOUN
ejpam-3177	55	40	2n	2n	NUM
ejpam-3177	55	41	+	+	CCONJ
ejpam-3177	55	42	s	s	NOUN
ejpam-3177	55	43	,	,	PUNCT
ejpam-3177	55	44	i.e.	i.e.	X
ejpam-3177	55	45	a	a	DET
ejpam-3177	55	46	tensor	tensor	NOUN
ejpam-3177	55	47	field	field	NOUN
ejpam-3177	55	48	of	of	ADP
ejpam-3177	55	49	type	type	NOUN
ejpam-3177	55	50	(	(	PUNCT
ejpam-3177	55	51	1,1	1,1	NUM
ejpam-3177	55	52	)	)	PUNCT
ejpam-3177	55	53	and	and	CCONJ
ejpam-3177	55	54	rank	rank	NOUN
ejpam-3177	55	55	2n	2n	NUM
ejpam-3177	55	56	satisfying	satisfy	VERB
ejpam-3177	55	57	f3	f3	PROPN
ejpam-3177	55	58	+	+	PROPN
ejpam-3177	55	59	f	f	NOUN
ejpam-3177	55	60	=	=	SYM
ejpam-3177	55	61	0	0	PROPN
ejpam-3177	55	62	.	.	PUNCT
ejpam-3177	56	1	the	the	DET
ejpam-3177	56	2	existence	existence	NOUN
ejpam-3177	56	3	of	of	ADP
ejpam-3177	56	4	such	such	DET
ejpam-3177	56	5	a	a	DET
ejpam-3177	56	6	structure	structure	NOUN
ejpam-3177	56	7	is	be	AUX
ejpam-3177	56	8	equivalent	equivalent	ADJ
ejpam-3177	56	9	to	to	ADP
ejpam-3177	56	10	a	a	DET
ejpam-3177	56	11	reduction	reduction	NOUN
ejpam-3177	56	12	of	of	ADP
ejpam-3177	56	13	the	the	DET
ejpam-3177	56	14	structural	structural	ADJ
ejpam-3177	56	15	group	group	NOUN
ejpam-3177	56	16	of	of	ADP
ejpam-3177	56	17	the	the	DET
ejpam-3177	56	18	tangent	tangent	NOUN
ejpam-3177	56	19	bundle	bundle	NOUN
ejpam-3177	56	20	to	to	ADP
ejpam-3177	56	21	u(n	u(n	PROPN
ejpam-3177	56	22	)	)	PUNCT
ejpam-3177	56	23	×	×	PROPN
ejpam-3177	56	24	o(s	o(s	PROPN
ejpam-3177	56	25	)	)	PUNCT
ejpam-3177	56	26	.	.	PUNCT
ejpam-3177	57	1	let	let	VERB
ejpam-3177	57	2	n	n	PRON
ejpam-3177	57	3	be	be	AUX
ejpam-3177	57	4	a	a	DET
ejpam-3177	57	5	(	(	PUNCT
ejpam-3177	57	6	2n	2n	ADJ
ejpam-3177	57	7	+	+	CCONJ
ejpam-3177	57	8	s)-dimensional	s)-dimensional	ADJ
ejpam-3177	57	9	manifold	manifold	NOUN
ejpam-3177	57	10	with	with	ADP
ejpam-3177	57	11	an	an	DET
ejpam-3177	57	12	f	f	NOUN
ejpam-3177	57	13	-structure	-structure	NOUN
ejpam-3177	57	14	of	of	ADP
ejpam-3177	57	15	rank	rank	NOUN
ejpam-3177	57	16	2n	2n	NUM
ejpam-3177	57	17	.	.	PUNCT
ejpam-3177	58	1	if	if	SCONJ
ejpam-3177	58	2	there	there	PRON
ejpam-3177	58	3	exist	exist	VERB
ejpam-3177	58	4	s	s	PART
ejpam-3177	58	5	global	global	ADJ
ejpam-3177	58	6	vector	vector	PROPN
ejpam-3177	58	7	fields	field	NOUN
ejpam-3177	58	8	ξ1	ξ1	NOUN
ejpam-3177	58	9	,	,	PUNCT
ejpam-3177	58	10	ξ2	ξ2	NOUN
ejpam-3177	58	11	,	,	PUNCT
ejpam-3177	58	12	.	.	PUNCT
ejpam-3177	59	1	.	.	PUNCT
ejpam-3177	60	1	.	.	PUNCT
ejpam-3177	61	1	,	,	PUNCT
ejpam-3177	61	2	ξs	ξs	VERB
ejpam-3177	61	3	on	on	ADP
ejpam-3177	61	4	n	n	CCONJ
ejpam-3177	61	5	such	such	ADJ
ejpam-3177	61	6	that	that	PRON
ejpam-3177	61	7	:	:	PUNCT
ejpam-3177	61	8	fξα	fξα	NOUN
ejpam-3177	61	9	=	=	SYM
ejpam-3177	61	10	0	0	PROPN
ejpam-3177	61	11	,	,	PUNCT
ejpam-3177	61	12	ηα	ηα	NOUN
ejpam-3177	61	13	◦	◦	NOUN
ejpam-3177	61	14	f	f	X
ejpam-3177	61	15	=	=	SYM
ejpam-3177	61	16	0	0	NUM
ejpam-3177	61	17	,	,	PUNCT
ejpam-3177	61	18	f2	f2	PROPN
ejpam-3177	61	19	=	=	PUNCT
ejpam-3177	61	20	−i	−i	PROPN
ejpam-3177	62	1	+	+	CCONJ
ejpam-3177	62	2	∑	∑	PUNCT
ejpam-3177	62	3	ξα	ξα	PROPN
ejpam-3177	62	4	⊗	⊗	PROPN
ejpam-3177	62	5	ηα	ηα	PROPN
ejpam-3177	62	6	,	,	PUNCT
ejpam-3177	62	7	(	(	PUNCT
ejpam-3177	62	8	5	5	NUM
ejpam-3177	62	9	)	)	PUNCT
ejpam-3177	62	10	where	where	SCONJ
ejpam-3177	62	11	ηα	ηα	PROPN
ejpam-3177	62	12	are	be	AUX
ejpam-3177	62	13	the	the	DET
ejpam-3177	62	14	dual	dual	ADJ
ejpam-3177	62	15	1	1	NUM
ejpam-3177	62	16	-	-	PUNCT
ejpam-3177	62	17	forms	form	NOUN
ejpam-3177	62	18	of	of	ADP
ejpam-3177	62	19	ξα	ξα	NOUN
ejpam-3177	62	20	,	,	PUNCT
ejpam-3177	62	21	we	we	PRON
ejpam-3177	62	22	say	say	VERB
ejpam-3177	62	23	that	that	SCONJ
ejpam-3177	62	24	the	the	DET
ejpam-3177	62	25	f	f	PROPN
ejpam-3177	62	26	-structure	-structure	NOUN
ejpam-3177	62	27	has	have	VERB
ejpam-3177	62	28	complemented	complement	VERB
ejpam-3177	62	29	frames	frame	NOUN
ejpam-3177	62	30	.	.	PUNCT
ejpam-3177	63	1	for	for	ADP
ejpam-3177	63	2	such	such	DET
ejpam-3177	63	3	a	a	DET
ejpam-3177	63	4	manifold	manifold	ADJ
ejpam-3177	63	5	there	there	PRON
ejpam-3177	63	6	exists	exist	VERB
ejpam-3177	63	7	a	a	DET
ejpam-3177	63	8	riemannian	riemannian	ADJ
ejpam-3177	63	9	metric	metric	NOUN
ejpam-3177	63	10	g	g	PROPN
ejpam-3177	63	11	such	such	ADJ
ejpam-3177	63	12	that	that	SCONJ
ejpam-3177	63	13	g(x	g(x	NOUN
ejpam-3177	63	14	,	,	PUNCT
ejpam-3177	63	15	y	y	NOUN
ejpam-3177	63	16	)	)	PUNCT
ejpam-3177	64	1	=	=	SYM
ejpam-3177	64	2	g(fx	g(fx	NOUN
ejpam-3177	64	3	,	,	PUNCT
ejpam-3177	64	4	fy	fy	PROPN
ejpam-3177	64	5	)	)	PUNCT
ejpam-3177	65	1	+	+	CCONJ
ejpam-3177	65	2	∑	∑	PART
ejpam-3177	65	3	ηα(x)ηα(y	ηα(x)ηα(y	NOUN
ejpam-3177	65	4	)	)	PUNCT
ejpam-3177	65	5	for	for	ADP
ejpam-3177	65	6	any	any	DET
ejpam-3177	65	7	vector	vector	NOUN
ejpam-3177	65	8	fields	field	NOUN
ejpam-3177	65	9	x	x	PUNCT
ejpam-3177	65	10	and	and	CCONJ
ejpam-3177	65	11	y	y	PROPN
ejpam-3177	65	12	on	on	ADP
ejpam-3177	65	13	n	n	PROPN
ejpam-3177	65	14	.	.	PUNCT
ejpam-3177	66	1	see	see	VERB
ejpam-3177	66	2	[	[	X
ejpam-3177	66	3	1	1	NUM
ejpam-3177	66	4	]	]	PUNCT
ejpam-3177	66	5	.	.	PUNCT
ejpam-3177	67	1	an	an	DET
ejpam-3177	67	2	f	f	PROPN
ejpam-3177	67	3	-structure	-structure	PROPN
ejpam-3177	67	4	f	f	PROPN
ejpam-3177	67	5	is	be	AUX
ejpam-3177	67	6	normal	normal	ADJ
ejpam-3177	67	7	,	,	PUNCT
ejpam-3177	67	8	if	if	SCONJ
ejpam-3177	67	9	it	it	PRON
ejpam-3177	67	10	has	have	AUX
ejpam-3177	67	11	complemented	complement	VERB
ejpam-3177	67	12	frames	frame	NOUN
ejpam-3177	67	13	and	and	CCONJ
ejpam-3177	67	14	[	[	X
ejpam-3177	67	15	f	f	X
ejpam-3177	67	16	,	,	PUNCT
ejpam-3177	67	17	f	f	X
ejpam-3177	67	18	]	]	PUNCT
ejpam-3177	68	1	+	+	CCONJ
ejpam-3177	68	2	2	2	NUM
ejpam-3177	68	3	∑	∑	ADP
ejpam-3177	68	4	ξα	ξα	PROPN
ejpam-3177	68	5	⊗	⊗	PROPN
ejpam-3177	68	6	dηα	dηα	NOUN
ejpam-3177	68	7	=	=	SYM
ejpam-3177	68	8	0	0	PROPN
ejpam-3177	68	9	,	,	PUNCT
ejpam-3177	68	10	where	where	SCONJ
ejpam-3177	68	11	[	[	X
ejpam-3177	68	12	f	f	X
ejpam-3177	68	13	,	,	PUNCT
ejpam-3177	68	14	f	f	X
ejpam-3177	68	15	]	]	PUNCT
ejpam-3177	68	16	is	be	AUX
ejpam-3177	68	17	nijenhuis	nijenhuis	NOUN
ejpam-3177	68	18	torsion	torsion	NOUN
ejpam-3177	68	19	of	of	ADP
ejpam-3177	68	20	f	f	PROPN
ejpam-3177	68	21	.	.	PUNCT
ejpam-3177	69	1	let	let	VERB
ejpam-3177	69	2	ω	ω	NUM
ejpam-3177	69	3	be	be	AUX
ejpam-3177	69	4	the	the	DET
ejpam-3177	69	5	fundamental	fundamental	ADJ
ejpam-3177	69	6	2	2	NUM
ejpam-3177	69	7	-	-	PUNCT
ejpam-3177	69	8	form	form	NOUN
ejpam-3177	69	9	defined	define	VERB
ejpam-3177	69	10	by	by	ADP
ejpam-3177	69	11	ω(x	ω(x	NOUN
ejpam-3177	69	12	,	,	PUNCT
ejpam-3177	69	13	y	y	NOUN
ejpam-3177	69	14	)	)	PUNCT
ejpam-3177	70	1	=	=	SYM
ejpam-3177	70	2	g(x	g(x	PROPN
ejpam-3177	70	3	,	,	PUNCT
ejpam-3177	70	4	fy	fy	PROPN
ejpam-3177	70	5	)	)	PUNCT
ejpam-3177	70	6	,	,	PUNCT
ejpam-3177	70	7	x	x	X
ejpam-3177	70	8	,	,	PUNCT
ejpam-3177	70	9	y	y	PROPN
ejpam-3177	70	10	∈	∈	PROPN
ejpam-3177	70	11	t	t	PROPN
ejpam-3177	70	12	(	(	PUNCT
ejpam-3177	70	13	n	n	CCONJ
ejpam-3177	70	14	)	)	PUNCT
ejpam-3177	70	15	.	.	PUNCT
ejpam-3177	71	1	a	a	DET
ejpam-3177	71	2	normal	normal	ADJ
ejpam-3177	71	3	f	f	NOUN
ejpam-3177	71	4	-structure	-structure	NOUN
ejpam-3177	71	5	for	for	ADP
ejpam-3177	71	6	which	which	PRON
ejpam-3177	71	7	the	the	DET
ejpam-3177	71	8	fundamental	fundamental	ADJ
ejpam-3177	71	9	form	form	NOUN
ejpam-3177	71	10	ω	ω	PROPN
ejpam-3177	71	11	is	be	AUX
ejpam-3177	71	12	closed	closed	ADJ
ejpam-3177	71	13	,	,	PUNCT
ejpam-3177	71	14	η1∧	η1∧	PROPN
ejpam-3177	71	15	·	·	PUNCT
ejpam-3177	71	16	·	·	PUNCT
ejpam-3177	71	17	·	·	PUNCT
ejpam-3177	71	18	∧ηs∧(dηα)n	∧ηs∧(dηα)n	PROPN
ejpam-3177	71	19	6=	6=	ADP
ejpam-3177	71	20	0	0	NUM
ejpam-3177	71	21	for	for	ADP
ejpam-3177	71	22	any	any	DET
ejpam-3177	71	23	α	α	NOUN
ejpam-3177	71	24	,	,	PUNCT
ejpam-3177	71	25	and	and	CCONJ
ejpam-3177	71	26	dη1	dη1	X
ejpam-3177	71	27	=	=	SYM
ejpam-3177	71	28	·	·	PUNCT
ejpam-3177	71	29	·	·	PUNCT
ejpam-3177	71	30	·	·	PUNCT
ejpam-3177	72	1	=	=	SYM
ejpam-3177	72	2	dηs	dηs	PROPN
ejpam-3177	72	3	=	=	SYM
ejpam-3177	72	4	ω	ω	PROPN
ejpam-3177	72	5	is	be	AUX
ejpam-3177	72	6	called	call	VERB
ejpam-3177	72	7	to	to	PART
ejpam-3177	72	8	be	be	AUX
ejpam-3177	72	9	an	an	DET
ejpam-3177	72	10	s	s	NOUN
ejpam-3177	72	11	-	-	NOUN
ejpam-3177	72	12	structure	structure	NOUN
ejpam-3177	72	13	.	.	PUNCT
ejpam-3177	73	1	a	a	DET
ejpam-3177	73	2	smooth	smooth	ADJ
ejpam-3177	73	3	manifold	manifold	NOUN
ejpam-3177	73	4	endowed	endow	VERB
ejpam-3177	73	5	with	with	ADP
ejpam-3177	73	6	an	an	DET
ejpam-3177	73	7	s	s	NOUN
ejpam-3177	73	8	-	-	NOUN
ejpam-3177	73	9	structure	structure	NOUN
ejpam-3177	73	10	will	will	AUX
ejpam-3177	73	11	be	be	AUX
ejpam-3177	73	12	called	call	VERB
ejpam-3177	73	13	an	an	DET
ejpam-3177	73	14	s	s	NOUN
ejpam-3177	73	15	-	-	ADJ
ejpam-3177	73	16	manifold	manifold	ADJ
ejpam-3177	73	17	.	.	PUNCT
ejpam-3177	74	1	these	these	DET
ejpam-3177	74	2	manifolds	manifold	NOUN
ejpam-3177	74	3	were	be	AUX
ejpam-3177	74	4	introduced	introduce	VERB
ejpam-3177	74	5	by	by	ADP
ejpam-3177	74	6	blair	blair	PROPN
ejpam-3177	74	7	in	in	ADP
ejpam-3177	74	8	[	[	X
ejpam-3177	74	9	1	1	NUM
ejpam-3177	74	10	]	]	PUNCT
ejpam-3177	74	11	.	.	PUNCT
ejpam-3177	75	1	n.	n.	PROPN
ejpam-3177	75	2	a.	a.	PROPN
ejpam-3177	75	3	rehman	rehman	PROPN
ejpam-3177	75	4	,	,	PUNCT
ejpam-3177	75	5	m.	m.	NOUN
ejpam-3177	75	6	bari	bari	NOUN
ejpam-3177	75	7	/	/	SYM
ejpam-3177	75	8	eur	eur	PROPN
ejpam-3177	75	9	.	.	PUNCT
ejpam-3177	76	1	j.	j.	PROPN
ejpam-3177	76	2	pure	pure	PROPN
ejpam-3177	76	3	appl	appl	PROPN
ejpam-3177	76	4	.	.	PROPN
ejpam-3177	76	5	math	math	PROPN
ejpam-3177	76	6	,	,	PUNCT
ejpam-3177	76	7	11	11	NUM
ejpam-3177	76	8	(	(	PUNCT
ejpam-3177	76	9	1	1	NUM
ejpam-3177	76	10	)	)	PUNCT
ejpam-3177	76	11	(	(	PUNCT
ejpam-3177	76	12	2018	2018	NUM
ejpam-3177	76	13	)	)	PUNCT
ejpam-3177	76	14	,	,	PUNCT
ejpam-3177	76	15	150	150	NUM
ejpam-3177	76	16	-	-	SYM
ejpam-3177	76	17	159	159	NUM
ejpam-3177	76	18	153	153	NUM
ejpam-3177	76	19	we	we	PRON
ejpam-3177	76	20	have	have	VERB
ejpam-3177	76	21	to	to	PART
ejpam-3177	76	22	remark	remark	VERB
ejpam-3177	76	23	that	that	SCONJ
ejpam-3177	76	24	if	if	SCONJ
ejpam-3177	76	25	we	we	PRON
ejpam-3177	76	26	take	take	VERB
ejpam-3177	76	27	s	s	NOUN
ejpam-3177	76	28	=	=	SYM
ejpam-3177	76	29	1	1	NUM
ejpam-3177	76	30	,	,	PUNCT
ejpam-3177	76	31	s	s	NOUN
ejpam-3177	76	32	-	-	PUNCT
ejpam-3177	76	33	manifolds	manifold	NOUN
ejpam-3177	76	34	are	be	AUX
ejpam-3177	76	35	natural	natural	ADJ
ejpam-3177	76	36	generalizations	generalization	NOUN
ejpam-3177	76	37	of	of	ADP
ejpam-3177	76	38	sasakian	sasakian	ADJ
ejpam-3177	76	39	manifolds	manifold	NOUN
ejpam-3177	76	40	.	.	PUNCT
ejpam-3177	77	1	in	in	ADP
ejpam-3177	77	2	the	the	DET
ejpam-3177	77	3	case	case	NOUN
ejpam-3177	77	4	s	s	PART
ejpam-3177	77	5	≥	≥	NOUN
ejpam-3177	77	6	2	2	NUM
ejpam-3177	77	7	some	some	DET
ejpam-3177	77	8	interesting	interesting	ADJ
ejpam-3177	77	9	examples	example	NOUN
ejpam-3177	77	10	are	be	AUX
ejpam-3177	77	11	given	give	VERB
ejpam-3177	77	12	in	in	ADP
ejpam-3177	77	13	[	[	X
ejpam-3177	77	14	1	1	NUM
ejpam-3177	77	15	]	]	PUNCT
ejpam-3177	77	16	.	.	PUNCT
ejpam-3177	78	1	if	if	SCONJ
ejpam-3177	78	2	n	n	PRON
ejpam-3177	78	3	is	be	AUX
ejpam-3177	78	4	an	an	DET
ejpam-3177	78	5	s	s	NOUN
ejpam-3177	78	6	-	-	ADJ
ejpam-3177	78	7	manifold	manifold	ADJ
ejpam-3177	78	8	,	,	PUNCT
ejpam-3177	78	9	then	then	ADV
ejpam-3177	78	10	the	the	DET
ejpam-3177	78	11	following	follow	VERB
ejpam-3177	78	12	formulas	formula	NOUN
ejpam-3177	78	13	are	be	AUX
ejpam-3177	78	14	true	true	ADJ
ejpam-3177	78	15	(	(	PUNCT
ejpam-3177	78	16	see	see	VERB
ejpam-3177	78	17	[	[	X
ejpam-3177	78	18	1	1	NUM
ejpam-3177	78	19	]	]	PUNCT
ejpam-3177	78	20	):	):	PUNCT
ejpam-3177	78	21	∇xξα	∇xξα	NOUN
ejpam-3177	78	22	=	=	SYM
ejpam-3177	78	23	−fx	−fx	PROPN
ejpam-3177	78	24	,	,	PUNCT
ejpam-3177	78	25	x	x	PROPN
ejpam-3177	78	26	∈	∈	PROPN
ejpam-3177	78	27	t	t	PROPN
ejpam-3177	78	28	(	(	PUNCT
ejpam-3177	78	29	n	n	CCONJ
ejpam-3177	78	30	)	)	PUNCT
ejpam-3177	78	31	,	,	PUNCT
