id	sid	tid	token	lemma	pos
ejpam-340	1	1	6_340_singh.dvi	6_340_singh.dvi	NUM
ejpam-340	1	2	european	european	ADJ
ejpam-340	1	3	journal	journal	NOUN
ejpam-340	1	4	of	of	ADP
ejpam-340	1	5	pure	pure	ADJ
ejpam-340	1	6	and	and	CCONJ
ejpam-340	1	7	applied	apply	VERB
ejpam-340	1	8	mathematics	mathematic	NOUN
ejpam-340	1	9	vol	vol	NOUN
ejpam-340	1	10	.	.	PUNCT
ejpam-340	2	1	3	3	NUM
ejpam-340	2	2	,	,	PUNCT
ejpam-340	2	3	no	no	INTJ
ejpam-340	2	4	.	.	NOUN
ejpam-340	2	5	5	5	NUM
ejpam-340	2	6	,	,	PUNCT
ejpam-340	2	7	2010	2010	NUM
ejpam-340	2	8	,	,	PUNCT
ejpam-340	2	9	839	839	NUM
ejpam-340	2	10	-	-	SYM
ejpam-340	2	11	852	852	NUM
ejpam-340	2	12	issn	issn	PROPN
ejpam-340	2	13	1307	1307	NUM
ejpam-340	2	14	-	-	SYM
ejpam-340	2	15	5543	5543	NUM
ejpam-340	2	16	–	–	PUNCT
ejpam-340	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-340	2	18	some	some	DET
ejpam-340	2	19	affine	affine	NOUN
ejpam-340	2	20	connexions	connexion	NOUN
ejpam-340	2	21	in	in	ADP
ejpam-340	2	22	a	a	DET
ejpam-340	2	23	generalised	generalise	VERB
ejpam-340	2	24	structure	structure	NOUN
ejpam-340	2	25	manifold	manifold	PROPN
ejpam-340	2	26	-	-	PUNCT
ejpam-340	2	27	ii	ii	PROPN
ejpam-340	2	28	r.	r.	PROPN
ejpam-340	2	29	p.	p.	PROPN
ejpam-340	2	30	singh∗and	singh∗and	PROPN
ejpam-340	3	1	s.	s.	PROPN
ejpam-340	3	2	d.	d.	PROPN
ejpam-340	3	3	singh	singh	PROPN
ejpam-340	3	4	department	department	PROPN
ejpam-340	3	5	of	of	ADP
ejpam-340	3	6	mathematics	mathematic	NOUN
ejpam-340	3	7	,	,	PUNCT
ejpam-340	3	8	faculty	faculty	NOUN
ejpam-340	3	9	of	of	ADP
ejpam-340	3	10	science	science	NOUN
ejpam-340	3	11	,	,	PUNCT
ejpam-340	3	12	banaras	banaras	PROPN
ejpam-340	3	13	hindu	hindu	PROPN
ejpam-340	3	14	university	university	PROPN
ejpam-340	3	15	,	,	PUNCT
ejpam-340	3	16	varanasi	varanasi	NOUN
ejpam-340	3	17	221005	221005	NUM
ejpam-340	3	18	,	,	PUNCT
ejpam-340	3	19	(	(	PUNCT
ejpam-340	3	20	u.	u.	PROPN
ejpam-340	3	21	p.	p.	PROPN
ejpam-340	3	22	)	)	PUNCT
ejpam-340	4	1	india	india	PROPN
ejpam-340	4	2	.	.	PUNCT
ejpam-340	5	1	abstract	abstract	PROPN
ejpam-340	5	2	.	.	PUNCT
ejpam-340	6	1	in	in	ADP
ejpam-340	6	2	this	this	DET
ejpam-340	6	3	paper	paper	NOUN
ejpam-340	6	4	we	we	PRON
ejpam-340	6	5	have	have	AUX
ejpam-340	6	6	studied	study	VERB
ejpam-340	6	7	some	some	DET
ejpam-340	6	8	affine	affine	NOUN
ejpam-340	6	9	connexions	connexion	NOUN
ejpam-340	6	10	in	in	ADP
ejpam-340	6	11	a	a	DET
ejpam-340	6	12	generalised	generalise	VERB
ejpam-340	6	13	structure	structure	NOUN
ejpam-340	6	14	manifold	manifold	NOUN
ejpam-340	6	15	.	.	PUNCT
ejpam-340	7	1	certain	certain	ADJ
ejpam-340	7	2	theorems	theorem	NOUN
ejpam-340	7	3	are	be	AUX
ejpam-340	7	4	also	also	ADV
ejpam-340	7	5	have	have	AUX
ejpam-340	7	6	been	be	AUX
ejpam-340	7	7	proved	prove	VERB
ejpam-340	7	8	which	which	PRON
ejpam-340	7	9	are	be	AUX
ejpam-340	7	10	of	of	ADP
ejpam-340	7	11	great	great	ADJ
ejpam-340	7	12	geometrical	geometrical	ADJ
ejpam-340	7	13	importance	importance	NOUN
ejpam-340	7	14	.	.	PUNCT
ejpam-340	8	1	2000	2000	NUM
ejpam-340	8	2	mathematics	mathematic	NOUN
ejpam-340	8	3	subject	subject	NOUN
ejpam-340	8	4	classifications	classification	NOUN
ejpam-340	8	5	:	:	PUNCT
ejpam-340	8	6	53b05	53b05	NUM
ejpam-340	8	7	,	,	PUNCT
ejpam-340	8	8	57p05	57p05	NUM
ejpam-340	8	9	,	,	PUNCT
ejpam-340	8	10	57r55	57r55	NUM
ejpam-340	8	11	key	key	ADJ
ejpam-340	8	12	words	word	NOUN
ejpam-340	8	13	and	and	CCONJ
ejpam-340	8	14	phrases	phrase	NOUN
ejpam-340	8	15	:	:	PUNCT
ejpam-340	8	16	c∞-manifold	c∞-manifold	ADJ
ejpam-340	8	17	,	,	PUNCT
ejpam-340	8	18	generalised	generalised	ADJ
ejpam-340	8	19	structure	structure	NOUN
ejpam-340	8	20	manifold	manifold	NOUN
ejpam-340	8	21	,	,	PUNCT
ejpam-340	8	22	π	π	NOUN
ejpam-340	8	23	-	-	ADJ
ejpam-340	8	24	structure	structure	ADJ
ejpam-340	8	25	manifold	manifold	NOUN
ejpam-340	8	26	,	,	PUNCT
ejpam-340	8	27	hsustructure	hsustructure	NOUN
ejpam-340	8	28	manifold	manifold	NOUN
ejpam-340	8	29	,	,	PUNCT
ejpam-340	8	30	f	f	PROPN
ejpam-340	8	31	-structure	-structure	NOUN
ejpam-340	8	32	manifold	manifold	ADJ
ejpam-340	8	33	,	,	PUNCT
ejpam-340	8	34	tangent	tangent	NOUN
ejpam-340	8	35	metric	metric	ADJ
ejpam-340	8	36	manifold	manifold	ADJ
ejpam-340	8	37	1	1	NUM
ejpam-340	8	38	.	.	PUNCT
ejpam-340	9	1	introduction	introduction	NOUN
ejpam-340	9	2	we	we	PRON
ejpam-340	9	3	consider	consider	VERB
ejpam-340	9	4	a	a	DET
ejpam-340	9	5	differentiable	differentiable	ADJ
ejpam-340	9	6	manifold	manifold	ADJ
ejpam-340	9	7	vn	vn	NOUN
ejpam-340	9	8	of	of	ADP
ejpam-340	9	9	differentiability	differentiability	NOUN
ejpam-340	9	10	class	class	NOUN
ejpam-340	9	11	c∞	c∞	PROPN
ejpam-340	9	12	and	and	CCONJ
ejpam-340	9	13	of	of	ADP
ejpam-340	9	14	dimension	dimension	NOUN
ejpam-340	9	15	n.	n.	PROPN
ejpam-340	9	16	let	let	VERB
ejpam-340	9	17	there	there	PRON
ejpam-340	9	18	exist	exist	VERB
ejpam-340	9	19	in	in	ADP
ejpam-340	9	20	vn	vn	PROPN
ejpam-340	9	21	a	a	DET
ejpam-340	9	22	tensor	tensor	NOUN
ejpam-340	9	23	field	field	NOUN
ejpam-340	9	24	f	f	PROPN
ejpam-340	9	25	of	of	ADP
ejpam-340	9	26	the	the	DET
ejpam-340	9	27	type	type	NOUN
ejpam-340	9	28	(	(	PUNCT
ejpam-340	9	29	1,1	1,1	NUM
ejpam-340	9	30	)	)	PUNCT
ejpam-340	9	31	,	,	PUNCT
ejpam-340	9	32	s	s	VERB
ejpam-340	9	33	linearly	linearly	ADV
ejpam-340	9	34	independent	independent	ADJ
ejpam-340	9	35	vector	vector	NOUN
ejpam-340	9	36	fields	field	NOUN
ejpam-340	9	37	ui	ui	PROPN
ejpam-340	9	38	,	,	PUNCT
ejpam-340	9	39	i	i	PRON
ejpam-340	9	40	=	=	NOUN
ejpam-340	9	41	1	1	NUM
ejpam-340	9	42	,	,	PUNCT