ejpam-3177	78	32	α	α	NOUN
ejpam-3177	78	33	=	=	SYM
ejpam-3177	78	34	1	1	NUM
ejpam-3177	78	35	,	,	PUNCT
ejpam-3177	78	36	.	.	PUNCT
ejpam-3177	78	37	.	.	PUNCT
ejpam-3177	79	1	.	.	PUNCT
ejpam-3177	80	1	,	,	PUNCT
ejpam-3177	80	2	s	s	X
ejpam-3177	80	3	,	,	PUNCT
ejpam-3177	80	4	(	(	PUNCT
ejpam-3177	80	5	6	6	NUM
ejpam-3177	80	6	)	)	PUNCT
ejpam-3177	80	7	(	(	PUNCT
ejpam-3177	80	8	∇xf)y	∇xf)y	NOUN
ejpam-3177	80	9	=	=	PUNCT
ejpam-3177	80	10	∑	∑	NOUN
ejpam-3177	80	11	{	{	PUNCT
ejpam-3177	80	12	g(fx	g(fx	NOUN
ejpam-3177	80	13	,	,	PUNCT
ejpam-3177	80	14	fy	fy	PROPN
ejpam-3177	80	15	)	)	PUNCT
ejpam-3177	80	16	ξα	ξα	VERB
ejpam-3177	80	17	+	+	CCONJ
ejpam-3177	80	18	ηα(y	ηα(y	NOUN
ejpam-3177	80	19	)	)	PUNCT
ejpam-3177	81	1	f2x	f2x	CCONJ
ejpam-3177	81	2	}	}	PUNCT
ejpam-3177	81	3	,	,	PUNCT
ejpam-3177	81	4	x	x	X
ejpam-3177	81	5	,	,	PUNCT
ejpam-3177	81	6	y	y	PROPN
ejpam-3177	81	7	∈	∈	PROPN
ejpam-3177	81	8	t	t	PROPN
ejpam-3177	81	9	(	(	PUNCT
ejpam-3177	81	10	n	n	CCONJ
ejpam-3177	81	11	)	)	PUNCT
ejpam-3177	81	12	,	,	PUNCT
ejpam-3177	81	13	(	(	PUNCT
ejpam-3177	81	14	7	7	X
ejpam-3177	81	15	)	)	PUNCT
ejpam-3177	81	16	where	where	SCONJ
ejpam-3177	81	17	∇	∇	PROPN
ejpam-3177	81	18	is	be	AUX
ejpam-3177	81	19	the	the	DET
ejpam-3177	81	20	riemannian	riemannian	ADJ
ejpam-3177	81	21	connection	connection	NOUN
ejpam-3177	81	22	of	of	ADP
ejpam-3177	81	23	g.	g.	PROPN
ejpam-3177	81	24	let	let	VERB
ejpam-3177	81	25	l	l	NOUN
ejpam-3177	81	26	be	be	AUX
ejpam-3177	81	27	the	the	DET
ejpam-3177	81	28	distribution	distribution	NOUN
ejpam-3177	81	29	determined	determine	VERB
ejpam-3177	81	30	by	by	ADP
ejpam-3177	81	31	the	the	DET
ejpam-3177	81	32	projection	projection	NOUN
ejpam-3177	81	33	tensor	tensor	NOUN
ejpam-3177	81	34	−f2	−f2	PROPN
ejpam-3177	81	35	and	and	CCONJ
ejpam-3177	81	36	let	let	VERB
ejpam-3177	81	37	k	k	PROPN
ejpam-3177	81	38	be	be	AUX
ejpam-3177	81	39	the	the	DET
ejpam-3177	81	40	complementary	complementary	ADJ
ejpam-3177	81	41	distribution	distribution	NOUN
ejpam-3177	81	42	which	which	PRON
ejpam-3177	81	43	is	be	AUX
ejpam-3177	81	44	determined	determine	VERB
ejpam-3177	81	45	by	by	ADP
ejpam-3177	81	46	f2	f2	PROPN
ejpam-3177	82	1	+	+	CCONJ
ejpam-3177	82	2	i	i	PRON
ejpam-3177	82	3	and	and	CCONJ
ejpam-3177	82	4	spanned	span	VERB
ejpam-3177	82	5	by	by	ADP
ejpam-3177	82	6	ξ1	ξ1	NOUN
ejpam-3177	82	7	,	,	PUNCT
ejpam-3177	82	8	.	.	PUNCT
ejpam-3177	82	9	.	.	PUNCT
ejpam-3177	83	1	.	.	PUNCT
ejpam-3177	84	1	,	,	PUNCT
ejpam-3177	84	2	ξs	ξs	VERB
ejpam-3177	84	3	.	.	PUNCT
ejpam-3177	85	1	it	it	PRON
ejpam-3177	85	2	is	be	AUX
ejpam-3177	85	3	clear	clear	ADJ
ejpam-3177	85	4	that	that	SCONJ
ejpam-3177	85	5	if	if	SCONJ
ejpam-3177	85	6	x	x	PROPN
ejpam-3177	85	7	∈	∈	PROPN
ejpam-3177	85	8	l	l	NOUN
ejpam-3177	85	9	then	then	ADV
ejpam-3177	85	10	ηα(x	ηα(x	PUNCT
ejpam-3177	85	11	)	)	PUNCT
ejpam-3177	85	12	=	=	SYM
ejpam-3177	85	13	0	0	NUM
ejpam-3177	85	14	for	for	ADP
ejpam-3177	85	15	any	any	DET
ejpam-3177	85	16	α	α	NOUN
ejpam-3177	85	17	,	,	PUNCT
ejpam-3177	85	18	and	and	CCONJ
ejpam-3177	85	19	if	if	SCONJ
ejpam-3177	85	20	x	x	SYM
ejpam-3177	85	21	∈	∈	PROPN
ejpam-3177	85	22	k	k	NOUN
ejpam-3177	85	23	,	,	PUNCT
ejpam-3177	85	24	then	then	ADV
ejpam-3177	85	25	fx	fx	VERB
ejpam-3177	85	26	=	=	PUNCT
ejpam-3177	85	27	0	0	X
ejpam-3177	85	28	.	.	PUNCT
ejpam-3177	86	1	a	a	DET
ejpam-3177	86	2	plane	plane	NOUN
ejpam-3177	86	3	section	section	NOUN
ejpam-3177	86	4	π	π	PROPN
ejpam-3177	86	5	on	on	ADP
ejpam-3177	86	6	n	n	PROPN
ejpam-3177	86	7	is	be	AUX
ejpam-3177	86	8	called	call	VERB
ejpam-3177	86	9	an	an	DET
ejpam-3177	86	10	invariant	invariant	ADJ
ejpam-3177	86	11	f	f	PROPN
ejpam-3177	86	12	-section	-section	PROPN
ejpam-3177	86	13	if	if	SCONJ
ejpam-3177	86	14	it	it	PRON
ejpam-3177	86	15	is	be	AUX
ejpam-3177	86	16	determined	determine	VERB
ejpam-3177	86	17	by	by	ADP
ejpam-3177	86	18	a	a	DET
ejpam-3177	86	19	vector	vector	NOUN
ejpam-3177	86	20	x	x	SYM
ejpam-3177	86	21	∈	∈	NOUN
ejpam-3177	86	22	l(x	l(x	PROPN
ejpam-3177	86	23	)	)	PUNCT
ejpam-3177	86	24	,	,	PUNCT
ejpam-3177	86	25	x	x	PUNCT
ejpam-3177	86	26	∈	∈	PROPN
ejpam-3177	86	27	n	n	CCONJ
ejpam-3177	86	28	,	,	PUNCT
ejpam-3177	86	29	such	such	ADJ
ejpam-3177	86	30	that	that	SCONJ
ejpam-3177	86	31	{	{	PUNCT
ejpam-3177	86	32	x	x	NOUN
ejpam-3177	86	33	,	,	PUNCT
ejpam-3177	86	34	fx	fx	PROPN
ejpam-3177	86	35	}	}	PUNCT
ejpam-3177	86	36	is	be	AUX
ejpam-3177	86	37	an	an	DET
ejpam-3177	86	38	orthonormal	orthonormal	ADJ
ejpam-3177	86	39	pair	pair	NOUN
ejpam-3177	86	40	spanning	span	VERB
ejpam-3177	86	41	the	the	DET
ejpam-3177	86	42	section	section	NOUN
ejpam-3177	86	43	.	.	PUNCT
ejpam-3177	87	1	the	the	DET
ejpam-3177	87	2	sectional	sectional	ADJ
ejpam-3177	87	3	curvature	curvature	NOUN
ejpam-3177	87	4	of	of	ADP
ejpam-3177	87	5	π	π	PROPN
ejpam-3177	87	6	is	be	AUX
ejpam-3177	87	7	called	call	VERB
ejpam-3177	87	8	the	the	DET
ejpam-3177	87	9	f	f	PROPN
ejpam-3177	87	10	-sectional	-sectional	PROPN
ejpam-3177	87	11	curvature	curvature	NOUN
ejpam-3177	87	12	.	.	PUNCT
ejpam-3177	88	1	if	if	SCONJ
ejpam-3177	88	2	n	n	PRON
ejpam-3177	88	3	is	be	AUX
ejpam-3177	88	4	an	an	DET
ejpam-3177	88	5	s	s	NOUN
ejpam-3177	88	6	-	-	ADJ
ejpam-3177	88	7	manifold	manifold	ADJ
ejpam-3177	88	8	of	of	ADP
ejpam-3177	88	9	constant	constant	ADJ
ejpam-3177	88	10	f	f	PROPN
ejpam-3177	88	11	-sectional	-sectional	ADJ
ejpam-3177	88	12	curvature	curvature	NOUN
ejpam-3177	88	13	k	k	NOUN
ejpam-3177	88	14	,	,	PUNCT
ejpam-3177	88	15	then	then	ADV
ejpam-3177	88	16	its	its	PRON
ejpam-3177	88	17	curvature	curvature	NOUN
ejpam-3177	88	18	tensor	tensor	NOUN
ejpam-3177	88	19	has	have	VERB
ejpam-3177	88	20	the	the	DET
ejpam-3177	88	21	form	form	NOUN
ejpam-3177	88	22	[	[	X
ejpam-3177	88	23	1	1	NUM
ejpam-3177	88	24	]	]	X
ejpam-3177	88	25	r(s	r(s	PROPN
ejpam-3177	88	26	,	,	PUNCT
ejpam-3177	88	27	t	t	PROPN
ejpam-3177	88	28	,	,	PUNCT
ejpam-3177	88	29	v	v	NOUN
ejpam-3177	88	30	,	,	PUNCT
ejpam-3177	88	31	w	w	NOUN
ejpam-3177	88	32	)	)	PUNCT
ejpam-3177	88	33	=	=	SYM
ejpam-3177	88	34	∑	∑	PUNCT
ejpam-3177	88	35	α	α	X
ejpam-3177	88	36	,	,	PUNCT
ejpam-3177	88	37	β	β	X
ejpam-3177	88	38	{	{	PUNCT
ejpam-3177	88	39	g(fs	g(fs	PROPN
ejpam-3177	88	40	,	,	PUNCT
ejpam-3177	88	41	fw	fw	ADJ
ejpam-3177	88	42	)	)	PUNCT
ejpam-3177	88	43	ηα(t	ηα(t	PUNCT
ejpam-3177	88	44	)	)	PUNCT
ejpam-3177	88	45	ηβ(v	ηβ(v	X
ejpam-3177	88	46	)	)	PUNCT
ejpam-3177	89	1	−	−	PROPN
ejpam-3177	89	2	g(fs	g(fs	PROPN
ejpam-3177	89	3	,	,	PUNCT
ejpam-3177	89	4	fv	fv	NOUN
ejpam-3177	89	5	)	)	PUNCT
ejpam-3177	89	6	ηα(t	ηα(t	PUNCT
ejpam-3177	89	7	)	)	PUNCT
ejpam-3177	89	8	ηβ(w	ηβ(w	PUNCT
ejpam-3177	89	9	)	)	PUNCT
ejpam-3177	90	1	+	+	CCONJ
ejpam-3177	91	1	+	+	PUNCT
ejpam-3177	91	2	g(ft	g(ft	PROPN
ejpam-3177	91	3	,	,	PUNCT
ejpam-3177	91	4	fv	fv	X
ejpam-3177	91	5	)	)	PUNCT
ejpam-3177	91	6	ηα(s)ηβ(w	ηα(s)ηβ(w	PART
ejpam-3177	91	7	)	)	PUNCT
ejpam-3177	91	8	−	−	PROPN
ejpam-3177	91	9	g(ft	g(ft	PROPN
ejpam-3177	91	10	,	,	PUNCT
ejpam-3177	91	11	fw	fw	ADJ
ejpam-3177	91	12	)	)	PUNCT
ejpam-3177	91	13	ηα(s)ηβ(v	ηα(s)ηβ(v	NOUN
ejpam-3177	91	14	)	)	PUNCT
ejpam-3177	91	15	}	}	PUNCT
ejpam-3177	91	16	+	+	PUNCT
ejpam-3177	91	17	+	+	CCONJ
ejpam-3177	91	18	1	1	NUM
ejpam-3177	91	19	4	4	NUM
ejpam-3177	91	20	(	(	PUNCT
ejpam-3177	91	21	k	k	PROPN
ejpam-3177	91	22	+	+	NUM
ejpam-3177	91	23	3s){g(fs	3s){g(fs	NUM
ejpam-3177	91	24	,	,	PUNCT
ejpam-3177	91	25	fw	fw	ADJ
ejpam-3177	91	26	)	)	PUNCT
ejpam-3177	91	27	g(ft	g(ft	PROPN
ejpam-3177	91	28	,	,	PUNCT
ejpam-3177	91	29	fv	fv	NOUN
ejpam-3177	91	30	)	)	PUNCT
ejpam-3177	91	31	−	−	PROPN
ejpam-3177	91	32	g(fs	g(fs	PROPN
ejpam-3177	91	33	,	,	PUNCT
ejpam-3177	91	34	fv	fv	INTJ
ejpam-3177	91	35	)	)	PUNCT
ejpam-3177	91	36	g(ft	g(ft	PROPN
ejpam-3177	91	37	,	,	PUNCT
ejpam-3177	91	38	fw	fw	NOUN
ejpam-3177	91	39	)	)	PUNCT
ejpam-3177	91	40	}	}	PUNCT
ejpam-3177	91	41	+	+	PUNCT
ejpam-3177	92	1	+	+	CCONJ
ejpam-3177	92	2	1	1	NUM
ejpam-3177	92	3	4	4	NUM
ejpam-3177	92	4	(	(	PUNCT
ejpam-3177	92	5	k	k	NOUN
ejpam-3177	92	6	−	−	NOUN
ejpam-3177	92	7	s){ω(s	s){ω(s	NOUN
ejpam-3177	92	8	,	,	PUNCT
ejpam-3177	92	9	w	w	NOUN
ejpam-3177	92	10	)	)	PUNCT
ejpam-3177	92	11	ω(t	ω(t	NOUN
ejpam-3177	92	12	,	,	PUNCT
ejpam-3177	92	13	v	v	NOUN
ejpam-3177	92	14	)	)	PUNCT
ejpam-3177	92	15	−	−	PROPN
ejpam-3177	92	16	ω(s	ω(s	PROPN
ejpam-3177	92	17	,	,	PUNCT
ejpam-3177	92	18	v	v	NOUN
ejpam-3177	92	19	)	)	PUNCT
ejpam-3177	92	20	ω(t	ω(t	NOUN
ejpam-3177	92	21	,	,	PUNCT
ejpam-3177	92	22	w	w	NOUN
ejpam-3177	92	23	)	)	PUNCT
ejpam-3177	92	24	−	−	PROPN
ejpam-3177	92	25	2ω(s	2ω(s	PROPN
ejpam-3177	92	26	,	,	PUNCT
ejpam-3177	92	27	t	t	NOUN
ejpam-3177	92	28	)	)	PUNCT
ejpam-3177	92	29	ω(v	ω(v	NOUN
ejpam-3177	92	30	,	,	PUNCT
ejpam-3177	92	31	w	w	NOUN
ejpam-3177	92	32	)	)	PUNCT
ejpam-3177	92	33	}	}	PUNCT
ejpam-3177	92	34	,	,	PUNCT
ejpam-3177	92	35	(	(	PUNCT
ejpam-3177	92	36	8)	8)	NUM
ejpam-3177	92	37	s	s	NOUN
ejpam-3177	92	38	,	,	PUNCT
ejpam-3177	92	39	t	t	PROPN
ejpam-3177	92	40	,	,	PUNCT
ejpam-3177	92	41	v	v	NOUN
ejpam-3177	92	42	,	,	PUNCT
ejpam-3177	92	43	w	w	PROPN
ejpam-3177	92	44	∈	∈	PROPN
ejpam-3177	92	45	t	t	PROPN
ejpam-3177	92	46	(	(	PUNCT
ejpam-3177	92	47	n	n	CCONJ
ejpam-3177	92	48	)	)	PUNCT
ejpam-3177	92	49	.	.	PUNCT
ejpam-3177	93	1	ω	ω	PROPN
ejpam-3177	93	2	is	be	AUX
ejpam-3177	93	3	fundamental	fundamental	ADJ
ejpam-3177	93	4	2	2	NUM
ejpam-3177	93	5	-	-	PUNCT
ejpam-3177	93	6	form	form	NOUN
ejpam-3177	93	7	.	.	PUNCT
ejpam-3177	94	1	such	such	DET
ejpam-3177	94	2	a	a	DET
ejpam-3177	94	3	manifold	manifold	ADJ
ejpam-3177	94	4	n(k	n(k	PROPN
ejpam-3177	94	5	)	)	PUNCT
ejpam-3177	94	6	will	will	AUX
ejpam-3177	94	7	be	be	AUX
ejpam-3177	94	8	called	call	VERB
ejpam-3177	94	9	an	an	DET
ejpam-3177	94	10	s	s	NOUN
ejpam-3177	94	11	-	-	PUNCT
ejpam-3177	94	12	space	space	NOUN
ejpam-3177	94	13	form	form	NOUN
ejpam-3177	94	14	.	.	PUNCT
ejpam-3177	95	1	the	the	DET
ejpam-3177	95	2	euclidean	euclidean	ADJ
ejpam-3177	95	3	space	space	NOUN
ejpam-3177	95	4	e2n+s	e2n+s	NOUN
ejpam-3177	95	5	and	and	CCONJ
ejpam-3177	95	6	the	the	DET
ejpam-3177	95	7	hyperbolic	hyperbolic	ADJ
ejpam-3177	95	8	space	space	NOUN
ejpam-3177	95	9	h2n+s	h2n+s	NOUN
ejpam-3177	95	10	are	be	AUX
ejpam-3177	95	11	examples	example	NOUN
ejpam-3177	95	12	of	of	ADP
ejpam-3177	95	13	s	s	NOUN
ejpam-3177	95	14	-	-	PUNCT
ejpam-3177	95	15	space	space	NOUN
ejpam-3177	95	16	forms	form	NOUN
ejpam-3177	95	17	.	.	PUNCT
ejpam-3177	96	1	let	let	VERB
ejpam-3177	96	2	m	m	PRON
ejpam-3177	96	3	be	be	AUX
ejpam-3177	96	4	an	an	DET
ejpam-3177	96	5	m	m	ADJ
ejpam-3177	96	6	-	-	ADJ
ejpam-3177	96	7	dimensional	dimensional	ADJ
ejpam-3177	96	8	submanifold	submanifold	NOUN
ejpam-3177	96	9	immersed	immerse	VERB
ejpam-3177	96	10	in	in	ADP
ejpam-3177	96	11	n.	n.	NOUN
ejpam-3177	96	12	then	then	ADV
ejpam-3177	96	13	m	m	VERB
ejpam-3177	96	14	is	be	AUX
ejpam-3177	96	15	an	an	DET
ejpam-3177	96	16	invariant	invariant	ADJ
ejpam-3177	96	17	submnaifold	submnaifold	NOUN
ejpam-3177	96	18	if	if	SCONJ
ejpam-3177	96	19	ξα	ξα	NOUN
ejpam-3177	96	20	∈	∈	PROPN
ejpam-3177	96	21	tm	tm	NOUN
ejpam-3177	96	22	for	for	ADP
ejpam-3177	96	23	any	any	DET
ejpam-3177	96	24	α	α	NOUN
ejpam-3177	96	25	and	and	CCONJ
ejpam-3177	96	26	fv	fv	PROPN
ejpam-3177	96	27	∈	∈	PROPN
ejpam-3177	96	28	tm	tm	PROPN
ejpam-3177	96	29	for	for	ADP
ejpam-3177	96	30	any	any	DET
ejpam-3177	96	31	v	v	NOUN
ejpam-3177	96	32	∈	∈	PROPN
ejpam-3177	96	33	tm	tm	NOUN
ejpam-3177	96	34	.	.	PUNCT
ejpam-3177	97	1	it	it	PRON
ejpam-3177	97	2	is	be	AUX
ejpam-3177	97	3	said	say	VERB
ejpam-3177	97	4	to	to	PART
ejpam-3177	97	5	be	be	AUX
ejpam-3177	97	6	anti	anti	ADJ
ejpam-3177	97	7	-	-	ADJ
ejpam-3177	97	8	invariant	invariant	ADJ
ejpam-3177	97	9	submanifold	submanifold	NOUN
ejpam-3177	97	10	if	if	SCONJ
ejpam-3177	97	11	fv	fv	PROPN
ejpam-3177	97	12	∈	∈	PROPN
ejpam-3177	97	13	tm⊥	tm⊥	PROPN
ejpam-3177	97	14	for	for	ADP
ejpam-3177	97	15	any	any	DET
ejpam-3177	97	16	v	v	NOUN
ejpam-3177	97	17	∈	∈	PROPN
ejpam-3177	97	18	tm	tm	NOUN
ejpam-3177	97	19	.	.	PUNCT
ejpam-3177	98	1	for	for	ADP
ejpam-3177	98	2	a	a	DET
ejpam-3177	98	3	vector	vector	NOUN
ejpam-3177	98	4	field	field	NOUN
ejpam-3177	98	5	x	x	PUNCT
ejpam-3177	98	6	∈	∈	PROPN
ejpam-3177	98	7	tm⊥	tm⊥	PROPN
ejpam-3177	98	8	,	,	PUNCT
ejpam-3177	98	9	it	it	PRON
ejpam-3177	98	10	can	can	AUX
ejpam-3177	98	11	be	be	AUX
ejpam-3177	98	12	written	write	VERB
ejpam-3177	98	13	as	as	ADP
ejpam-3177	98	14	fx	fx	NOUN
ejpam-3177	98	15	=	=	SYM
ejpam-3177	98	16	tx	tx	PROPN
ejpam-3177	98	17	+	+	CCONJ
ejpam-3177	98	18	nx	nx	NUM
ejpam-3177	98	19	,	,	PUNCT
ejpam-3177	98	20	where	where	SCONJ
ejpam-3177	98	21	tx	tx	PROPN
ejpam-3177	98	22	is	be	AUX
ejpam-3177	98	23	tangent	tangent	ADJ
ejpam-3177	98	24	component	component	NOUN
ejpam-3177	98	25	of	of	ADP
ejpam-3177	98	26	fx	fx	PROPN
ejpam-3177	98	27	,	,	PUNCT
ejpam-3177	98	28	nx	nx	PROPN
ejpam-3177	98	29	is	be	AUX
ejpam-3177	98	30	normal	normal	ADJ
ejpam-3177	98	31	component	component	NOUN
ejpam-3177	98	32	of	of	ADP
ejpam-3177	98	33	f	f	PROPN
ejpam-3177	98	34	x.	x.	NOUN
ejpam-3177	98	35	if	if	SCONJ
ejpam-3177	98	36	n	n	PRON
ejpam-3177	98	37	does	do	AUX
ejpam-3177	98	38	not	not	PART
ejpam-3177	98	39	vanishes	vanish	VERB
ejpam-3177	98	40	,	,	PUNCT
ejpam-3177	98	41	then	then	ADV
ejpam-3177	98	42	its	its	PRON
ejpam-3177	98	43	an	an	DET
ejpam-3177	98	44	f	f	NOUN
ejpam-3177	98	45	-	-	PUNCT
ejpam-3177	98	46	structure	structure	NOUN
ejpam-3177	98	47	[	[	X
ejpam-3177	98	48	4	4	NUM
ejpam-3177	98	49	]	]	PUNCT
ejpam-3177	98	50	.	.	PUNCT
ejpam-3177	99	1	consider	consider	VERB
ejpam-3177	99	2	the	the	DET
ejpam-3177	99	3	structure	structure	NOUN
ejpam-3177	99	4	vector	vector	NOUN
ejpam-3177	99	5	fields	field	NOUN
ejpam-3177	99	6	ξ1	ξ1	NOUN
ejpam-3177	99	7	,	,	PUNCT
ejpam-3177	99	8	ξ2	ξ2	NOUN
ejpam-3177	99	9	,	,	PUNCT
ejpam-3177	99	10	.	.	PUNCT
ejpam-3177	99	11	.	.	PUNCT
ejpam-3177	100	1	.	.	PUNCT
ejpam-3177	101	1	,	,	PUNCT
ejpam-3177	101	2	ξs	ξs	PROPN
ejpam-3177	101	3	are	be	AUX
ejpam-3177	101	4	tangent	tangent	ADJ
ejpam-3177	101	5	to	to	ADP
ejpam-3177	101	6	m	m	PROPN
ejpam-3177	101	7	,	,	PUNCT
ejpam-3177	101	8	dim(m	dim(m	PROPN
ejpam-3177	101	9	)	)	PUNCT
ejpam-3177	101	10	≥	≥	NOUN
ejpam-3177	102	1	s.	s.	PROPN
ejpam-3177	102	2	then	then	ADV
ejpam-3177	102	3	m	m	PROPN
ejpam-3177	102	4	is	be	AUX
ejpam-3177	102	5	cr	cr	NOUN
ejpam-3177	102	6	-	-	PUNCT
ejpam-3177	102	7	submaifold	submaifold	NOUN
ejpam-3177	102	8	of	of	ADP
ejpam-3177	102	9	n	n	PRON
ejpam-3177	102	10	if	if	SCONJ
ejpam-3177	102	11	there	there	PRON
ejpam-3177	102	12	are	be	VERB
ejpam-3177	102	13	two	two	NUM
ejpam-3177	102	14	differentiable	differentiable	ADJ
ejpam-3177	102	15	distributions	distribution	NOUN
ejpam-3177	102	16	d	d	NOUN
ejpam-3177	102	17	and	and	CCONJ
ejpam-3177	102	18	d⊥	d⊥	NOUN
ejpam-3177	102	19	on	on	ADP
ejpam-3177	102	20	m	m	PROPN
ejpam-3177	102	21	,	,	PUNCT
ejpam-3177	103	1	tm	tm	NOUN
ejpam-3177	103	2	=	=	PROPN
ejpam-3177	103	3	d	d	X
ejpam-3177	104	1	+	+	NOUN
ejpam-3177	104	2	d⊥	d⊥	NOUN
ejpam-3177	104	3	such	such	ADJ
ejpam-3177	104	4	that	that	PRON
ejpam-3177	104	5	•	•	NUM
ejpam-3177	104	6	d	d	NOUN
ejpam-3177	104	7	and	and	CCONJ
ejpam-3177	104	8	d⊥	d⊥	NOUN
ejpam-3177	104	9	are	be	AUX
ejpam-3177	104	10	mutually	mutually	ADV
ejpam-3177	104	11	orthogonal	orthogonal	ADJ
ejpam-3177	104	12	to	to	ADP
ejpam-3177	104	13	each	each	DET
ejpam-3177	104	14	other	other	ADJ
ejpam-3177	104	15	.	.	PUNCT
ejpam-3177	105	1	•	•	NUM
ejpam-3177	105	2	the	the	DET
ejpam-3177	105	3	distribution	distribution	NOUN
ejpam-3177	105	4	d	d	NOUN
ejpam-3177	105	5	is	be	AUX
ejpam-3177	105	6	invariant	invariant	ADJ
ejpam-3177	105	7	under	under	ADP
ejpam-3177	105	8	f	f	PROPN
ejpam-3177	105	9	,	,	PUNCT
ejpam-3177	105	10	i.e.	i.e.	X
ejpam-3177	105	11	fdp	fdp	X
ejpam-3177	105	12	=	=	SYM
ejpam-3177	105	13	dp	dp	PROPN
ejpam-3177	105	14	,	,	PUNCT
ejpam-3177	105	15	for	for	ADP
ejpam-3177	105	16	any	any	DET
ejpam-3177	105	17	p	p	NOUN
ejpam-3177	105	18	∈m	∈m	NOUN
ejpam-3177	105	19	•	•	NOUN
ejpam-3177	105	20	the	the	DET
ejpam-3177	105	21	distribution	distribution	NOUN
ejpam-3177	105	22	d⊥	d⊥	NOUN
ejpam-3177	105	23	is	be	AUX
ejpam-3177	105	24	anti	anti	X
ejpam-3177	105	25	invariant	invariant	ADJ
ejpam-3177	105	26	under	under	ADP
ejpam-3177	105	27	f	f	PROPN
ejpam-3177	105	28	,	,	PUNCT
ejpam-3177	105	29	i.e.	i.e.	X
ejpam-3177	105	30	fd⊥p	fd⊥p	NOUN
ejpam-3177	105	31	⊆	⊆	NUM
ejpam-3177	105	32	tpm⊥	tpm⊥	NOUN
ejpam-3177	105	33	for	for	ADP
ejpam-3177	105	34	any	any	DET
ejpam-3177	105	35	p	p	NOUN
ejpam-3177	105	36	∈m	∈m	NOUN
ejpam-3177	105	37	.	.	PUNCT
ejpam-3177	106	1	it	it	PRON
ejpam-3177	106	2	can	can	AUX
ejpam-3177	106	3	be	be	AUX
ejpam-3177	106	4	proved	prove	VERB
ejpam-3177	106	5	that	that	SCONJ
ejpam-3177	106	6	each	each	DET
ejpam-3177	106	7	hypersurface	hypersurface	NOUN
ejpam-3177	106	8	of	of	ADP
ejpam-3177	106	9	n	n	PRON
ejpam-3177	106	10	which	which	PRON
ejpam-3177	106	11	is	be	AUX
ejpam-3177	106	12	tangent	tangent	NOUN
ejpam-3177	106	13	to	to	ADP
ejpam-3177	106	14	ξ1	ξ1	NOUN
ejpam-3177	106	15	,	,	PUNCT
ejpam-3177	106	16	ξ2	ξ2	NOUN
ejpam-3177	106	17	,	,	PUNCT
ejpam-3177	106	18	.	.	PUNCT
ejpam-3177	106	19	.	.	PUNCT
ejpam-3177	107	1	.	.	PUNCT
ejpam-3177	108	1	,	,	PUNCT
ejpam-3177	108	2	ξs	ξs	PROPN
ejpam-3177	108	3	,	,	PUNCT
ejpam-3177	108	4	has	have	VERB
ejpam-3177	108	5	the	the	DET
ejpam-3177	108	6	structure	structure	NOUN
ejpam-3177	108	7	of	of	ADP
ejpam-3177	108	8	cr	cr	NOUN
ejpam-3177	108	9	-	-	PUNCT
ejpam-3177	108	10	submnaifold	submnaifold	NOUN
ejpam-3177	108	11	of	of	ADP
ejpam-3177	108	12	n	n	CCONJ
ejpam-3177	108	13	,	,	PUNCT
ejpam-3177	108	14	for	for	ADP
ejpam-3177	108	15	detail	detail	NOUN
ejpam-3177	108	16	see	see	VERB
ejpam-3177	108	17	[	[	X
ejpam-3177	108	18	4	4	NUM
ejpam-3177	108	19	]	]	PUNCT
ejpam-3177	108	20	.	.	PUNCT
ejpam-3177	109	1	n.	n.	PROPN
ejpam-3177	109	2	a.	a.	PROPN
ejpam-3177	109	3	rehman	rehman	PROPN
ejpam-3177	109	4	,	,	PUNCT
ejpam-3177	109	5	m.	m.	NOUN
ejpam-3177	109	6	bari	bari	NOUN
ejpam-3177	109	7	/	/	SYM
ejpam-3177	109	8	eur	eur	PROPN
ejpam-3177	109	9	.	.	PUNCT
ejpam-3177	110	1	j.	j.	PROPN
ejpam-3177	110	2	pure	pure	PROPN
ejpam-3177	110	3	appl	appl	PROPN
ejpam-3177	110	4	.	.	PROPN
ejpam-3177	110	5	math	math	PROPN
ejpam-3177	110	6	,	,	PUNCT
ejpam-3177	110	7	11	11	NUM
ejpam-3177	110	8	(	(	PUNCT
ejpam-3177	110	9	1	1	NUM
ejpam-3177	110	10	)	)	PUNCT
ejpam-3177	110	11	(	(	PUNCT
ejpam-3177	110	12	2018	2018	NUM
ejpam-3177	110	13	)	)	PUNCT
ejpam-3177	110	14	,	,	PUNCT
ejpam-3177	110	15	150	150	NUM
ejpam-3177	110	16	-	-	SYM
ejpam-3177	110	17	159	159	NUM
ejpam-3177	110	18	154	154	NUM
ejpam-3177	110	19	3	3	NUM
ejpam-3177	110	20	.	.	PUNCT
ejpam-3177	110	21	biharmonic	biharmonic	NOUN
ejpam-3177	110	22	maps	map	NOUN
ejpam-3177	110	23	into	into	ADP
ejpam-3177	110	24	s	s	NOUN
ejpam-3177	110	25	-	-	PUNCT
ejpam-3177	110	26	space	space	NOUN
ejpam-3177	110	27	form	form	NOUN
ejpam-3177	110	28	before	before	SCONJ
ejpam-3177	110	29	the	the	DET
ejpam-3177	110	30	main	main	ADJ
ejpam-3177	110	31	results	result	NOUN
ejpam-3177	110	32	recall	recall	VERB
ejpam-3177	110	33	the	the	DET
ejpam-3177	110	34	following	follow	VERB
ejpam-3177	110	35	results	result	NOUN
ejpam-3177	110	36	by	by	ADP
ejpam-3177	110	37	jiang	jiang	PROPN
ejpam-3177	110	38	:	:	PUNCT
ejpam-3177	110	39	lemma	lemma	PROPN
ejpam-3177	110	40	1	1	NUM
ejpam-3177	110	41	.	.	PUNCT
ejpam-3177	111	1	[	[	X
ejpam-3177	111	2	8	8	NUM
ejpam-3177	111	3	]	]	PUNCT
ejpam-3177	111	4	let	let	VERB
ejpam-3177	111	5	f	f	PRON
ejpam-3177	111	6	:	:	PUNCT
ejpam-3177	111	7	(	(	PUNCT
ejpam-3177	111	8	mm	mm	INTJ
ejpam-3177	111	9	,	,	PUNCT
ejpam-3177	111	10	g)→	g)→	PROPN
ejpam-3177	111	11	(	(	PUNCT
ejpam-3177	111	12	nn	nn	X
ejpam-3177	111	13	,	,	PUNCT
ejpam-3177	111	14	h	h	NOUN
ejpam-3177	111	15	)	)	PUNCT
ejpam-3177	111	16	be	be	VERB
ejpam-3177	111	17	an	an	DET
ejpam-3177	111	18	isometric	isometric	ADJ
ejpam-3177	111	19	immersion	immersion	NOUN
ejpam-3177	111	20	whose	whose	DET
ejpam-3177	111	21	mean	mean	NOUN
ejpam-3177	111	22	curvature	curvature	NOUN
ejpam-3177	111	23	vector	vector	NOUN
ejpam-3177	111	24	field	field	NOUN
ejpam-3177	111	25	h	h	NOUN
ejpam-3177	111	26	=	=	NOUN
ejpam-3177	111	27	1	1	NUM
ejpam-3177	111	28	mτ(f	mτ(f	NOUN
ejpam-3177	111	29	)	)	PUNCT
ejpam-3177	111	30	is	be	AUX
ejpam-3177	111	31	parallel	parallel	ADJ
ejpam-3177	111	32	;	;	PUNCT
ejpam-3177	111	33	∇⊥h	∇⊥h	NOUN
ejpam-3177	111	34	=	=	SYM
ejpam-3177	111	35	0	0	NUM
ejpam-3177	111	36	,	,	PUNCT
ejpam-3177	111	37	where	where	SCONJ
ejpam-3177	111	38	∇⊥	∇⊥	NOUN
ejpam-3177	111	39	is	be	AUX
ejpam-3177	111	40	the	the	DET
ejpam-3177	111	41	induced	induced	ADJ
ejpam-3177	111	42	connection	connection	NOUN
ejpam-3177	111	43	of	of	ADP
ejpam-3177	111	44	the	the	DET
ejpam-3177	111	45	normal	normal	ADJ
ejpam-3177	111	46	bundle	bundle	NOUN
ejpam-3177	111	47	t⊥m	t⊥m	PROPN
ejpam-3177	111	48	by	by	ADP
ejpam-3177	111	49	f.	f.	PROPN
ejpam-3177	111	50	then	then	ADV
ejpam-3177	111	51	,	,	PUNCT
ejpam-3177	111	52	4τ(f	4τ(f	NUM
ejpam-3177	111	53	)	)	PUNCT
ejpam-3177	112	1	=	=	PUNCT
ejpam-3177	112	2	m∑	m∑	CCONJ
ejpam-3177	112	3	i=1	i=1	PROPN
ejpam-3177	112	4	h(4τ(f	h(4τ(f	NOUN
ejpam-3177	112	5	)	)	PUNCT
ejpam-3177	112	6	,	,	PUNCT
ejpam-3177	112	7	df(ei))df(ei)−	df(ei))df(ei)−	NOUN
ejpam-3177	112	8	m∑	m∑	INTJ
ejpam-3177	113	1	i	i	PROPN
ejpam-3177	113	2	,	,	PUNCT
ejpam-3177	113	3	j=1	j=1	ADJ
ejpam-3177	113	4	h(∇̃eiτ(f	h(∇̃eiτ(f	PROPN
ejpam-3177	113	5	)	)	PUNCT
ejpam-3177	113	6	,	,	PUNCT
ejpam-3177	113	7	df(ej))(∇̃eidf)(ej	df(ej))(∇̃eidf)(ej	PROPN
ejpam-3177	113	8	)	)	PUNCT
ejpam-3177	113	9	,	,	PUNCT
ejpam-3177	113	10	where	where	SCONJ
ejpam-3177	113	11	{	{	PUNCT
ejpam-3177	113	12	ei	ei	AUX
ejpam-3177	113	13	}	}	PUNCT
ejpam-3177	113	14	is	be	AUX
ejpam-3177	113	15	a	a	DET
ejpam-3177	113	16	locally	locally	ADV
ejpam-3177	113	17	defined	define	VERB
ejpam-3177	113	18	orthonormal	orthonormal	ADJ
ejpam-3177	113	19	frame	frame	NOUN
ejpam-3177	113	20	field	field	NOUN
ejpam-3177	113	21	of	of	ADP
ejpam-3177	113	22	(	(	PUNCT
ejpam-3177	113	23	m	m	PROPN
ejpam-3177	113	24	,	,	PUNCT
ejpam-3177	113	25	g	g	NOUN
ejpam-3177	113	26	)	)	PUNCT
ejpam-3177	113	27	.	.	PUNCT
ejpam-3177	114	1	lemma	lemma	PROPN
ejpam-3177	114	2	2	2	NUM
ejpam-3177	114	3	.	.	PUNCT
ejpam-3177	115	1	[	[	X
ejpam-3177	115	2	8	8	NUM
ejpam-3177	115	3	]	]	PUNCT
ejpam-3177	115	4	let	let	VERB
ejpam-3177	115	5	f	f	PRON
ejpam-3177	115	6	:	:	PUNCT
ejpam-3177	115	7	(	(	PUNCT
ejpam-3177	115	8	mm	mm	INTJ
ejpam-3177	115	9	,	,	PUNCT
ejpam-3177	115	10	g)→	g)→	PROPN
ejpam-3177	115	11	(	(	PUNCT
ejpam-3177	115	12	nn	nn	X
ejpam-3177	115	13	,	,	PUNCT
ejpam-3177	115	14	h	h	NOUN
ejpam-3177	115	15	)	)	PUNCT
ejpam-3177	115	16	be	be	VERB
ejpam-3177	115	17	an	an	DET
ejpam-3177	115	18	isometric	isometric	ADJ
ejpam-3177	115	19	immersion	immersion	NOUN
ejpam-3177	115	20	whose	whose	DET
ejpam-3177	115	21	mean	mean	NOUN
ejpam-3177	115	22	curvature	curvature	NOUN
ejpam-3177	115	23	vector	vector	NOUN
ejpam-3177	115	24	field	field	NOUN
ejpam-3177	115	25	h	h	NOUN
ejpam-3177	115	26	=	=	NOUN
ejpam-3177	115	27	1	1	NUM
ejpam-3177	115	28	mτ(f	mτ(f	NOUN
ejpam-3177	115	29	)	)	PUNCT
ejpam-3177	115	30	is	be	AUX
ejpam-3177	115	31	parallel	parallel	ADJ
ejpam-3177	115	32	;	;	PUNCT
ejpam-3177	115	33	∇⊥h	∇⊥h	NOUN
ejpam-3177	115	34	=	=	SYM
ejpam-3177	115	35	0	0	NUM
ejpam-3177	115	36	,	,	PUNCT
ejpam-3177	115	37	where	where	SCONJ
ejpam-3177	115	38	∇⊥	∇⊥	NOUN
ejpam-3177	115	39	is	be	AUX
ejpam-3177	115	40	the	the	DET
ejpam-3177	115	41	induced	induced	ADJ
ejpam-3177	115	42	connection	connection	NOUN
ejpam-3177	115	43	of	of	ADP
ejpam-3177	115	44	the	the	DET
ejpam-3177	115	45	normal	normal	ADJ
ejpam-3177	115	46	bundle	bundle	NOUN
ejpam-3177	115	47	t⊥m	t⊥m	PROPN
ejpam-3177	115	48	by	by	ADP
ejpam-3177	115	49	f.	f.	PROPN
ejpam-3177	115	50	then	then	ADV
ejpam-3177	115	51	,	,	PUNCT
ejpam-3177	115	52	4τ(f	4τ(f	NUM
ejpam-3177	115	53	)	)	PUNCT
ejpam-3177	116	1	=	=	SYM
ejpam-3177	116	2	−	−	PROPN
ejpam-3177	116	3	m∑	m∑	INTJ
ejpam-3177	116	4	j	j	PROPN
ejpam-3177	116	5	,	,	PUNCT
ejpam-3177	116	6	k=1	k=1	PROPN
ejpam-3177	116	7	h(τ(f	h(τ(f	PROPN
ejpam-3177	116	8	)	)	PUNCT
ejpam-3177	116	9	,	,	PUNCT
ejpam-3177	116	10	rn	rn	PROPN
ejpam-3177	116	11	(	(	PUNCT
ejpam-3177	116	12	df(ej	df(ej	PROPN
ejpam-3177	116	13	)	)	PUNCT
ejpam-3177	116	14	,	,	PUNCT
ejpam-3177	116	15	df(ek))df(ej)df(ek)−	df(ek))df(ej)df(ek)−	VERB
ejpam-3177	116	16	−	−	NOUN
ejpam-3177	116	17	m∑	m∑	INTJ
ejpam-3177	117	1	i	i	PRON
ejpam-3177	117	2	,	,	PUNCT
ejpam-3177	117	3	j=1	j=1	PROPN
ejpam-3177	117	4	h(τ(f	h(τ(f	PROPN
ejpam-3177	117	5	)	)	PUNCT
ejpam-3177	117	6	,	,	PUNCT
ejpam-3177	117	7	(	(	PUNCT
ejpam-3177	117	8	∇̃eidf)(ej))(∇̃eidf)(ej	∇̃eidf)(ej))(∇̃eidf)(ej	ADJ
ejpam-3177	117	9	)	)	PUNCT
ejpam-3177	117	10	,	,	PUNCT
ejpam-3177	117	11	where	where	SCONJ
ejpam-3177	117	12	{	{	PUNCT
ejpam-3177	117	13	ei	ei	AUX
ejpam-3177	117	14	}	}	PUNCT
ejpam-3177	117	15	is	be	AUX
ejpam-3177	117	16	a	a	DET
ejpam-3177	117	17	locally	locally	ADV
ejpam-3177	117	18	defined	define	VERB
ejpam-3177	117	19	orthonormal	orthonormal	ADJ
ejpam-3177	117	20	frame	frame	NOUN
ejpam-3177	117	21	field	field	NOUN
ejpam-3177	117	22	of	of	ADP
ejpam-3177	117	23	(	(	PUNCT
ejpam-3177	117	24	m	m	PROPN
ejpam-3177	117	25	,	,	PUNCT
ejpam-3177	117	26	g	g	NOUN
ejpam-3177	117	27	)	)	PUNCT
ejpam-3177	117	28	.	.	PUNCT
ejpam-3177	118	1	lemma	lemma	PROPN
ejpam-3177	118	2	3	3	X
ejpam-3177	118	3	.	.	PUNCT
ejpam-3177	119	1	[	[	X
ejpam-3177	119	2	8	8	NUM
ejpam-3177	119	3	]	]	PUNCT
ejpam-3177	119	4	let	let	VERB
ejpam-3177	119	5	f	f	PRON
ejpam-3177	119	6	:	:	PUNCT
ejpam-3177	119	7	(	(	PUNCT
ejpam-3177	119	8	mm	mm	INTJ
ejpam-3177	119	9	,	,	PUNCT
ejpam-3177	119	10	g	g	NOUN
ejpam-3177	119	11	)	)	PUNCT
ejpam-3177	119	12	→	→	SYM
ejpam-3177	119	13	(	(	PUNCT
ejpam-3177	119	14	nm+1	nm+1	PROPN
ejpam-3177	119	15	,	,	PUNCT
ejpam-3177	119	16	h	h	NOUN
ejpam-3177	119	17	)	)	PUNCT
ejpam-3177	119	18	be	be	VERB
ejpam-3177	119	19	an	an	DET
ejpam-3177	119	20	isometric	isometric	ADJ
ejpam-3177	119	21	immersion	immersion	NOUN
ejpam-3177	119	22	which	which	PRON
ejpam-3177	119	23	is	be	AUX
ejpam-3177	119	24	not	not	PART
ejpam-3177	119	25	harmonic	harmonic	ADJ
ejpam-3177	119	26	.	.	PUNCT
ejpam-3177	120	1	then	then	ADV
ejpam-3177	120	2	,	,	PUNCT
ejpam-3177	120	3	the	the	DET
ejpam-3177	120	4	condition	condition	NOUN
ejpam-3177	120	5	that	that	PRON
ejpam-3177	120	6	‖	‖	ADJ
ejpam-3177	120	7	τ(f	τ(f	NOUN
ejpam-3177	120	8	)	)	PUNCT
ejpam-3177	120	9	‖	‖	PROPN
ejpam-3177	120	10	is	be	AUX
ejpam-3177	120	11	constant	constant	ADJ
ejpam-3177	120	12	is	be	AUX
ejpam-3177	120	13	equivalent	equivalent	ADJ
ejpam-3177	120	14	to	to	ADP
ejpam-3177	120	15	the	the	DET
ejpam-3177	120	16	one	one	NOUN
ejpam-3177	120	17	that	that	DET
ejpam-3177	120	18	∇xτ(f	∇xτ(f	NOUN
ejpam-3177	120	19	)	)	PUNCT
ejpam-3177	120	20	∈	∈	NOUN
ejpam-3177	120	21	γ(f∗tm	γ(f∗tm	NOUN
ejpam-3177	120	22	)	)	PUNCT
ejpam-3177	120	23	,	,	PUNCT
ejpam-3177	120	24	for	for	SCONJ
ejpam-3177	120	25	all	all	DET
ejpam-3177	120	26	x	x	SYM
ejpam-3177	120	27	∈	∈	PROPN
ejpam-3177	120	28	tm	tm	NOUN
ejpam-3177	120	29	,	,	PUNCT
ejpam-3177	120	30	that	that	PRON
ejpam-3177	120	31	is	be	AUX
ejpam-3177	120	32	the	the	DET
ejpam-3177	120	33	mean	mean	ADJ
ejpam-3177	120	34	curvature	curvature	NOUN
ejpam-3177	120	35	tensor	tensor	NOUN
ejpam-3177	120	36	is	be	AUX
ejpam-3177	120	37	parallel	parallel	ADJ
ejpam-3177	120	38	with	with	ADP
ejpam-3177	120	39	respect	respect	NOUN
ejpam-3177	120	40	to	to	ADP
ejpam-3177	120	41	5⊥.	5⊥.	NUM
ejpam-3177	120	42	for	for	ADP
ejpam-3177	120	43	details	detail	NOUN
ejpam-3177	120	44	and	and	CCONJ
ejpam-3177	120	45	proof	proof	NOUN
ejpam-3177	120	46	of	of	ADP
ejpam-3177	120	47	these	these	DET
ejpam-3177	120	48	lemmas	lemma	NOUN
ejpam-3177	120	49	,	,	PUNCT
ejpam-3177	120	50	see	see	VERB
ejpam-3177	120	51	[	[	X
ejpam-3177	120	52	5	5	NUM
ejpam-3177	120	53	]	]	PUNCT
ejpam-3177	120	54	,	,	PUNCT
ejpam-3177	120	55	[	[	X
ejpam-3177	120	56	8	8	NUM
ejpam-3177	120	57	]	]	PUNCT
ejpam-3177	120	58	.	.	PUNCT
ejpam-3177	121	1	now	now	ADV
ejpam-3177	121	2	the	the	DET
ejpam-3177	121	3	main	main	ADJ
ejpam-3177	121	4	result	result	NOUN
ejpam-3177	121	5	of	of	ADP
ejpam-3177	121	6	this	this	DET
ejpam-3177	121	7	article	article	NOUN
ejpam-3177	121	8	;	;	PUNCT
ejpam-3177	121	9	3.1	3.1	NUM
ejpam-3177	121	10	.	.	PUNCT
ejpam-3177	121	11	main	main	ADJ
ejpam-3177	121	12	results	result	NOUN
ejpam-3177	121	13	theorem	theorem	VERB
ejpam-3177	121	14	1	1	NUM
ejpam-3177	121	15	.	.	PUNCT
ejpam-3177	122	1	let	let	VERB
ejpam-3177	122	2	(	(	PUNCT
ejpam-3177	122	3	m	m	NOUN
ejpam-3177	122	4	,	,	PUNCT
ejpam-3177	122	5	g	g	NOUN
ejpam-3177	122	6	)	)	PUNCT
ejpam-3177	122	7	be	be	AUX
ejpam-3177	122	8	a	a	DET
ejpam-3177	122	9	2m+s	2m+s	NUM
ejpam-3177	122	10	-	-	PUNCT
ejpam-3177	122	11	dimensional	dimensional	ADJ
ejpam-3177	122	12	submanifold	submanifold	NOUN
ejpam-3177	122	13	of	of	ADP
ejpam-3177	122	14	s	s	NOUN
ejpam-3177	122	15	-	-	PUNCT
ejpam-3177	122	16	space	space	NOUN
ejpam-3177	122	17	form	form	NOUN
ejpam-3177	122	18	n	n	PROPN
ejpam-3177	122	19	of	of	ADP
ejpam-3177	122	20	dimension	dimension	NOUN
ejpam-3177	122	21	(	(	PUNCT
ejpam-3177	122	22	2n+s	2n+s	NUM
ejpam-3177	122	23	)	)	PUNCT
ejpam-3177	122	24	,	,	PUNCT
ejpam-3177	122	25	and	and	CCONJ
ejpam-3177	122	26	φ	φ	NUM
ejpam-3177	122	27	:	:	PUNCT
ejpam-3177	122	28	(	(	PUNCT
ejpam-3177	122	29	m	m	NOUN
ejpam-3177	122	30	,	,	PUNCT
ejpam-3177	122	31	g	g	NOUN
ejpam-3177	122	32	)	)	PUNCT
ejpam-3177	122	33	→	→	SYM
ejpam-3177	122	34	(	(	PUNCT
ejpam-3177	122	35	n	n	CCONJ
ejpam-3177	122	36	,	,	PUNCT
ejpam-3177	122	37	h	h	NOUN
ejpam-3177	122	38	)	)	PUNCT
ejpam-3177	122	39	be	be	VERB
ejpam-3177	122	40	an	an	DET
ejpam-3177	122	41	isometric	isometric	ADJ
ejpam-3177	122	42	immersion	immersion	NOUN
ejpam-3177	122	43	with	with	ADP
ejpam-3177	122	44	non	non	ADJ
ejpam-3177	122	45	zero	zero	NUM
ejpam-3177	122	46	constant	constant	ADJ
ejpam-3177	122	47	parallel	parallel	ADJ
ejpam-3177	122	48	mean	mean	NOUN
ejpam-3177	122	49	curvature	curvature	NOUN
ejpam-3177	122	50	with	with	ADP
ejpam-3177	122	51	respect	respect	NOUN
ejpam-3177	122	52	to	to	ADP
ejpam-3177	122	53	connection	connection	NOUN
ejpam-3177	122	54	on	on	ADP
ejpam-3177	122	55	normal	normal	ADJ
ejpam-3177	122	56	bundle	bundle	NOUN
ejpam-3177	122	57	,	,	PUNCT
ejpam-3177	122	58	then	then	ADV
ejpam-3177	122	59	necessary	necessary	ADJ
ejpam-3177	122	60	and	and	CCONJ
ejpam-3177	122	61	sufficient	sufficient	ADJ
ejpam-3177	122	62	conditions	condition	NOUN
ejpam-3177	122	63	for	for	SCONJ
ejpam-3177	122	64	φ	φ	PROPN
ejpam-3177	122	65	to	to	PART
ejpam-3177	122	66	be	be	AUX
ejpam-3177	122	67	biharmonic	biharmonic	NOUN
ejpam-3177	122	68	is	be	AUX
ejpam-3177	122	69	•	•	ADV
ejpam-3177	122	70	‖	‖	ADJ
ejpam-3177	122	71	b(φ	b(φ	PROPN
ejpam-3177	122	72	)	)	PUNCT
ejpam-3177	123	1	‖2=	‖2=	PROPN
ejpam-3177	123	2	k+3s	k+3s	PROPN
ejpam-3177	123	3	4	4	NUM
ejpam-3177	123	4	(	(	PUNCT
ejpam-3177	123	5	2n−	2n−	PROPN
ejpam-3177	123	6	1	1	NUM
ejpam-3177	123	7	+	+	NUM
ejpam-3177	123	8	s	s	NOUN
ejpam-3177	123	9	)	)	PUNCT
ejpam-3177	123	10	+	+	NUM
ejpam-3177	123	11	3(k−s	3(k−s	X
ejpam-3177	123	12	)	)	PUNCT
ejpam-3177	123	13	4	4	NUM
ejpam-3177	123	14	,	,	PUNCT
ejpam-3177	123	15	for	for	SCONJ
ejpam-3177	123	16	m2m+s	m2m+s	PROPN
ejpam-3177	123	17	to	to	PART
ejpam-3177	123	18	be	be	AUX
ejpam-3177	123	19	a	a	DET
ejpam-3177	123	20	hypersurface	hypersurface	NOUN
ejpam-3177	123	21	,	,	PUNCT
ejpam-3177	123	22	2m=2n-1	2m=2n-1	NUM
ejpam-3177	123	23	•	•	NUM
ejpam-3177	123	24	‖	‖	PROPN
ejpam-3177	123	25	b(φ	b(φ	PROPN
ejpam-3177	123	26	)	)	PUNCT
ejpam-3177	123	27	‖2=	‖2=	PROPN
ejpam-3177	124	1	k+3s	k+3s	PROPN
ejpam-3177	124	2	4	4	NUM
ejpam-3177	124	3	(	(	PUNCT
ejpam-3177	124	4	2m+	2m+	NUM
ejpam-3177	124	5	s	s	NOUN
ejpam-3177	124	6	)	)	PUNCT
ejpam-3177	124	7	,	,	PUNCT
ejpam-3177	124	8	for	for	SCONJ
ejpam-3177	124	9	m2m+s	m2m+s	PROPN
ejpam-3177	124	10	to	to	PART
ejpam-3177	124	11	be	be	AUX
ejpam-3177	124	12	an	an	DET
ejpam-3177	124	13	inavriant	inavriant	ADJ
ejpam-3177	124	14	submanifold	submanifold	NOUN
ejpam-3177	124	15	,	,	PUNCT
ejpam-3177	124	16	m	m	VERB
ejpam-3177	124	17	<	<	X
ejpam-3177	124	18	n	n	X
ejpam-3177	124	19	n.	n.	PROPN
ejpam-3177	124	20	a.	a.	PROPN
ejpam-3177	124	21	rehman	rehman	PROPN
ejpam-3177	124	22	,	,	PUNCT
ejpam-3177	124	23	m.	m.	NOUN
ejpam-3177	124	24	bari	bari	NOUN
ejpam-3177	124	25	/	/	SYM
ejpam-3177	124	26	eur	eur	PROPN
ejpam-3177	124	27	.	.	PUNCT
ejpam-3177	125	1	j.	j.	PROPN
ejpam-3177	125	2	pure	pure	PROPN
ejpam-3177	125	3	appl	appl	PROPN
ejpam-3177	125	4	.	.	PROPN
ejpam-3177	125	5	math	math	PROPN
ejpam-3177	125	6	,	,	PUNCT
ejpam-3177	125	7	11	11	NUM
ejpam-3177	125	8	(	(	PUNCT
ejpam-3177	125	9	1	1	NUM
ejpam-3177	125	10	)	)	PUNCT
ejpam-3177	125	11	(	(	PUNCT
ejpam-3177	125	12	2018	2018	NUM
ejpam-3177	125	13	)	)	PUNCT
ejpam-3177	125	14	,	,	PUNCT
ejpam-3177	125	15	150	150	NUM
ejpam-3177	125	16	-	-	SYM
ejpam-3177	125	17	159	159	NUM
ejpam-3177	125	18	155	155	NUM
ejpam-3177	125	19	proof	proof	NOUN
ejpam-3177	125	20	.	.	PUNCT
ejpam-3177	126	1	consider	consider	VERB
ejpam-3177	126	2	an	an	DET
ejpam-3177	126	3	s	s	NOUN
ejpam-3177	126	4	-	-	ADJ
ejpam-3177	126	5	manifold	manifold	ADJ
ejpam-3177	126	6	with	with	ADP
ejpam-3177	126	7	constant	constant	ADJ
ejpam-3177	126	8	f	f	PROPN
ejpam-3177	126	9	-sectional	-sectional	ADJ
ejpam-3177	126	10	curvature	curvature	NOUN
ejpam-3177	126	11	k.	k.	PROPN
ejpam-3177	126	12	let	let	VERB
ejpam-3177	126	13	{	{	PUNCT
ejpam-3177	126	14	vi}2m+s	vi}2m+s	NOUN
ejpam-3177	126	15	i=1	i=1	PROPN
ejpam-3177	126	16	be	be	AUX
ejpam-3177	126	17	orthonormal	orthonormal	ADJ
ejpam-3177	126	18	basis	basis	NOUN
ejpam-3177	126	19	on	on	ADP
ejpam-3177	126	20	m	m	PROPN
ejpam-3177	126	21	.	.	PUNCT
ejpam-3177	127	1	then	then	ADV
ejpam-3177	127	2	from	from	ADP
ejpam-3177	127	3	equation	equation	NOUN
ejpam-3177	127	4	(	(	PUNCT
ejpam-3177	127	5	8)	8)	NUM
ejpam-3177	127	6	we	we	PRON
ejpam-3177	127	7	have	have	VERB
ejpam-3177	127	8	rn	rn	PROPN
ejpam-3177	127	9	(	(	PUNCT
ejpam-3177	127	10	dφ(vj	dφ(vj	PROPN
ejpam-3177	127	11	)	)	PUNCT
ejpam-3177	127	12	,	,	PUNCT
ejpam-3177	127	13	dφ(vk))dφ(vk	dφ(vk))dφ(vk	PROPN
ejpam-3177	127	14	)	)	PUNCT
ejpam-3177	128	1	=	=	PUNCT
ejpam-3177	128	2	∑	∑	PUNCT
ejpam-3177	128	3	α	α	X
ejpam-3177	128	4	,	,	PUNCT
ejpam-3177	128	5	β	β	X
ejpam-3177	128	6	{	{	PUNCT
ejpam-3177	128	7	−f2dφ(vj)ηα(dφvk)ηβ(dφvk)−	−f2dφ(vj)ηα(dφvk)ηβ(dφvk)−	ADJ
ejpam-3177	128	8	h(fdφvj	h(fdφvj	NOUN
ejpam-3177	128	9	,	,	PUNCT
ejpam-3177	128	10	dφvk	dφvk	ADJ
ejpam-3177	128	11	)	)	PUNCT
ejpam-3177	128	12	.	.	PUNCT
ejpam-3177	129	1	.ηα(dφvk)ξβ	.ηα(dφvk)ξβ	PUNCT
ejpam-3177	130	1	+	+	CCONJ
ejpam-3177	130	2	h(fdφ(vk	h(fdφ(vk	PROPN
ejpam-3177	130	3	)	)	PUNCT
ejpam-3177	130	4	,	,	PUNCT
ejpam-3177	130	5	fdφ(vk))ηα(dφvj)ξβ+	fdφ(vk))ηα(dφvj)ξβ+	PUNCT
ejpam-3177	131	1	+	+	PUNCT
ejpam-3177	131	2	f2dφ(vk)ηα(dφvj)ηβ(dφvk	f2dφ(vk)ηα(dφvj)ηβ(dφvk	NOUN
ejpam-3177	131	3	)	)	PUNCT
ejpam-3177	131	4	}	}	PUNCT
ejpam-3177	132	1	+	+	CCONJ
ejpam-3177	132	2	1	1	NUM
ejpam-3177	132	3	4	4	NUM
ejpam-3177	132	4	(	(	PUNCT
ejpam-3177	132	5	k	k	NOUN
ejpam-3177	132	6	+	+	NUM
ejpam-3177	132	7	3s	3s	NUM
ejpam-3177	132	8	)	)	PUNCT
ejpam-3177	132	9	{	{	PUNCT
ejpam-3177	132	10	−f2dφ(vj	−f2dφ(vj	NOUN
ejpam-3177	132	11	)	)	PUNCT
ejpam-3177	132	12	.	.	PUNCT
ejpam-3177	133	1	.h(fdφvk	.h(fdφvk	INTJ
ejpam-3177	133	2	,	,	PUNCT
ejpam-3177	133	3	fdφvk	fdφvk	NOUN
ejpam-3177	133	4	)	)	PUNCT
ejpam-3177	134	1	+	+	NUM
ejpam-3177	134	2	h(fdφvj	h(fdφvj	NOUN
ejpam-3177	134	3	,	,	PUNCT
ejpam-3177	134	4	fdφvk)f	fdφvk)f	PROPN
ejpam-3177	134	5	2dφ(vk	2dφ(vk	NUM
ejpam-3177	134	6	)	)	PUNCT
ejpam-3177	134	7	}	}	PUNCT
ejpam-3177	135	1	+	+	CCONJ
ejpam-3177	135	2	1	1	NUM
ejpam-3177	135	3	4	4	NUM
ejpam-3177	135	4	(	(	PUNCT
ejpam-3177	135	5	k	k	NOUN
ejpam-3177	135	6	−	−	PROPN
ejpam-3177	135	7	s	s	PART
ejpam-3177	135	8	)	)	PUNCT
ejpam-3177	135	9	{	{	PUNCT
ejpam-3177	135	10	−fdφ(vj)h(dφvk	−fdφ(vj)h(dφvk	NOUN
ejpam-3177	135	11	,	,	PUNCT
ejpam-3177	135	12	dφvk	dφvk	ADJ
ejpam-3177	135	13	)	)	PUNCT
ejpam-3177	135	14	+	+	CCONJ
ejpam-3177	135	15	fdφ(vk	fdφ(vk	NOUN
ejpam-3177	135	16	)	)	PUNCT
ejpam-3177	135	17	.h(dφvj	.h(dφvj	NOUN
ejpam-3177	135	18	,	,	PUNCT
ejpam-3177	135	19	fdφvk	fdφvk	PROPN
ejpam-3177	135	20	)	)	PUNCT
ejpam-3177	135	21	+	+	CCONJ
ejpam-3177	135	22	2fdφ(vk)h(dφvj	2fdφ(vk)h(dφvj	NUM
ejpam-3177	135	23	,	,	PUNCT
ejpam-3177	135	24	fdφvk	fdφvk	NOUN
ejpam-3177	135	25	)	)	PUNCT
ejpam-3177	135	26	}	}	PUNCT
ejpam-3177	135	27	,	,	PUNCT
ejpam-3177	135	28	and	and	CCONJ
ejpam-3177	135	29	rn	rn	PROPN
ejpam-3177	135	30	(	(	PUNCT
ejpam-3177	135	31	dφ(vj	dφ(vj	PROPN
ejpam-3177	135	32	)	)	PUNCT
ejpam-3177	135	33	,	,	PUNCT
ejpam-3177	135	34	dφ(vk))dφ(vk	dφ(vk))dφ(vk	PROPN
ejpam-3177	135	35	)	)	PUNCT
ejpam-3177	135	36	=	=	SYM
ejpam-3177	135	37	1	1	NUM
ejpam-3177	135	38	4	4	NUM
ejpam-3177	135	39	(	(	PUNCT
ejpam-3177	135	40	k	k	NOUN
ejpam-3177	135	41	+	+	NUM
ejpam-3177	135	42	3s	3s	NUM
ejpam-3177	135	43	)	)	PUNCT
ejpam-3177	135	44	{	{	PUNCT
ejpam-3177	135	45	dφ(vj	dφ(vj	NOUN
ejpam-3177	135	46	)	)	PUNCT
ejpam-3177	135	47	+	+	CCONJ
ejpam-3177	135	48	δjk(−dφvk	δjk(−dφvk	NOUN
ejpam-3177	135	49	)	)	PUNCT
ejpam-3177	135	50	}	}	PUNCT
ejpam-3177	136	1	+	+	CCONJ
ejpam-3177	136	2	3	3	NUM
ejpam-3177	136	3	4	4	NUM
ejpam-3177	136	4	(	(	PUNCT
ejpam-3177	136	5	k	k	NOUN
ejpam-3177	136	6	−	−	PROPN
ejpam-3177	137	1	s)h(dφvj	s)h(dφvj	INTJ
ejpam-3177	137	2	,	,	PUNCT
ejpam-3177	137	3	fdφvk)fdφ(vk	fdφvk)fdφ(vk	PROPN
ejpam-3177	137	4	)	)	PUNCT
ejpam-3177	137	5	.	.	PUNCT
ejpam-3177	138	1	then	then	ADV
ejpam-3177	138	2	we	we	PRON
ejpam-3177	138	3	have	have	VERB
ejpam-3177	138	4	m∑	m∑	PROPN
ejpam-3177	139	1	j	j	NOUN
ejpam-3177	139	2	,	,	PUNCT
ejpam-3177	139	3	k=1	k=1	PROPN
ejpam-3177	139	4	h(τ(φ	h(τ(φ	PROPN
ejpam-3177	139	5	)	)	PUNCT
ejpam-3177	139	6	,	,	PUNCT
ejpam-3177	139	7	rn	rn	PROPN
ejpam-3177	139	8	(	(	PUNCT
ejpam-3177	139	9	df	df	PROPN
ejpam-3177	139	10	(	(	PUNCT
ejpam-3177	139	11	vj	vj	PROPN
ejpam-3177	139	12	)	)	PUNCT
ejpam-3177	139	13	,	,	PUNCT
ejpam-3177	139	14	df	df	PROPN
ejpam-3177	139	15	(	(	PUNCT
ejpam-3177	139	16	vk))df	vk))df	NOUN
ejpam-3177	139	17	(	(	PUNCT
ejpam-3177	139	18	vk))df	vk))df	NOUN
ejpam-3177	139	19	(	(	PUNCT
ejpam-3177	139	20	vj	vj	PROPN
ejpam-3177	139	21	)	)	PUNCT
ejpam-3177	139	22	=	=	SYM
ejpam-3177	139	23	1	1	NUM
ejpam-3177	139	24	4	4	NUM
ejpam-3177	139	25	(	(	PUNCT
ejpam-3177	139	26	k	k	NOUN
ejpam-3177	139	27	+	+	NUM
ejpam-3177	139	28	3s	3s	NUM
ejpam-3177	139	29	)	)	PUNCT
ejpam-3177	139	30	{	{	PUNCT
ejpam-3177	139	31	h(τ(φ	h(τ(φ	PROPN
ejpam-3177	139	32	)	)	PUNCT
ejpam-3177	139	33	,	,	PUNCT
ejpam-3177	139	34	dφ(vj))−	dφ(vj))−	PROPN
ejpam-3177	139	35	δjkh(τ(φ	δjkh(τ(φ	NOUN
ejpam-3177	139	36	)	)	PUNCT
ejpam-3177	139	37	,	,	PUNCT
ejpam-3177	139	38	dφvk	dφvk	ADJ
ejpam-3177	139	39	)	)	PUNCT
ejpam-3177	139	40	}	}	PUNCT
ejpam-3177	140	1	+	+	CCONJ
ejpam-3177	140	2	3	3	NUM
ejpam-3177	140	3	4	4	NUM
ejpam-3177	140	4	(	(	PUNCT
ejpam-3177	140	5	k	k	NOUN
ejpam-3177	140	6	−	−	PROPN
ejpam-3177	140	7	s	s	PART
ejpam-3177	140	8	)	)	PUNCT
ejpam-3177	140	9	{	{	PUNCT
ejpam-3177	140	10	h(dφvj	h(dφvj	NOUN
ejpam-3177	140	11	,	,	PUNCT
ejpam-3177	140	12	fdφvk)h(τ	fdφvk)h(τ	PROPN
ejpam-3177	140	13	,	,	PUNCT
ejpam-3177	140	14	fdφ(ek	fdφ(ek	NOUN
ejpam-3177	140	15	)	)	PUNCT
ejpam-3177	140	16	)	)	PUNCT
ejpam-3177	140	17	}	}	PUNCT
ejpam-3177	140	18	.	.	PUNCT
ejpam-3177	141	1	(	(	PUNCT
ejpam-3177	141	2	9	9	X
ejpam-3177	141	3	)	)	PUNCT
ejpam-3177	141	4	let	let	VERB
ejpam-3177	141	5	τ(φ	τ(φ	NUM
ejpam-3177	141	6	)	)	PUNCT
ejpam-3177	141	7	∈	∈	PROPN
ejpam-3177	141	8	tm⊥	tm⊥	PROPN
ejpam-3177	141	9	,	,	PUNCT
ejpam-3177	141	10	then	then	ADV
ejpam-3177	141	11	m∑	m∑	SCONJ
ejpam-3177	141	12	j	j	PROPN
ejpam-3177	141	13	,	,	PUNCT
ejpam-3177	141	14	k=1	k=1	PROPN
ejpam-3177	141	15	h	h	NOUN
ejpam-3177	141	16	(	(	PUNCT
ejpam-3177	141	17	τ(φ	τ(φ	PROPN
ejpam-3177	141	18	)	)	PUNCT
ejpam-3177	141	19	,	,	PUNCT
ejpam-3177	141	20	rn	rn	PROPN
ejpam-3177	141	21	(	(	PUNCT
ejpam-3177	141	22	dφ(vj	dφ(vj	PROPN
ejpam-3177	141	23	)	)	PUNCT
ejpam-3177	141	24	,	,	PUNCT
ejpam-3177	141	25	dφ(vk	dφ(vk	PROPN
ejpam-3177	141	26	)	)	PUNCT
ejpam-3177	141	27	)	)	PUNCT
ejpam-3177	141	28	dφ(vk))dφ(vj	dφ(vk))dφ(vj	ADP
ejpam-3177	141	29	)	)	PUNCT
ejpam-3177	141	30	=	=	SYM
ejpam-3177	142	1	0	0	X
ejpam-3177	142	2	.	.	PUNCT
ejpam-3177	143	1	let	let	VERB
ejpam-3177	143	2	m2m+s	m2m+s	PROPN
ejpam-3177	143	3	be	be	AUX
ejpam-3177	143	4	a	a	DET
ejpam-3177	143	5	hyperspace	hyperspace	NOUN
ejpam-3177	143	6	of	of	ADP
ejpam-3177	143	7	s	s	NOUN
ejpam-3177	143	8	-	-	ADJ
ejpam-3177	143	9	manifold	manifold	ADJ
ejpam-3177	143	10	n.	n.	NOUN
ejpam-3177	143	11	each	each	DET
ejpam-3177	143	12	hypersurface	hypersurface	NOUN
ejpam-3177	143	13	of	of	ADP
ejpam-3177	143	14	s	s	NOUN
ejpam-3177	143	15	-	-	PUNCT
ejpam-3177	143	16	manifolds	manifold	NOUN
ejpam-3177	143	17	has	have	VERB
ejpam-3177	143	18	the	the	DET
ejpam-3177	143	19	structure	structure	NOUN
ejpam-3177	143	20	of	of	ADP
ejpam-3177	143	21	cr	cr	NOUN
ejpam-3177	143	22	-	-	PUNCT
ejpam-3177	143	23	submanifold	submanifold	NOUN
ejpam-3177	143	24	.	.	PUNCT
ejpam-3177	144	1	for	for	ADP
ejpam-3177	144	2	τ(φ	τ(φ	NOUN
ejpam-3177	144	3	)	)	PUNCT
ejpam-3177	144	4	∈	∈	PROPN
ejpam-3177	144	5	tm⊥	tm⊥	PROPN
ejpam-3177	144	6	,	,	PUNCT
ejpam-3177	144	7	we	we	PRON
ejpam-3177	144	8	can	can	AUX
ejpam-3177	144	9	take	take	VERB
ejpam-3177	144	10	fτ(φ	fτ(φ	ADJ
ejpam-3177	144	11	)	)	PUNCT
ejpam-3177	144	12	∈	∈	NOUN
ejpam-3177	144	13	γtm	γtm	NOUN
ejpam-3177	144	14	.	.	PUNCT
ejpam-3177	145	1	now	now	ADV
ejpam-3177	145	2	dim(m	dim(m	NOUN
ejpam-3177	145	3	)	)	PUNCT
ejpam-3177	145	4	=	=	SYM
ejpam-3177	146	1	2	2	NUM
ejpam-3177	146	2	m	m	NOUN
ejpam-3177	146	3	+	+	NOUN
ejpam-3177	146	4	s	s	X
ejpam-3177	146	5	=	=	X
ejpam-3177	146	6	2n	2n	NUM
ejpam-3177	146	7	−	−	NOUN
ejpam-3177	146	8	1	1	NUM
ejpam-3177	147	1	+	+	CCONJ
ejpam-3177	147	2	s.	s.	PROPN
ejpam-3177	147	3	for	for	ADP
ejpam-3177	147	4	orthonormal	orthonormal	ADJ
ejpam-3177	147	5	basis	basis	NOUN
ejpam-3177	147	6	{	{	PUNCT
ejpam-3177	147	7	dφ(vk)}mk=1	dφ(vk)}mk=1	NOUN
ejpam-3177	147	8	of	of	ADP
ejpam-3177	147	9	dφ(txm	dφ(txm	NOUN
ejpam-3177	147	10	)	)	PUNCT
ejpam-3177	147	11	at	at	ADP
ejpam-3177	147	12	all	all	DET
ejpam-3177	147	13	points	point	NOUN
ejpam-3177	147	14	on	on	ADP
ejpam-3177	147	15	m	m	PROPN
ejpam-3177	147	16	,	,	PUNCT
ejpam-3177	147	17	we	we	PRON
ejpam-3177	147	18	can	can	AUX
ejpam-3177	147	19	write	write	VERB
ejpam-3177	147	20	fτ(φ	fτ(φ	NOUN
ejpam-3177	147	21	)	)	PUNCT
ejpam-3177	147	22	=	=	SYM
ejpam-3177	148	1	2n−1+s∑	2n−1+s∑	NUM
ejpam-3177	148	2	k=1	k=1	X
ejpam-3177	148	3	h(fτ(φ	h(fτ(φ	PROPN
ejpam-3177	148	4	)	)	PUNCT
ejpam-3177	148	5	,	,	PUNCT
ejpam-3177	148	6	dφ(vk))dφ(vk	dφ(vk))dφ(vk	PROPN
ejpam-3177	148	7	)	)	PUNCT
ejpam-3177	148	8	.	.	PUNCT
ejpam-3177	149	1	by	by	ADP
ejpam-3177	149	2	lemma	lemma	PROPN
ejpam-3177	149	3	2	2	NUM
ejpam-3177	149	4	,	,	PUNCT
ejpam-3177	149	5	∆τ(φ	∆τ(φ	ADJ
ejpam-3177	149	6	)	)	PUNCT
ejpam-3177	149	7	=	=	SYM
ejpam-3177	150	1	2n−1+s∑	2n−1+s∑	NUM
ejpam-3177	150	2	i	i	PRON
ejpam-3177	150	3	,	,	PUNCT
ejpam-3177	150	4	j=1	j=1	PROPN
ejpam-3177	150	5	h	h	PROPN
ejpam-3177	150	6	(	(	PUNCT
ejpam-3177	150	7	τ(f	τ(f	PROPN
ejpam-3177	150	8	)	)	PUNCT
ejpam-3177	150	9	,	,	PUNCT
ejpam-3177	150	10	(	(	PUNCT
ejpam-3177	150	11	∇̃vidφ)(vj	∇̃vidφ)(vj	PROPN
ejpam-3177	150	12	)	)	PUNCT
ejpam-3177	150	13	)	)	PUNCT
ejpam-3177	151	1	(	(	PUNCT
ejpam-3177	151	2	∇̃vidφ)(vj	∇̃vidφ)(vj	NOUN
ejpam-3177	151	3	)	)	PUNCT
ejpam-3177	151	4	n.	n.	NOUN
ejpam-3177	151	5	a.	a.	PROPN
ejpam-3177	151	6	rehman	rehman	PROPN
ejpam-3177	151	7	,	,	PUNCT
ejpam-3177	151	8	m.	m.	NOUN
ejpam-3177	151	9	bari	bari	NOUN
ejpam-3177	151	10	/	/	SYM
ejpam-3177	151	11	eur	eur	PROPN
ejpam-3177	151	12	.	.	PUNCT
ejpam-3177	152	1	j.	j.	PROPN
ejpam-3177	152	2	pure	pure	PROPN
ejpam-3177	152	3	appl	appl	PROPN
ejpam-3177	152	4	.	.	PROPN
ejpam-3177	152	5	math	math	PROPN
ejpam-3177	152	6	,	,	PUNCT
ejpam-3177	152	7	11	11	NUM
ejpam-3177	152	8	(	(	PUNCT
ejpam-3177	152	9	1	1	NUM
ejpam-3177	152	10	)	)	PUNCT
ejpam-3177	152	11	(	(	PUNCT
ejpam-3177	152	12	2018	2018	NUM
ejpam-3177	152	13	)	)	PUNCT
ejpam-3177	152	14	,	,	PUNCT
ejpam-3177	152	15	150	150	NUM
ejpam-3177	152	16	-	-	SYM
ejpam-3177	152	17	159	159	NUM
ejpam-3177	152	18	156	156	NUM
ejpam-3177	152	19	furthermore	furthermore	ADV
ejpam-3177	152	20	,	,	PUNCT
ejpam-3177	152	21	we	we	PRON
ejpam-3177	152	22	have	have	VERB
ejpam-3177	152	23	r(τ(φ	r(τ(φ	ADJ
ejpam-3177	152	24	)	)	PUNCT
ejpam-3177	152	25	)	)	PUNCT
ejpam-3177	153	1	=	=	PUNCT
ejpam-3177	154	1	2n−1+s∑	2n−1+s∑	NUM
ejpam-3177	154	2	k=1	k=1	X
ejpam-3177	154	3	rn	rn	PROPN
ejpam-3177	154	4	(	(	PUNCT
ejpam-3177	154	5	τ(φ	τ(φ	PROPN
ejpam-3177	154	6	)	)	PUNCT
ejpam-3177	154	7	,	,	PUNCT
ejpam-3177	154	8	dφ(ek))dφ	dφ(ek))dφ	PROPN
ejpam-3177	154	9	=	=	PUNCT
ejpam-3177	154	10	k	k	PROPN
ejpam-3177	155	1	+	+	NOUN
ejpam-3177	155	2	3s	3s	NUM
ejpam-3177	155	3	4	4	NUM
ejpam-3177	155	4	(	(	PUNCT
ejpam-3177	155	5	2n−	2n−	PROPN
ejpam-3177	155	6	1	1	NUM
ejpam-3177	155	7	+	+	CCONJ
ejpam-3177	155	8	s)τ(φ	s)τ(φ	ADV
ejpam-3177	155	9	)	)	PUNCT
ejpam-3177	155	10	+	+	CCONJ
ejpam-3177	155	11	3(k	3(k	NUM
ejpam-3177	155	12	−	−	PROPN
ejpam-3177	155	13	s	s	NOUN
ejpam-3177	155	14	)	)	PUNCT
ejpam-3177	155	15	4	4	NUM
ejpam-3177	155	16	τ(φ	τ(φ	NUM
ejpam-3177	155	17	)	)	PUNCT
ejpam-3177	155	18	.	.	PUNCT
ejpam-3177	156	1	(	(	PUNCT
ejpam-3177	156	2	10	10	NUM
ejpam-3177	156	3	)	)	PUNCT
ejpam-3177	156	4	now	now	ADV
ejpam-3177	156	5	the	the	DET
ejpam-3177	156	6	necessary	necessary	ADJ
ejpam-3177	156	7	and	and	CCONJ
ejpam-3177	156	8	sufficient	sufficient	ADJ
ejpam-3177	156	9	conditions	condition	NOUN
ejpam-3177	156	10	f	f	PRON
ejpam-3177	156	11	to	to	PART
ejpam-3177	156	12	be	be	AUX
ejpam-3177	156	13	biharmonic	biharmonic	NOUN
ejpam-3177	156	14	is	be	AUX
ejpam-3177	156	15	that	that	SCONJ
ejpam-3177	156	16	τ2(f	τ2(f	X
ejpam-3177	156	17	)	)	PUNCT
ejpam-3177	157	1	=	=	SYM
ejpam-3177	157	2	4̄τ(f	4̄τ(f	NUM
ejpam-3177	157	3	)	)	PUNCT
ejpam-3177	157	4	−r(τ(f	−r(τ(f	NOUN
ejpam-3177	157	5	)	)	PUNCT
ejpam-3177	157	6	)	)	PUNCT
ejpam-3177	158	1	=	=	PUNCT
ejpam-3177	158	2	0	0	NUM
ejpam-3177	158	3	,	,	PUNCT
ejpam-3177	158	4	(	(	PUNCT
ejpam-3177	158	5	11	11	NUM
ejpam-3177	158	6	)	)	PUNCT
ejpam-3177	158	7	this	this	PRON
ejpam-3177	158	8	becomes	become	VERB
ejpam-3177	158	9	2n−1+s∑	2n−1+s∑	NOUN
ejpam-3177	159	1	i	i	PRON
ejpam-3177	159	2	,	,	PUNCT
ejpam-3177	159	3	j=1	j=1	PROPN
ejpam-3177	159	4	h	h	PROPN
ejpam-3177	159	5	(	(	PUNCT
ejpam-3177	159	6	τ(f	τ(f	PROPN
ejpam-3177	159	7	)	)	PUNCT
ejpam-3177	159	8	,	,	PUNCT
ejpam-3177	159	9	∇̃vjdf	∇̃vjdf	NOUN
ejpam-3177	159	10	(	(	PUNCT
ejpam-3177	159	11	vk	vk	PROPN
ejpam-3177	159	12	)	)	PUNCT
ejpam-3177	159	13	)	)	PUNCT
ejpam-3177	159	14	∇̃vjdf	∇̃vjdf	NOUN
ejpam-3177	159	15	(	(	PUNCT
ejpam-3177	159	16	vk)−	vk)−	X
ejpam-3177	159	17	[	[	PUNCT
ejpam-3177	159	18	k	k	X
ejpam-3177	159	19	+	+	NOUN
ejpam-3177	159	20	3s	3s	NUM
ejpam-3177	159	21	4	4	NUM
ejpam-3177	159	22	(	(	PUNCT
ejpam-3177	159	23	2n−	2n−	PROPN
ejpam-3177	159	24	1	1	NUM
ejpam-3177	159	25	+	+	CCONJ
ejpam-3177	159	26	s)τ(φ	s)τ(φ	ADV
ejpam-3177	159	27	)	)	PUNCT
ejpam-3177	159	28	+	+	CCONJ
ejpam-3177	159	29	3(k	3(k	NUM
ejpam-3177	159	30	−	−	PROPN
ejpam-3177	159	31	s	s	NOUN
ejpam-3177	159	32	)	)	PUNCT
ejpam-3177	159	33	4	4	NUM
ejpam-3177	159	34	τ(φ	τ(φ	NUM
ejpam-3177	159	35	)	)	PUNCT
ejpam-3177	159	36	]	]	PUNCT
ejpam-3177	160	1	=	=	PUNCT
ejpam-3177	160	2	0(12	0(12	NUM
ejpam-3177	160	3	)	)	PUNCT
ejpam-3177	160	4	now	now	ADV
ejpam-3177	160	5	let	let	VERB
ejpam-3177	160	6	b(φ)(ej	b(φ)(ej	PROPN
ejpam-3177	160	7	,	,	PUNCT
ejpam-3177	160	8	ek	ek	NOUN
ejpam-3177	160	9	)	)	PUNCT
ejpam-3177	160	10	=	=	SYM
ejpam-3177	161	1	(	(	PUNCT
ejpam-3177	161	2	∇̃vjdφ)vk	∇̃vjdφ)vk	ADP
ejpam-3177	161	3	=	=	SYM
ejpam-3177	161	4	h(dφ(vj	h(dφ(vj	NOUN
ejpam-3177	161	5	)	)	PUNCT
ejpam-3177	162	1	,	,	PUNCT
ejpam-3177	162	2	dφ(vk))v	dφ(vk))v	NOUN
ejpam-3177	162	3	=	=	PROPN
ejpam-3177	162	4	hjku	hjku	PROPN
ejpam-3177	162	5	,	,	PUNCT
ejpam-3177	162	6	where	where	SCONJ
ejpam-3177	162	7	u	u	NOUN
ejpam-3177	162	8	is	be	AUX
ejpam-3177	162	9	the	the	DET
ejpam-3177	162	10	unit	unit	NOUN
ejpam-3177	162	11	normal	normal	ADJ
ejpam-3177	162	12	vector	vector	NOUN
ejpam-3177	162	13	along	along	ADP
ejpam-3177	162	14	f	f	PROPN
ejpam-3177	162	15	(	(	PUNCT
ejpam-3177	162	16	m	m	PROPN
ejpam-3177	162	17	)	)	PUNCT
ejpam-3177	162	18	.	.	PUNCT
ejpam-3177	163	1	then	then	ADV
ejpam-3177	163	2	τ(f	τ(f	X
ejpam-3177	163	3	)	)	PUNCT
ejpam-3177	163	4	=	=	SYM
ejpam-3177	163	5	2n−1+s∑	2n−1+s∑	NUM
ejpam-3177	163	6	r=1	r=1	NOUN
ejpam-3177	163	7	(	(	PUNCT
ejpam-3177	163	8	∇̃vrdf	∇̃vrdf	NOUN
ejpam-3177	163	9	)	)	PUNCT
ejpam-3177	163	10	(	(	PUNCT
ejpam-3177	163	11	vr	vr	NOUN
ejpam-3177	163	12	)	)	PUNCT
ejpam-3177	163	13	=	=	SYM
ejpam-3177	163	14	2n−1+s∑	2n−1+s∑	NUM
ejpam-3177	163	15	r=1	r=1	NOUN
ejpam-3177	163	16	hrru	hrru	NOUN
ejpam-3177	163	17	,	,	PUNCT
ejpam-3177	163	18	where	where	SCONJ
ejpam-3177	163	19	u	u	NOUN
ejpam-3177	163	20	is	be	AUX
ejpam-3177	163	21	the	the	DET
ejpam-3177	163	22	unit	unit	NOUN
ejpam-3177	163	23	normal	normal	ADJ
ejpam-3177	163	24	vector	vector	NOUN
ejpam-3177	163	25	along	along	ADP
ejpam-3177	163	26	f	f	PROPN
ejpam-3177	163	27	(	(	PUNCT
ejpam-3177	163	28	m	m	PROPN
ejpam-3177	163	29	)	)	PUNCT
ejpam-3177	163	30	.	.	PUNCT
ejpam-3177	164	1	thus	thus	ADV
ejpam-3177	164	2	,	,	PUNCT
ejpam-3177	164	3	the	the	DET
ejpam-3177	164	4	left	left	ADJ
ejpam-3177	164	5	hand	hand	NOUN
ejpam-3177	164	6	side	side	NOUN
ejpam-3177	164	7	of	of	ADP
ejpam-3177	164	8	(	(	PUNCT
ejpam-3177	164	9	15	15	NUM
ejpam-3177	164	10	)	)	PUNCT
ejpam-3177	164	11	becomes	become	VERB
ejpam-3177	164	12	as	as	ADP
ejpam-3177	164	13	:	:	PUNCT
ejpam-3177	164	14	2n−1+s∑	2n−1+s∑	NUM
ejpam-3177	164	15	j	j	PROPN
ejpam-3177	164	16	,	,	PUNCT
ejpam-3177	164	17	k	k	PROPN
ejpam-3177	164	18	,	,	PUNCT
ejpam-3177	164	19	r=1	r=1	NOUN
ejpam-3177	164	20	{	{	PUNCT
ejpam-3177	164	21	hrrhjkhjku	hrrhjkhjku	NOUN
ejpam-3177	164	22	−	−	PROPN
ejpam-3177	164	23	[	[	PUNCT
ejpam-3177	164	24	k	k	X
ejpam-3177	165	1	+	+	CCONJ
ejpam-3177	165	2	3s	3s	NUM
ejpam-3177	165	3	4	4	NUM
ejpam-3177	165	4	(	(	PUNCT
ejpam-3177	165	5	2n−	2n−	PROPN
ejpam-3177	165	6	1	1	NUM
ejpam-3177	165	7	+	+	CCONJ
ejpam-3177	165	8	s)τ(φ	s)τ(φ	ADV
ejpam-3177	165	9	)	)	PUNCT
ejpam-3177	165	10	+	+	CCONJ
ejpam-3177	165	11	3(k	3(k	NUM
ejpam-3177	165	12	−	−	PROPN
ejpam-3177	165	13	s	s	NOUN
ejpam-3177	165	14	)	)	PUNCT
ejpam-3177	165	15	4	4	NUM
ejpam-3177	165	16	τ(φ	τ(φ	NUM
ejpam-3177	165	17	)	)	PUNCT
ejpam-3177	165	18	]	]	PUNCT
ejpam-3177	165	19	}	}	PUNCT
ejpam-3177	165	20	=	=	SYM
ejpam-3177	165	21	0	0	NUM
ejpam-3177	165	22	,	,	PUNCT
ejpam-3177	165	23	(	(	PUNCT
ejpam-3177	165	24	2n−1+s∑	2n−1+s∑	NUM
ejpam-3177	165	25	r=1	r=1	NOUN
ejpam-3177	165	26	hrr	hrr	PROPN
ejpam-3177	165	27	)	)	PUNCT
ejpam-3177	165	28			PROPN
ejpam-3177	165	29	m∑	m∑	PROPN
ejpam-3177	165	30	j	j	NOUN
ejpam-3177	165	31	,	,	PUNCT
ejpam-3177	165	32	k=1	k=1	PROPN
ejpam-3177	165	33	hjkhjku	hjkhjku	PROPN
ejpam-3177	165	34	−	−	PROPN
ejpam-3177	166	1	[	[	PUNCT
ejpam-3177	166	2	k	k	X
ejpam-3177	166	3	+	+	CCONJ
ejpam-3177	166	4	3s	3s	NUM
ejpam-3177	166	5	4	4	NUM
ejpam-3177	166	6	(	(	PUNCT
ejpam-3177	166	7	2n−	2n−	PROPN
ejpam-3177	166	8	1	1	NUM
ejpam-3177	166	9	+	+	CCONJ
ejpam-3177	166	10	s)u	s)u	X
ejpam-3177	166	11	+	+	CCONJ
ejpam-3177	166	12	3(k	3(k	NUM
ejpam-3177	166	13	−	−	NUM
ejpam-3177	166	14	s	s	NOUN
ejpam-3177	166	15	)	)	PUNCT
ejpam-3177	166	16	4	4	NUM
ejpam-3177	166	17	u	u	NOUN
ejpam-3177	166	18	]	]	X
ejpam-3177	166	19			NOUN
ejpam-3177	166	20	=	=	SYM
ejpam-3177	166	21	0	0	NUM
ejpam-3177	166	22	,	,	PUNCT
ejpam-3177	166	23	‖	‖	ADJ
ejpam-3177	166	24	τ(φ	τ(φ	X
ejpam-3177	166	25	)	)	PUNCT
ejpam-3177	166	26	‖	‖	PROPN
ejpam-3177	166	27	{	{	PUNCT
ejpam-3177	166	28	‖	‖	PROPN
ejpam-3177	166	29	b(φ	b(φ	PROPN
ejpam-3177	166	30	)	)	PUNCT
ejpam-3177	166	31	‖2	‖2	NOUN
ejpam-3177	166	32	u	u	NOUN
ejpam-3177	166	33	−	−	PROPN
ejpam-3177	167	1	[	[	PUNCT
ejpam-3177	167	2	k	k	X
ejpam-3177	167	3	+	+	CCONJ
ejpam-3177	167	4	3s	3s	NUM
ejpam-3177	167	5	4	4	NUM
ejpam-3177	167	6	(	(	PUNCT
ejpam-3177	167	7	2n−	2n−	PROPN
ejpam-3177	167	8	1	1	NUM
ejpam-3177	167	9	+	+	CCONJ
ejpam-3177	167	10	s)u	s)u	X
ejpam-3177	167	11	+	+	CCONJ
ejpam-3177	167	12	3(k	3(k	NUM
ejpam-3177	167	13	−	−	NUM
ejpam-3177	167	14	s	s	NOUN
ejpam-3177	167	15	)	)	PUNCT
ejpam-3177	167	16	4	4	NUM
ejpam-3177	167	17	u	u	NOUN
ejpam-3177	167	18	]	]	X
ejpam-3177	167	19	}	}	PUNCT
ejpam-3177	167	20	=	=	SYM
ejpam-3177	167	21	0	0	X
ejpam-3177	167	22	.	.	PUNCT
ejpam-3177	167	23	since	since	SCONJ
ejpam-3177	167	24	τ(φ	τ(φ	NUM
ejpam-3177	167	25	)	)	PUNCT
ejpam-3177	167	26	6=	6=	ADP
ejpam-3177	167	27	0	0	NUM
ejpam-3177	167	28	,	,	PUNCT
ejpam-3177	167	29	by	by	ADP
ejpam-3177	167	30	assumption	assumption	NOUN
ejpam-3177	167	31	,	,	PUNCT
ejpam-3177	167	32	then	then	ADV
ejpam-3177	167	33	we	we	PRON
ejpam-3177	167	34	have	have	AUX
ejpam-3177	167	35	‖	‖	VERB
ejpam-3177	167	36	b(φ	b(φ	ADV
ejpam-3177	167	37	)	)	PUNCT
ejpam-3177	167	38	‖2	‖2	NOUN
ejpam-3177	168	1	−	−	PROPN
ejpam-3177	169	1	[	[	PUNCT
ejpam-3177	169	2	k	k	X
ejpam-3177	169	3	+	+	CCONJ
ejpam-3177	169	4	3s	3s	NUM
ejpam-3177	169	5	4	4	NUM
ejpam-3177	169	6	(	(	PUNCT
ejpam-3177	169	7	2n−	2n−	PROPN
ejpam-3177	169	8	1	1	NUM
ejpam-3177	169	9	+	+	NUM
ejpam-3177	169	10	s	s	NOUN
ejpam-3177	169	11	)	)	PUNCT
ejpam-3177	169	12	+	+	CCONJ
ejpam-3177	170	1	3(k	3(k	NUM
ejpam-3177	170	2	−	−	PROPN
ejpam-3177	170	3	s	s	NOUN
ejpam-3177	170	4	)	)	PUNCT
ejpam-3177	170	5	4	4	NUM
ejpam-3177	170	6	]	]	PUNCT
ejpam-3177	170	7	=	=	SYM
ejpam-3177	170	8	0	0	NUM
ejpam-3177	170	9	,	,	PUNCT
ejpam-3177	170	10	and	and	CCONJ
ejpam-3177	170	11	‖	‖	PROPN
ejpam-3177	170	12	b(φ	b(φ	PROPN
ejpam-3177	170	13	)	)	PUNCT
ejpam-3177	170	14	‖2=	‖2=	PROPN
ejpam-3177	171	1	[	[	PUNCT
ejpam-3177	171	2	k	k	X
ejpam-3177	171	3	+	+	CCONJ
ejpam-3177	171	4	3s	3s	NUM
ejpam-3177	171	5	4	4	NUM
ejpam-3177	171	6	(	(	PUNCT
ejpam-3177	171	7	2n−	2n−	PROPN
ejpam-3177	171	8	1	1	NUM
ejpam-3177	171	9	+	+	NUM
ejpam-3177	171	10	s	s	NOUN
ejpam-3177	171	11	)	)	PUNCT
ejpam-3177	171	12	+	+	CCONJ
ejpam-3177	172	1	3(k	3(k	NUM
ejpam-3177	172	2	−	−	PROPN
ejpam-3177	172	3	s	s	NOUN
ejpam-3177	172	4	)	)	PUNCT
ejpam-3177	172	5	4	4	NUM
ejpam-3177	172	6	]	]	PUNCT
ejpam-3177	172	7	.	.	PUNCT
ejpam-3177	173	1	(	(	PUNCT
ejpam-3177	173	2	13	13	X
ejpam-3177	173	3	)	)	PUNCT
ejpam-3177	173	4	n.	n.	NOUN
ejpam-3177	173	5	a.	a.	PROPN
ejpam-3177	173	6	rehman	rehman	PROPN
ejpam-3177	173	7	,	,	PUNCT
ejpam-3177	173	8	m.	m.	NOUN
ejpam-3177	173	9	bari	bari	NOUN
ejpam-3177	173	10	/	/	SYM
ejpam-3177	173	11	eur	eur	PROPN
ejpam-3177	173	12	.	.	PUNCT
ejpam-3177	174	1	j.	j.	PROPN
ejpam-3177	174	2	pure	pure	PROPN
ejpam-3177	174	3	appl	appl	PROPN
ejpam-3177	174	4	.	.	PROPN
ejpam-3177	174	5	math	math	PROPN
ejpam-3177	174	6	,	,	PUNCT
ejpam-3177	174	7	11	11	NUM
ejpam-3177	174	8	(	(	PUNCT
ejpam-3177	174	9	1	1	NUM
ejpam-3177	174	10	)	)	PUNCT
ejpam-3177	174	11	(	(	PUNCT
ejpam-3177	174	12	2018	2018	NUM
ejpam-3177	174	13	)	)	PUNCT
ejpam-3177	174	14	,	,	PUNCT
ejpam-3177	174	15	150	150	NUM
ejpam-3177	174	16	-	-	SYM
ejpam-3177	174	17	159	159	NUM
ejpam-3177	174	18	157	157	NUM
ejpam-3177	174	19	next	next	ADV
ejpam-3177	174	20	let	let	VERB
ejpam-3177	174	21	m2m+s	m2m+s	PROPN
ejpam-3177	174	22	be	be	AUX
ejpam-3177	174	23	an	an	DET
ejpam-3177	174	24	invariant	invariant	ADJ
ejpam-3177	174	25	submanifold	submanifold	NOUN
ejpam-3177	174	26	of	of	ADP
ejpam-3177	174	27	s	s	NOUN
ejpam-3177	174	28	-	-	ADJ
ejpam-3177	174	29	manifold	manifold	ADJ
ejpam-3177	174	30	n.	n.	NOUN
ejpam-3177	174	31	then	then	ADV
ejpam-3177	174	32	for	for	ADP
ejpam-3177	174	33	τ(φ	τ(φ	NOUN
ejpam-3177	174	34	)	)	PUNCT
ejpam-3177	174	35	∈	∈	PROPN
ejpam-3177	174	36	γtm⊥	γtm⊥	PROPN
ejpam-3177	174	37	,	,	PUNCT
ejpam-3177	174	38	fτ(φ	fτ(φ	ADJ
ejpam-3177	174	39	)	)	PUNCT
ejpam-3177	174	40	∈	∈	NOUN
ejpam-3177	174	41	γtm⊥.	γtm⊥.	PROPN
ejpam-3177	174	42	for	for	ADP
ejpam-3177	174	43	orthonormal	orthonormal	ADJ
ejpam-3177	174	44	basis	basis	NOUN
ejpam-3177	174	45	{	{	PUNCT
ejpam-3177	174	46	dφ(vk)}mk=1	dφ(vk)}mk=1	NOUN
ejpam-3177	174	47	of	of	ADP
ejpam-3177	174	48	dφ(txm	dφ(txm	NOUN
ejpam-3177	174	49	)	)	PUNCT
ejpam-3177	174	50	at	at	ADV
ejpam-3177	174	51	all	all	DET
ejpam-3177	174	52	points	point	NOUN
ejpam-3177	174	53	x	x	SYM
ejpam-3177	174	54	∈m	∈m	NOUN
ejpam-3177	174	55	,	,	PUNCT
ejpam-3177	174	56	we	we	PRON
ejpam-3177	174	57	have	have	VERB
ejpam-3177	174	58	h(fτ(φ	h(fτ(φ	ADJ
ejpam-3177	174	59	)	)	PUNCT
ejpam-3177	174	60	,	,	PUNCT
ejpam-3177	174	61	dφ(vk	dφ(vk	PROPN
ejpam-3177	174	62	)	)	PUNCT
ejpam-3177	174	63	)	)	PUNCT
ejpam-3177	175	1	=	=	PUNCT
ejpam-3177	175	2	0	0	NUM
ejpam-3177	175	3	,	,	PUNCT
ejpam-3177	175	4	then	then	ADV
ejpam-3177	175	5	in	in	ADP
ejpam-3177	175	6	this	this	DET
ejpam-3177	175	7	case	case	NOUN
ejpam-3177	175	8	r(τ(φ	r(τ(φ	ADJ
ejpam-3177	175	9	)	)	PUNCT
ejpam-3177	175	10	)	)	PUNCT
ejpam-3177	176	1	=	=	PUNCT
ejpam-3177	177	1	2n−1+s∑	2n−1+s∑	NUM
ejpam-3177	177	2	k=1	k=1	X
ejpam-3177	177	3	rn	rn	PROPN
ejpam-3177	177	4	(	(	PUNCT
ejpam-3177	177	5	τ(φ	τ(φ	PROPN
ejpam-3177	177	6	)	)	PUNCT
ejpam-3177	177	7	,	,	PUNCT
ejpam-3177	177	8	dφ(ek))dφ	dφ(ek))dφ	PROPN
ejpam-3177	177	9	=	=	PUNCT
ejpam-3177	177	10	k	k	PROPN
ejpam-3177	178	1	+	+	NOUN
ejpam-3177	178	2	3s	3s	NUM
ejpam-3177	178	3	4	4	NUM
ejpam-3177	178	4	(	(	PUNCT
ejpam-3177	178	5	2m+	2m+	NUM
ejpam-3177	178	6	s)τ(φ	s)τ(φ	ADV
ejpam-3177	178	7	)	)	PUNCT
ejpam-3177	178	8	.	.	PUNCT
ejpam-3177	179	1	(	(	PUNCT
ejpam-3177	179	2	14	14	NUM
ejpam-3177	179	3	)	)	PUNCT
ejpam-3177	179	4	then	then	ADV
ejpam-3177	179	5	by	by	ADP
ejpam-3177	179	6	equation	equation	NOUN
ejpam-3177	179	7	(	(	PUNCT
ejpam-3177	179	8	11	11	NUM
ejpam-3177	179	9	)	)	PUNCT
ejpam-3177	179	10	,	,	PUNCT
ejpam-3177	179	11	2m+s∑	2m+s∑	NUM
ejpam-3177	179	12	i	i	NOUN
ejpam-3177	179	13	,	,	PUNCT
ejpam-3177	179	14	j=1	j=1	PROPN
ejpam-3177	179	15	h	h	PROPN
ejpam-3177	179	16	(	(	PUNCT
ejpam-3177	179	17	τ(f	τ(f	PROPN
ejpam-3177	179	18	)	)	PUNCT
ejpam-3177	179	19	,	,	PUNCT
ejpam-3177	179	20	∇̃vjdf	∇̃vjdf	NOUN
ejpam-3177	179	21	(	(	PUNCT
ejpam-3177	179	22	vk	vk	PROPN
ejpam-3177	179	23	)	)	PUNCT
ejpam-3177	179	24	)	)	PUNCT
ejpam-3177	179	25	∇̃vjdf	∇̃vjdf	NOUN
ejpam-3177	179	26	(	(	PUNCT
ejpam-3177	179	27	vk)−	vk)−	NOUN
ejpam-3177	179	28	k	k	NOUN
ejpam-3177	180	1	+	+	NOUN
ejpam-3177	180	2	3s	3s	NUM
ejpam-3177	180	3	4	4	NUM
ejpam-3177	180	4	(	(	PUNCT
ejpam-3177	180	5	2m+	2m+	NUM
ejpam-3177	180	6	s)τ(φ	s)τ(φ	ADV
ejpam-3177	180	7	)	)	PUNCT
ejpam-3177	180	8	=	=	SYM
ejpam-3177	180	9	0	0	PUNCT
ejpam-3177	180	10	(	(	PUNCT
ejpam-3177	180	11	15	15	NUM
ejpam-3177	180	12	)	)	PUNCT
ejpam-3177	180	13	with	with	ADP
ejpam-3177	180	14	similar	similar	ADJ
ejpam-3177	180	15	computations	computation	NOUN
ejpam-3177	180	16	as	as	ADP
ejpam-3177	180	17	above	above	ADV
ejpam-3177	180	18	we	we	PRON
ejpam-3177	180	19	have	have	AUX
ejpam-3177	180	20	‖	‖	VERB
ejpam-3177	180	21	τ(φ	τ(φ	ADV
ejpam-3177	180	22	)	)	PUNCT
ejpam-3177	180	23	‖	‖	PROPN
ejpam-3177	180	24	{	{	PUNCT
ejpam-3177	181	1	‖	‖	PROPN
ejpam-3177	181	2	b(φ	b(φ	PROPN
ejpam-3177	181	3	)	)	PUNCT
ejpam-3177	181	4	‖2	‖2	NOUN
ejpam-3177	181	5	u	u	NOUN
ejpam-3177	181	6	−	−	PROPN
ejpam-3177	182	1	[	[	PUNCT
ejpam-3177	182	2	k	k	X
ejpam-3177	182	3	+	+	CCONJ
ejpam-3177	182	4	3s	3s	NUM
ejpam-3177	182	5	4	4	NUM
ejpam-3177	182	6	(	(	PUNCT
ejpam-3177	182	7	2m+	2m+	NUM
ejpam-3177	182	8	s)u	s)u	X
ejpam-3177	182	9	]	]	X
ejpam-3177	182	10	}	}	PUNCT
ejpam-3177	182	11	=	=	SYM
ejpam-3177	182	12	0	0	X
ejpam-3177	182	13	.	.	PUNCT
ejpam-3177	183	1	this	this	PRON
ejpam-3177	183	2	implies	imply	VERB
ejpam-3177	183	3	‖	‖	PROPN
ejpam-3177	183	4	b(φ	b(φ	PROPN
ejpam-3177	183	5	)	)	PUNCT
ejpam-3177	183	6	‖2=	‖2=	PROPN
ejpam-3177	184	1	k	k	X
ejpam-3177	185	1	+	+	CCONJ
ejpam-3177	185	2	3s	3s	NUM
ejpam-3177	185	3	4	4	NUM
ejpam-3177	185	4	(	(	PUNCT
ejpam-3177	185	5	2m+	2m+	NUM
ejpam-3177	185	6	s	s	NOUN
ejpam-3177	185	7	)	)	PUNCT
ejpam-3177	185	8	corollary	corollary	ADJ
ejpam-3177	185	9	1	1	NUM
ejpam-3177	185	10	.	.	PUNCT
ejpam-3177	186	1	let	let	VERB
ejpam-3177	186	2	(	(	PUNCT
ejpam-3177	186	3	m	m	NOUN
ejpam-3177	186	4	,	,	PUNCT
ejpam-3177	186	5	g	g	NOUN
ejpam-3177	186	6	)	)	PUNCT
ejpam-3177	186	7	be	be	AUX
ejpam-3177	186	8	a	a	DET
ejpam-3177	186	9	2n−1	2n−1	ADJ
ejpam-3177	186	10	-	-	PUNCT
ejpam-3177	186	11	dimensional	dimensional	ADJ
ejpam-3177	186	12	submanifold	submanifold	NOUN
ejpam-3177	186	13	of	of	ADP
ejpam-3177	186	14	complex	complex	ADJ
ejpam-3177	186	15	space	space	NOUN
ejpam-3177	186	16	form	form	NOUN
ejpam-3177	186	17	n	n	PROPN
ejpam-3177	186	18	of	of	ADP
ejpam-3177	186	19	dimension	dimension	NOUN
ejpam-3177	186	20	2n	2n	NUM
ejpam-3177	186	21	,	,	PUNCT
ejpam-3177	186	22	and	and	CCONJ
ejpam-3177	186	23	φ	φ	NUM
ejpam-3177	186	24	:	:	PUNCT
ejpam-3177	186	25	(	(	PUNCT
ejpam-3177	186	26	m	m	NOUN
ejpam-3177	186	27	,	,	PUNCT
ejpam-3177	186	28	g)→	g)→	NOUN
ejpam-3177	186	29	(	(	PUNCT
ejpam-3177	186	30	n	n	CCONJ
ejpam-3177	186	31	,	,	PUNCT
ejpam-3177	186	32	h	h	NOUN
ejpam-3177	186	33	)	)	PUNCT
ejpam-3177	186	34	be	be	VERB
ejpam-3177	186	35	an	an	DET
ejpam-3177	186	36	isometric	isometric	ADJ
ejpam-3177	186	37	immersion	immersion	NOUN
ejpam-3177	186	38	with	with	ADP
ejpam-3177	186	39	non	non	ADJ
ejpam-3177	186	40	zero	zero	NUM
ejpam-3177	186	41	constant	constant	ADJ
ejpam-3177	186	42	parallel	parallel	ADJ
ejpam-3177	186	43	mean	mean	NOUN
ejpam-3177	186	44	curvature	curvature	NOUN
ejpam-3177	186	45	with	with	ADP
ejpam-3177	186	46	respect	respect	NOUN
ejpam-3177	186	47	to	to	ADP
ejpam-3177	186	48	connection	connection	NOUN
ejpam-3177	186	49	on	on	ADP
ejpam-3177	186	50	normal	normal	ADJ
ejpam-3177	186	51	bundle	bundle	NOUN
ejpam-3177	186	52	,	,	PUNCT
ejpam-3177	186	53	then	then	ADV
ejpam-3177	186	54	necessary	necessary	ADJ
ejpam-3177	186	55	and	and	CCONJ
ejpam-3177	186	56	sufficient	sufficient	ADJ
ejpam-3177	186	57	conditions	condition	NOUN
ejpam-3177	186	58	for	for	SCONJ
ejpam-3177	186	59	φ	φ	PROPN
ejpam-3177	186	60	to	to	PART
ejpam-3177	186	61	be	be	AUX
ejpam-3177	186	62	biharmonic	biharmonic	NOUN
ejpam-3177	186	63	is	be	AUX
ejpam-3177	186	64	‖	‖	ADJ
ejpam-3177	186	65	b(φ	b(φ	PROPN
ejpam-3177	186	66	)	)	PUNCT
ejpam-3177	186	67	‖2=	‖2=	PROPN
ejpam-3177	187	1	k	k	PROPN
ejpam-3177	187	2	2	2	NUM
ejpam-3177	187	3	(	(	PUNCT
ejpam-3177	187	4	n+	n+	NOUN
ejpam-3177	187	5	1	1	NUM
ejpam-3177	187	6	)	)	PUNCT
ejpam-3177	187	7	proof	proof	NOUN
ejpam-3177	187	8	.	.	PUNCT
ejpam-3177	188	1	in	in	ADP
ejpam-3177	188	2	equation	equation	NOUN
ejpam-3177	188	3	(	(	PUNCT
ejpam-3177	188	4	13	13	NUM
ejpam-3177	188	5	)	)	PUNCT
ejpam-3177	188	6	,	,	PUNCT
ejpam-3177	188	7	for	for	ADP
ejpam-3177	188	8	s=0	s=0	PROPN
ejpam-3177	188	9	we	we	PRON
ejpam-3177	188	10	get	get	VERB
ejpam-3177	188	11	result	result	NOUN
ejpam-3177	188	12	.	.	PUNCT
ejpam-3177	189	1	corollary	corollary	ADJ
ejpam-3177	189	2	2	2	NUM
ejpam-3177	189	3	.	.	PUNCT
ejpam-3177	190	1	let	let	VERB
ejpam-3177	190	2	(	(	PUNCT
ejpam-3177	190	3	m	m	NOUN
ejpam-3177	190	4	,	,	PUNCT
ejpam-3177	190	5	g	g	NOUN
ejpam-3177	190	6	)	)	PUNCT
ejpam-3177	190	7	be	be	VERB
ejpam-3177	190	8	a	a	DET
ejpam-3177	190	9	(	(	PUNCT
ejpam-3177	190	10	2n	2n	NUM
ejpam-3177	190	11	−	−	NOUN
ejpam-3177	190	12	1	1	NUM
ejpam-3177	190	13	)	)	PUNCT
ejpam-3177	190	14	+	+	CCONJ
ejpam-3177	190	15	1	1	NUM
ejpam-3177	190	16	-	-	PUNCT
ejpam-3177	190	17	dimensional	dimensional	ADJ
ejpam-3177	190	18	submanifold	submanifold	NOUN
ejpam-3177	190	19	of	of	ADP
ejpam-3177	190	20	sasakian	sasakian	ADJ
ejpam-3177	190	21	space	space	NOUN
ejpam-3177	190	22	form	form	NOUN
ejpam-3177	190	23	n	n	PROPN
ejpam-3177	190	24	of	of	ADP
ejpam-3177	190	25	dimension	dimension	NOUN
ejpam-3177	190	26	2n+1	2n+1	PROPN
ejpam-3177	190	27	,	,	PUNCT
ejpam-3177	190	28	and	and	CCONJ
ejpam-3177	190	29	φ	φ	NUM
ejpam-3177	190	30	:	:	PUNCT
ejpam-3177	190	31	(	(	PUNCT
ejpam-3177	190	32	m	m	NOUN
ejpam-3177	190	33	,	,	PUNCT
ejpam-3177	190	34	g)→	g)→	NOUN
ejpam-3177	190	35	(	(	PUNCT
ejpam-3177	190	36	n	n	CCONJ
ejpam-3177	190	37	,	,	PUNCT
ejpam-3177	190	38	h	h	NOUN
ejpam-3177	190	39	)	)	PUNCT
ejpam-3177	190	40	be	be	VERB
ejpam-3177	190	41	an	an	DET
ejpam-3177	190	42	isometric	isometric	ADJ
ejpam-3177	190	43	immersion	immersion	NOUN
ejpam-3177	190	44	with	with	ADP
ejpam-3177	190	45	non	non	ADJ
ejpam-3177	190	46	zero	zero	NUM
ejpam-3177	190	47	constant	constant	ADJ
ejpam-3177	190	48	parallel	parallel	ADJ
ejpam-3177	190	49	mean	mean	NOUN
ejpam-3177	190	50	curvature	curvature	NOUN
ejpam-3177	190	51	with	with	ADP
ejpam-3177	190	52	respect	respect	NOUN
ejpam-3177	190	53	to	to	ADP
ejpam-3177	190	54	connection	connection	NOUN
ejpam-3177	190	55	on	on	ADP
ejpam-3177	190	56	normal	normal	ADJ
ejpam-3177	190	57	bundle	bundle	NOUN
ejpam-3177	190	58	,	,	PUNCT
ejpam-3177	190	59	then	then	ADV
ejpam-3177	190	60	necessary	necessary	ADJ
ejpam-3177	190	61	and	and	CCONJ
ejpam-3177	190	62	sufficient	sufficient	ADJ
ejpam-3177	190	63	conditions	condition	NOUN
ejpam-3177	190	64	for	for	SCONJ
ejpam-3177	190	65	φ	φ	PROPN
ejpam-3177	190	66	to	to	PART
ejpam-3177	190	67	be	be	AUX
ejpam-3177	190	68	biharmonic	biharmonic	NOUN
ejpam-3177	190	69	is	be	AUX
ejpam-3177	190	70	‖	‖	ADJ
ejpam-3177	190	71	b(φ	b(φ	PROPN
ejpam-3177	190	72	)	)	PUNCT
ejpam-3177	190	73	‖2=	‖2=	PROPN
ejpam-3177	191	1	k	k	PROPN
ejpam-3177	191	2	4	4	NUM
ejpam-3177	191	3	(	(	PUNCT
ejpam-3177	191	4	2n+	2n+	NUM
ejpam-3177	191	5	3	3	NUM
ejpam-3177	191	6	)	)	PUNCT
ejpam-3177	191	7	+	+	CCONJ
ejpam-3177	191	8	3	3	NUM
ejpam-3177	191	9	4	4	NUM
ejpam-3177	191	10	(	(	PUNCT
ejpam-3177	191	11	2n−	2n−	PROPN
ejpam-3177	191	12	1	1	NUM
ejpam-3177	191	13	)	)	PUNCT
ejpam-3177	191	14	proof	proof	NOUN
ejpam-3177	191	15	.	.	PUNCT
ejpam-3177	192	1	in	in	ADP
ejpam-3177	192	2	equation	equation	NOUN
ejpam-3177	192	3	(	(	PUNCT
ejpam-3177	192	4	13	13	NUM
ejpam-3177	192	5	)	)	PUNCT
ejpam-3177	192	6	,	,	PUNCT
ejpam-3177	192	7	for	for	ADP
ejpam-3177	192	8	s=1	s=1	ADP
ejpam-3177	192	9	we	we	PRON
ejpam-3177	192	10	get	get	VERB
ejpam-3177	192	11	result	result	NOUN
ejpam-3177	192	12	.	.	PUNCT
ejpam-3177	193	1	acknowledgements	acknowledgement	NOUN
ejpam-3177	193	2	first	first	ADJ
ejpam-3177	193	3	author	author	NOUN
ejpam-3177	193	4	is	be	AUX
ejpam-3177	193	5	supported	support	VERB
ejpam-3177	193	6	by	by	ADP
ejpam-3177	193	7	nrpu	nrpu	NOUN
ejpam-3177	193	8	research	research	NOUN
ejpam-3177	193	9	project	project	NOUN
ejpam-3177	193	10	of	of	ADP
ejpam-3177	193	11	hec	hec	PROPN
ejpam-3177	193	12	,	,	PUNCT
ejpam-3177	193	13	pakistan	pakistan	PROPN
ejpam-3177	193	14	.	.	PUNCT
ejpam-3177	194	1	references	reference	NOUN
ejpam-3177	194	2	158	158	NUM
ejpam-3177	194	3	references	reference	NOUN
ejpam-3177	194	4	[	[	X
ejpam-3177	194	5	1	1	NUM
ejpam-3177	194	6	]	]	X
ejpam-3177	194	7	d.e	d.e	PROPN
ejpam-3177	194	8	.	.	PROPN
ejpam-3177	194	9	blair	blair	PROPN
ejpam-3177	194	10	,	,	PUNCT
ejpam-3177	194	11	geometry	geometry	NOUN
ejpam-3177	194	12	of	of	ADP
ejpam-3177	194	13	manifolds	manifold	NOUN
ejpam-3177	194	14	with	with	ADP
ejpam-3177	194	15	structural	structural	ADJ
ejpam-3177	194	16	group	group	NOUN
ejpam-3177	194	17	u(n)×o(s	u(n)×o(s	PROPN
ejpam-3177	194	18	)	)	PUNCT
ejpam-3177	194	19	,	,	PUNCT
ejpam-3177	194	20	j.	j.	PROPN
ejpam-3177	194	21	differential	differential	PROPN
ejpam-3177	194	22	geom	geom	PROPN
ejpam-3177	194	23	.	.	PUNCT
ejpam-3177	195	1	4	4	NUM
ejpam-3177	195	2	(	(	PUNCT
ejpam-3177	195	3	1970	1970	NUM
ejpam-3177	195	4	)	)	PUNCT
ejpam-3177	195	5	.	.	PUNCT
ejpam-3177	196	1	155	155	NUM
ejpam-3177	196	2	-	-	SYM
ejpam-3177	196	3	167	167	NUM
ejpam-3177	196	4	.	.	PUNCT
ejpam-3177	197	1	[	[	X
ejpam-3177	197	2	2	2	NUM
ejpam-3177	197	3	]	]	PUNCT
ejpam-3177	197	4	a.	a.	NOUN
ejpam-3177	197	5	balmus	balmus	PROPN
ejpam-3177	197	6	,	,	PUNCT
ejpam-3177	197	7	biharmonic	biharmonic	NOUN
ejpam-3177	197	8	properties	property	NOUN
ejpam-3177	197	9	and	and	CCONJ
ejpam-3177	197	10	conformal	conformal	ADJ
ejpam-3177	197	11	changes	change	NOUN
ejpam-3177	197	12	.	.	PUNCT
ejpam-3177	197	13	,	,	PUNCT
ejpam-3177	197	14	an	an	PROPN
ejpam-3177	197	15	.	.	NOUN
ejpam-3177	197	16	stiint	stiint	PROPN
ejpam-3177	197	17	.	.	PUNCT
ejpam-3177	198	1	univ	univ	PROPN
ejpam-3177	198	2	.	.	PUNCT
ejpam-3177	199	1	al.i	al.i	PROPN
ejpam-3177	199	2	.	.	PUNCT
ejpam-3177	200	1	cuza	cuza	PROPN
ejpam-3177	200	2	iasi	iasi	PROPN
ejpam-3177	200	3	mat	mat	NOUN
ejpam-3177	200	4	.	.	PUNCT
ejpam-3177	201	1	(	(	PUNCT
ejpam-3177	201	2	n.s	n.s	PROPN
ejpam-3177	201	3	.	.	PROPN
ejpam-3177	201	4	)	)	PUNCT
ejpam-3177	202	1	50	50	NUM
ejpam-3177	202	2	(	(	PUNCT
ejpam-3177	202	3	2004	2004	NUM
ejpam-3177	202	4	)	)	PUNCT
ejpam-3177	202	5	,	,	PUNCT
ejpam-3177	202	6	361372	361372	NUM
ejpam-3177	202	7	.	.	PUNCT
ejpam-3177	203	1	[	[	X
ejpam-3177	203	2	3	3	NUM
ejpam-3177	203	3	]	]	PUNCT
ejpam-3177	203	4	a.	a.	NOUN
ejpam-3177	203	5	balmus	balmus	PROPN
ejpam-3177	203	6	,	,	PUNCT
ejpam-3177	203	7	c.	c.	PROPN
ejpam-3177	203	8	oniciuc	oniciuc	NOUN
ejpam-3177	203	9	,	,	PUNCT
ejpam-3177	203	10	some	some	DET
ejpam-3177	203	11	remarks	remark	NOUN
ejpam-3177	203	12	on	on	ADP
ejpam-3177	203	13	the	the	DET
ejpam-3177	203	14	biharmonic	biharmonic	NOUN
ejpam-3177	203	15	submanifolds	submanifold	NOUN
ejpam-3177	203	16	of	of	ADP
ejpam-3177	203	17	s3	s3	PROPN
ejpam-3177	203	18	and	and	CCONJ
ejpam-3177	203	19	their	their	PRON
ejpam-3177	203	20	stability	stability	NOUN
ejpam-3177	203	21	,	,	PUNCT
ejpam-3177	203	22	an	an	PROPN
ejpam-3177	203	23	.	.	NOUN
ejpam-3177	203	24	stiint	stiint	PROPN
ejpam-3177	203	25	.	.	PUNCT
ejpam-3177	204	1	univ	univ	PROPN
ejpam-3177	204	2	.	.	PUNCT
ejpam-3177	205	1	al.i	al.i	PROPN
ejpam-3177	205	2	.	.	PUNCT
ejpam-3177	206	1	cuza	cuza	PROPN
ejpam-3177	206	2	iasi	iasi	PROPN
ejpam-3177	206	3	,	,	PUNCT
ejpam-3177	206	4	mat	mat	NOUN
ejpam-3177	206	5	.	.	PUNCT
ejpam-3177	207	1	(	(	PUNCT
ejpam-3177	207	2	n.s	n.s	PROPN
ejpam-3177	207	3	)	)	PUNCT
ejpam-3177	207	4	,	,	PUNCT
ejpam-3177	207	5	51	51	NUM
ejpam-3177	207	6	(	(	PUNCT
ejpam-3177	207	7	2005	2005	NUM
ejpam-3177	207	8	)	)	PUNCT
ejpam-3177	207	9	,	,	PUNCT
ejpam-3177	207	10	171190	171190	NUM
ejpam-3177	207	11	.	.	PUNCT
ejpam-3177	208	1	[	[	X
ejpam-3177	208	2	4	4	X
ejpam-3177	208	3	]	]	X
ejpam-3177	208	4	jose	jose	PROPN
ejpam-3177	208	5	l.	l.	PROPN
ejpam-3177	208	6	cabrerizo	cabrerizo	PROPN
ejpam-3177	208	7	,	,	PUNCT
ejpam-3177	208	8	luis	luis	PROPN
ejpam-3177	208	9	m.	m.	PROPN
ejpam-3177	208	10	fernandez	fernandez	PROPN
ejpam-3177	208	11	,	,	PUNCT
ejpam-3177	208	12	manuel	manuel	PROPN
ejpam-3177	208	13	fernandez	fernandez	PROPN
ejpam-3177	208	14	(	(	PUNCT
ejpam-3177	208	15	sevilla	sevilla	PROPN
ejpam-3177	208	16	)	)	PUNCT
ejpam-3177	208	17	,	,	PUNCT
ejpam-3177	208	18	on	on	ADP
ejpam-3177	208	19	normal	normal	ADJ
ejpam-3177	208	20	crsubmanifolds	crsubmanifold	NOUN
ejpam-3177	208	21	of	of	ADP
ejpam-3177	208	22	s	s	NOUN
ejpam-3177	208	23	-	-	PUNCT
ejpam-3177	208	24	manifolds	manifold	NOUN
ejpam-3177	208	25	,	,	PUNCT
ejpam-3177	208	26	colloquim	colloquim	ADJ
ejpam-3177	208	27	mathematicum	mathematicum	NOUN
ejpam-3177	208	28	,	,	PUNCT
ejpam-3177	208	29	vol	vol	NOUN
ejpam-3177	208	30	.	.	PUNCT
ejpam-3177	208	31	lxiv	lxiv	PROPN
ejpam-3177	208	32	,	,	PUNCT
ejpam-3177	208	33	(	(	PUNCT
ejpam-3177	208	34	1993	1993	NUM
ejpam-3177	208	35	)	)	PUNCT
ejpam-3177	208	36	,	,	PUNCT
ejpam-3177	208	37	fasc	fasc	PROPN
ejpam-3177	208	38	.	.	PROPN
ejpam-3177	208	39	2	2	NUM
ejpam-3177	208	40	.	.	PUNCT
ejpam-3177	209	1	[	[	X
ejpam-3177	209	2	5	5	NUM
ejpam-3177	209	3	]	]	PUNCT
ejpam-3177	209	4	toshiyuki	toshiyuki	NOUN
ejpam-3177	209	5	ichiyama	ichiyama	NOUN
ejpam-3177	209	6	,	,	PUNCT
ejpam-3177	209	7	jun	jun	PROPN
ejpam-3177	209	8	-	-	PUNCT
ejpam-3177	209	9	ichi	ichi	ADJ
ejpam-3177	209	10	inoguchi	inoguchi	NOUN
ejpam-3177	209	11	,	,	PUNCT
ejpam-3177	209	12	hajim	hajim	PROPN
ejpam-3177	209	13	urakawa	urakawa	PROPN
ejpam-3177	209	14	bi	bi	ADJ
ejpam-3177	209	15	-	-	ADJ
ejpam-3177	209	16	harmonic	harmonic	ADJ
ejpam-3177	209	17	maps	map	NOUN
ejpam-3177	209	18	and	and	CCONJ
ejpam-3177	209	19	biyang	biyang	PROPN
ejpam-3177	209	20	-	-	PUNCT
ejpam-3177	209	21	mills	mill	NOUN
ejpam-3177	209	22	fields	field	NOUN
ejpam-3177	209	23	,	,	PUNCT
ejpam-3177	209	24	note	note	VERB
ejpam-3177	209	25	di	di	PROPN
ejpam-3177	209	26	matematica	matematica	PROPN
ejpam-3177	209	27	,	,	PUNCT
ejpam-3177	209	28	note	note	VERB
ejpam-3177	209	29	mat	mat	NOUN
ejpam-3177	209	30	.	.	PUNCT
ejpam-3177	209	31	1(2008	1(2008	NUM
ejpam-3177	209	32	)	)	PUNCT
ejpam-3177	209	33	,	,	PUNCT
ejpam-3177	209	34	suppl	suppl	PROPN
ejpam-3177	209	35	.	.	PUNCT
ejpam-3177	210	1	n.	n.	PROPN
ejpam-3177	210	2	1	1	NUM
ejpam-3177	210	3	,	,	PUNCT
ejpam-3177	210	4	233	233	NUM
ejpam-3177	210	5	-	-	SYM
ejpam-3177	210	6	275	275	NUM
ejpam-3177	210	7	.	.	PUNCT
ejpam-3177	211	1	[	[	X
ejpam-3177	211	2	6	6	NUM
ejpam-3177	211	3	]	]	PUNCT
ejpam-3177	211	4	j.	j.	PROPN
ejpam-3177	211	5	davidov	davidov	PROPN
ejpam-3177	211	6	,	,	PUNCT
ejpam-3177	211	7	a.	a.	PROPN
ejpam-3177	211	8	g.	g.	PROPN
ejpam-3177	211	9	sergeev	sergeev	PROPN
ejpam-3177	211	10	,	,	PUNCT
ejpam-3177	211	11	twistor	twistor	NOUN
ejpam-3177	211	12	spaces	space	NOUN
ejpam-3177	211	13	and	and	CCONJ
ejpam-3177	211	14	harmonic	harmonic	ADJ
ejpam-3177	211	15	maps	map	NOUN
ejpam-3177	211	16	,	,	PUNCT
ejpam-3177	211	17	uspekhi	uspekhi	PROPN
ejpam-3177	211	18	mat	mat	PROPN
ejpam-3177	211	19	.	.	PUNCT
ejpam-3177	211	20	nauk	nauk	PROPN
ejpam-3177	211	21	,	,	PUNCT
ejpam-3177	211	22	1993	1993	NUM
ejpam-3177	211	23	,	,	PUNCT
ejpam-3177	211	24	volume	volume	NOUN
ejpam-3177	211	25	48	48	NUM
ejpam-3177	211	26	,	,	PUNCT
ejpam-3177	211	27	issue	issue	NOUN
ejpam-3177	211	28	3(291	3(291	NUM
ejpam-3177	211	29	)	)	PUNCT
ejpam-3177	211	30	,	,	PUNCT
ejpam-3177	211	31	396	396	NUM
ejpam-3177	211	32	.	.	PUNCT
ejpam-3177	212	1	[	[	X
ejpam-3177	212	2	7	7	X
ejpam-3177	212	3	]	]	X
ejpam-3177	212	4	j.	j.	PROPN
ejpam-3177	212	5	eells	eells	PROPN
ejpam-3177	212	6	,	,	PUNCT
ejpam-3177	212	7	j.	j.	PROPN
ejpam-3177	212	8	h.	h.	PROPN
ejpam-3177	212	9	sampson	sampson	PROPN
ejpam-3177	212	10	,	,	PUNCT
ejpam-3177	212	11	harmonic	harmonic	ADJ
ejpam-3177	212	12	mappings	mapping	NOUN
ejpam-3177	212	13	of	of	ADP
ejpam-3177	212	14	riemannian	riemannian	ADJ
ejpam-3177	212	15	manifolds	manifold	NOUN
ejpam-3177	212	16	,	,	PUNCT
ejpam-3177	212	17	amer	amer	PROPN
ejpam-3177	212	18	.	.	PUNCT
ejpam-3177	212	19	j.	j.	PROPN
ejpam-3177	212	20	math	math	PROPN
ejpam-3177	212	21	.	.	PUNCT
ejpam-3177	213	1	86	86	NUM
ejpam-3177	213	2	(	(	PUNCT
ejpam-3177	213	3	1964	1964	NUM
ejpam-3177	213	4	)	)	PUNCT
ejpam-3177	213	5	,	,	PUNCT
ejpam-3177	213	6	109	109	NUM
ejpam-3177	213	7	-	-	SYM
ejpam-3177	213	8	160	160	NUM
ejpam-3177	213	9	[	[	NOUN
ejpam-3177	213	10	8	8	NUM
ejpam-3177	213	11	]	]	X
ejpam-3177	213	12	g.	g.	PROPN
ejpam-3177	213	13	y.	y.	PROPN
ejpam-3177	213	14	jiang	jiang	PROPN
ejpam-3177	214	1	2	2	NUM
ejpam-3177	214	2	-	-	PUNCT
ejpam-3177	214	3	harmonic	harmonic	ADJ
ejpam-3177	214	4	maps	map	NOUN
ejpam-3177	214	5	and	and	CCONJ
ejpam-3177	214	6	their	their	PRON
ejpam-3177	214	7	first	first	ADJ
ejpam-3177	214	8	and	and	CCONJ
ejpam-3177	214	9	second	second	ADJ
ejpam-3177	214	10	variational	variational	ADJ
ejpam-3177	214	11	formulas	formula	NOUN
ejpam-3177	214	12	,	,	PUNCT
ejpam-3177	214	13	chinese	chinese	PROPN
ejpam-3177	214	14	ann	ann	PROPN
ejpam-3177	214	15	.	.	PUNCT
ejpam-3177	214	16	math	math	PROPN
ejpam-3177	214	17	.	.	PUNCT
ejpam-3177	215	1	ser	ser	PROPN
ejpam-3177	215	2	.	.	PUNCT
ejpam-3177	215	3	a7(4	a7(4	PROPN
ejpam-3177	215	4	)	)	PUNCT
ejpam-3177	215	5	(	(	PUNCT
ejpam-3177	215	6	1986	1986	NUM
ejpam-3177	215	7	)	)	PUNCT
ejpam-3177	215	8	,	,	PUNCT
ejpam-3177	215	9	389	389	NUM
ejpam-3177	215	10	-	-	SYM
ejpam-3177	215	11	402	402	NUM
ejpam-3177	215	12	.	.	PUNCT
ejpam-3177	216	1	[	[	X
ejpam-3177	216	2	9	9	NUM
ejpam-3177	216	3	]	]	X
ejpam-3177	216	4	j.	j.	PROPN
ejpam-3177	216	5	eells	eells	PROPN
ejpam-3177	216	6	and	and	CCONJ
ejpam-3177	216	7	l.	l.	PROPN
ejpam-3177	216	8	lemaire	lemaire	PROPN
ejpam-3177	216	9	,	,	PUNCT
ejpam-3177	216	10	report	report	VERB
ejpam-3177	216	11	on	on	ADP
ejpam-3177	216	12	harmonic	harmonic	ADJ
ejpam-3177	216	13	maps	map	NOUN
ejpam-3177	216	14	,	,	PUNCT
ejpam-3177	216	15	bull	bull	NOUN
ejpam-3177	216	16	,	,	PUNCT
ejpam-3177	216	17	london	london	PROPN
ejpam-3177	216	18	math	math	PROPN
ejpam-3177	216	19	.	.	PUNCT
ejpam-3177	217	1	soc	soc	PROPN
ejpam-3177	217	2	.	.	PUNCT
ejpam-3177	218	1	20	20	NUM
ejpam-3177	218	2	(	(	PUNCT
ejpam-3177	218	3	1988	1988	NUM
ejpam-3177	218	4	)	)	PUNCT
ejpam-3177	218	5	,	,	PUNCT
ejpam-3177	218	6	385	385	NUM
ejpam-3177	218	7	-	-	SYM
ejpam-3177	218	8	524	524	NUM
ejpam-3177	218	9	.	.	PUNCT
ejpam-3177	219	1	[	[	X
ejpam-3177	219	2	10	10	NUM
ejpam-3177	219	3	]	]	X
ejpam-3177	219	4	c.	c.	NOUN
ejpam-3177	219	5	gherghe	gherghe	PROPN
ejpam-3177	219	6	,	,	PUNCT
ejpam-3177	219	7	harmonicity	harmonicity	NOUN
ejpam-3177	219	8	on	on	ADP
ejpam-3177	219	9	cosymplectic	cosymplectic	ADJ
ejpam-3177	219	10	manifolds	manifold	NOUN
ejpam-3177	219	11	,	,	PUNCT
ejpam-3177	219	12	rocky	rocky	ADJ
ejpam-3177	219	13	mountain	mountain	NOUN
ejpam-3177	219	14	j.math	j.math	NOUN
ejpam-3177	219	15	.	.	PROPN
ejpam-3177	219	16	40	40	NUM
ejpam-3177	219	17	,	,	PUNCT
ejpam-3177	219	18	no.6,(2010	no.6,(2010	NOUN
ejpam-3177	219	19	)	)	PUNCT
ejpam-3177	219	20	,	,	PUNCT
ejpam-3177	219	21	247	247	NUM
ejpam-3177	219	22	-	-	SYM
ejpam-3177	219	23	254	254	NUM
ejpam-3177	219	24	.	.	PUNCT
ejpam-3177	220	1	[	[	X
ejpam-3177	220	2	11	11	NUM
ejpam-3177	220	3	]	]	X
ejpam-3177	220	4	c.	c.	PROPN
ejpam-3177	220	5	gherghe	gherghe	PROPN
ejpam-3177	220	6	,	,	PUNCT
ejpam-3177	220	7	s.	s.	PROPN
ejpam-3177	220	8	ianus	ianus	PROPN
ejpam-3177	220	9	,	,	PUNCT
ejpam-3177	220	10	a.	a.	PROPN
ejpam-3177	220	11	m.	m.	PROPN
ejpam-3177	220	12	pastore	pastore	PROPN
ejpam-3177	220	13	,	,	PUNCT
ejpam-3177	220	14	cr	cr	NOUN
ejpam-3177	220	15	-	-	PUNCT
ejpam-3177	220	16	manifolds	manifold	NOUN
ejpam-3177	220	17	,	,	PUNCT
ejpam-3177	220	18	harmonic	harmonic	ADJ
ejpam-3177	220	19	maps	map	NOUN
ejpam-3177	220	20	and	and	CCONJ
ejpam-3177	220	21	and	and	CCONJ
ejpam-3177	220	22	stability	stability	NOUN
ejpam-3177	220	23	,	,	PUNCT
ejpam-3177	220	24	j.geom	j.geom	NOUN
ejpam-3177	220	25	.	.	PUNCT
ejpam-3177	221	1	71(2001	71(2001	NUM
ejpam-3177	221	2	)	)	PUNCT
ejpam-3177	221	3	,	,	PUNCT
ejpam-3177	221	4	42	42	NUM
ejpam-3177	221	5	-	-	SYM
ejpam-3177	221	6	53	53	NUM
ejpam-3177	221	7	.	.	PUNCT
ejpam-3177	222	1	[	[	X
ejpam-3177	222	2	12	12	NUM
ejpam-3177	222	3	]	]	X
ejpam-3177	222	4	c.	c.	PROPN
ejpam-3177	222	5	gherghe	gherghe	PROPN
ejpam-3177	222	6	,	,	PUNCT
ejpam-3177	222	7	k.kenmotsu	k.kenmotsu	NOUN
ejpam-3177	222	8	,	,	PUNCT
ejpam-3177	222	9	energy	energy	NOUN
ejpam-3177	222	10	minimizer	minimizer	NOUN
ejpam-3177	222	11	maps	map	NOUN
ejpam-3177	222	12	on	on	ADP
ejpam-3177	222	13	c	c	NOUN
ejpam-3177	222	14	-	-	PUNCT
ejpam-3177	222	15	manifolds	manifold	NOUN
ejpam-3177	222	16	,	,	PUNCT
ejpam-3177	222	17	diff	diff	PROPN
ejpam-3177	222	18	.	.	PUNCT
ejpam-3177	223	1	geom	geom	PROPN
ejpam-3177	223	2	.	.	PUNCT
ejpam-3177	224	1	appl	appl	PROPN
ejpam-3177	224	2	.	.	PUNCT
ejpam-3177	225	1	21(2004	21(2004	NUM
ejpam-3177	225	2	)	)	PUNCT
ejpam-3177	225	3	,	,	PUNCT
ejpam-3177	225	4	55	55	NUM
ejpam-3177	225	5	-	-	SYM
ejpam-3177	225	6	63	63	NUM
ejpam-3177	225	7	.	.	PUNCT
ejpam-3177	226	1	[	[	X
ejpam-3177	226	2	13	13	NUM
ejpam-3177	226	3	]	]	PUNCT
ejpam-3177	226	4	a.	a.	NOUN
ejpam-3177	226	5	lichnerowicz	lichnerowicz	PROPN
ejpam-3177	226	6	,	,	PUNCT
ejpam-3177	226	7	applications	application	NOUN
ejpam-3177	226	8	harmoniques	harmonique	NOUN
ejpam-3177	226	9	et	et	PROPN
ejpam-3177	226	10	varietes	variete	VERB
ejpam-3177	226	11	khleriennes	khleriennes	PROPN
ejpam-3177	226	12	,	,	PUNCT
ejpam-3177	226	13	sympos	sympos	PROPN
ejpam-3177	226	14	.	.	PUNCT
ejpam-3177	227	1	math	math	NOUN
ejpam-3177	227	2	.	.	PUNCT
ejpam-3177	228	1	3	3	NUM
ejpam-3177	228	2	(	(	PUNCT
ejpam-3177	228	3	1970	1970	NUM
ejpam-3177	228	4	)	)	PUNCT
ejpam-3177	228	5	341402	341402	NUM
ejpam-3177	228	6	.	.	PUNCT
ejpam-3177	229	1	[	[	X
ejpam-3177	229	2	14	14	NUM
ejpam-3177	229	3	]	]	X
ejpam-3177	229	4	j.	j.	PROPN
ejpam-3177	229	5	rawnsley	rawnsley	PROPN
ejpam-3177	229	6	,	,	PUNCT
ejpam-3177	229	7	f	f	PROPN
ejpam-3177	229	8	-structures	-structures	PROPN
ejpam-3177	229	9	,	,	PUNCT
ejpam-3177	229	10	f	f	PROPN
ejpam-3177	229	11	-twistor	-twistor	PROPN
ejpam-3177	229	12	spaces	space	NOUN
ejpam-3177	229	13	and	and	CCONJ
ejpam-3177	229	14	harmonic	harmonic	ADJ
ejpam-3177	229	15	maps	map	NOUN
ejpam-3177	229	16	,	,	PUNCT
ejpam-3177	229	17	lecture	lecture	NOUN
ejpam-3177	229	18	notes	note	NOUN
ejpam-3177	229	19	in	in	ADP
ejpam-3177	229	20	math	math	NOUN
ejpam-3177	229	21	.	.	PUNCT
ejpam-3177	229	22	,	,	PUNCT
ejpam-3177	229	23	vol	vol	NOUN
ejpam-3177	229	24	.	.	PUNCT
ejpam-3177	229	25	1164	1164	NUM
ejpam-3177	229	26	,	,	PUNCT
ejpam-3177	229	27	springer	springer	NOUN
ejpam-3177	229	28	-	-	PUNCT
ejpam-3177	229	29	verlag	verlag	PROPN
ejpam-3177	229	30	,	,	PUNCT
ejpam-3177	229	31	1984	1984	NUM
ejpam-3177	229	32	,	,	PUNCT
ejpam-3177	229	33	pp	pp	ADJ
ejpam-3177	229	34	.	.	PUNCT
ejpam-3177	229	35	85159	85159	NUM
ejpam-3177	229	36	.	.	PUNCT
ejpam-3177	230	1	[	[	X
ejpam-3177	230	2	15	15	NUM
ejpam-3177	230	3	]	]	X
ejpam-3177	230	4	n.a	n.a	PROPN
ejpam-3177	230	5	.	.	PROPN
ejpam-3177	230	6	rehman	rehman	PROPN
ejpam-3177	230	7	harmonic	harmonic	PROPN
ejpam-3177	230	8	maps	map	NOUN
ejpam-3177	230	9	on	on	ADP
ejpam-3177	230	10	s	s	NOUN
ejpam-3177	230	11	-	-	PUNCT
ejpam-3177	230	12	manifolds	manifold	NOUN
ejpam-3177	230	13	,	,	PUNCT
ejpam-3177	230	14	an	an	PROPN
ejpam-3177	230	15	.	.	PUNCT
ejpam-3177	230	16	st	st	PROPN
ejpam-3177	230	17	.	.	PROPN
ejpam-3177	230	18	univ	univ	PROPN
ejpam-3177	230	19	.	.	PUNCT
ejpam-3177	231	1	ovidius	ovidius	PROPN
ejpam-3177	231	2	constanta	constanta	PROPN
ejpam-3177	231	3	,	,	PUNCT
ejpam-3177	231	4	vol	vol	NOUN
ejpam-3177	231	5	21(3	21(3	NUM
ejpam-3177	231	6	)	)	PUNCT
ejpam-3177	231	7	,	,	PUNCT
ejpam-3177	231	8	2013	2013	NUM
ejpam-3177	231	9	,	,	PUNCT
ejpam-3177	231	10	197	197	NUM
ejpam-3177	231	11	-	-	SYM
ejpam-3177	231	12	208	208	NUM
ejpam-3177	231	13	.	.	PUNCT
ejpam-3177	232	1	[	[	X
ejpam-3177	232	2	16	16	NUM
ejpam-3177	232	3	]	]	PUNCT
ejpam-3177	232	4	hajime	hajime	NOUN
ejpam-3177	232	5	urakawa	urakawa	NOUN
ejpam-3177	232	6	,	,	PUNCT
ejpam-3177	232	7	harmonic	harmonic	ADJ
ejpam-3177	232	8	and	and	CCONJ
ejpam-3177	232	9	biharmonic	biharmonic	NOUN
ejpam-3177	232	10	maps	map	NOUN
ejpam-3177	232	11	,	,	PUNCT
ejpam-3177	232	12	symmetry	symmetry	NOUN
ejpam-3177	232	13	2015	2015	NUM
ejpam-3177	232	14	,	,	PUNCT
ejpam-3177	232	15	7	7	NUM
ejpam-3177	232	16	,	,	PUNCT
ejpam-3177	232	17	651	651	NUM
ejpam-3177	232	18	-	-	SYM
ejpam-3177	232	19	674	674	NUM
ejpam-3177	232	20	.	.	PUNCT
ejpam-3177	233	1	references	reference	NOUN
ejpam-3177	233	2	159	159	NUM
ejpam-3177	233	3	[	[	X
ejpam-3177	233	4	17	17	NUM
ejpam-3177	233	5	]	]	PUNCT
ejpam-3177	233	6	k.	k.	PROPN
ejpam-3177	233	7	yano	yano	PROPN
ejpam-3177	233	8	and	and	CCONJ
ejpam-3177	233	9	m.	m.	PROPN
ejpam-3177	233	10	kon	kon	PROPN
ejpam-3177	233	11	,	,	PUNCT
ejpam-3177	233	12	structures	structure	NOUN
ejpam-3177	233	13	on	on	ADP
ejpam-3177	233	14	manifolds	manifold	NOUN
ejpam-3177	233	15	,	,	PUNCT
ejpam-3177	233	16	vol	vol	NOUN
ejpam-3177	233	17	.	.	PROPN
ejpam-3177	233	18	3	3	NUM
ejpam-3177	233	19	,	,	PUNCT
ejpam-3177	233	20	series	series	NOUN
ejpam-3177	233	21	in	in	ADP
ejpam-3177	233	22	pure	pure	ADJ
ejpam-3177	233	23	math	math	NOUN
ejpam-3177	233	24	.	.	PUNCT
ejpam-3177	233	25	,	,	PUNCT
ejpam-3177	233	26	world	world	PROPN
ejpam-3177	233	27	scientific	scientific	PROPN
ejpam-3177	233	28	,	,	PUNCT
ejpam-3177	233	29	singapore	singapore	PROPN
ejpam-3177	233	30	,	,	PUNCT
ejpam-3177	233	31	1984	1984	NUM
ejpam-3177	233	32	.	.	PUNCT