ejpam-340	9	43	2	2	NUM
ejpam-340	9	44	,	,	PUNCT
ejpam-340	9	45	.	.	PUNCT
ejpam-340	9	46	.	.	PUNCT
ejpam-340	10	1	.	.	PUNCT
ejpam-340	11	1	,	,	PUNCT
ejpam-340	11	2	s	s	PART
ejpam-340	11	3	and	and	CCONJ
ejpam-340	11	4	s	s	VERB
ejpam-340	11	5	linearly	linearly	ADV
ejpam-340	11	6	independent	independent	ADJ
ejpam-340	11	7	1	1	NUM
ejpam-340	11	8	-	-	PUNCT
ejpam-340	11	9	forms	form	NOUN
ejpam-340	11	10	ui	ui	NOUN
ejpam-340	11	11	such	such	ADJ
ejpam-340	11	12	that	that	PRON
ejpam-340	11	13	for	for	ADP
ejpam-340	11	14	any	any	DET
ejpam-340	11	15	arbitrary	arbitrary	ADJ
ejpam-340	11	16	vector	vector	NOUN
ejpam-340	11	17	field	field	NOUN
ejpam-340	11	18	x	x	PUNCT
ejpam-340	11	19	,	,	PUNCT
ejpam-340	11	20	we	we	PRON
ejpam-340	11	21	have	have	VERB
ejpam-340	11	22	x	x	X
ejpam-340	11	23	=	=	SYM
ejpam-340	11	24	b2x	b2x	PROPN
ejpam-340	11	25	+	+	CCONJ
ejpam-340	11	26	c	c	NOUN
ejpam-340	11	27	ui(x	ui(x	PUNCT
ejpam-340	11	28	)	)	PUNCT
ejpam-340	11	29	ui	ui	NOUN
ejpam-340	12	1	(	(	PUNCT
ejpam-340	12	2	1	1	NUM
ejpam-340	12	3	)	)	PUNCT
ejpam-340	12	4	ui	ui	NOUN
ejpam-340	13	1	=	=	PUNCT
ejpam-340	14	1	p	p	X
ejpam-340	14	2	j	j	PROPN
ejpam-340	15	1	i	i	PRON
ejpam-340	15	2	u	u	VERB
ejpam-340	15	3	j	j	PROPN
ejpam-340	15	4	(	(	PUNCT
ejpam-340	15	5	2	2	NUM
ejpam-340	15	6	)	)	PUNCT
ejpam-340	15	7	where	where	SCONJ
ejpam-340	15	8	f(x	f(x	PROPN
ejpam-340	15	9	)	)	PUNCT
ejpam-340	16	1	de	de	PROPN
ejpam-340	16	2	f	f	PROPN
ejpam-340	16	3	=	=	PUNCT
ejpam-340	16	4	x	x	PROPN
ejpam-340	16	5	and	and	CCONJ
ejpam-340	16	6	b2	b2	NOUN
ejpam-340	16	7	,	,	PUNCT
ejpam-340	16	8	c	c	PROPN
ejpam-340	16	9	are	be	AUX
ejpam-340	16	10	constants	constant	NOUN
ejpam-340	16	11	.	.	PUNCT
ejpam-340	17	1	then	then	ADV
ejpam-340	17	2	the	the	DET
ejpam-340	17	3	structure	structure	NOUN
ejpam-340	17	4	{	{	PUNCT
ejpam-340	17	5	f	f	PROPN
ejpam-340	17	6	,	,	PUNCT
ejpam-340	17	7	ui	ui	PROPN
ejpam-340	17	8	,	,	PUNCT
ejpam-340	17	9	ui	ui	PROPN
ejpam-340	17	10	,	,	PUNCT
ejpam-340	17	11	p	p	PROPN
ejpam-340	17	12	j	j	PROPN
ejpam-340	17	13	i	i	PRON
ejpam-340	17	14	;	;	PUNCT
ejpam-340	17	15	i	i	PRON
ejpam-340	17	16	,	,	PUNCT
ejpam-340	17	17	j	j	PROPN
ejpam-340	17	18	=	=	SYM
ejpam-340	17	19	1,2	1,2	NUM
ejpam-340	17	20	,	,	PUNCT
ejpam-340	17	21	.	.	PUNCT
ejpam-340	17	22	.	.	PUNCT
ejpam-340	17	23	.	.	PUNCT
ejpam-340	18	1	,	,	PUNCT
ejpam-340	18	2	s	s	AUX
ejpam-340	18	3	}	}	PUNCT
ejpam-340	18	4	will	will	AUX
ejpam-340	18	5	be	be	AUX
ejpam-340	18	6	known	know	VERB
ejpam-340	18	7	as	as	ADP
ejpam-340	18	8	generalised	generalise	VERB
ejpam-340	18	9	structure	structure	NOUN
ejpam-340	18	10	and	and	CCONJ
ejpam-340	18	11	vn	vn	PROPN
ejpam-340	18	12	will	will	AUX
ejpam-340	18	13	be	be	AUX
ejpam-340	18	14	known	know	VERB
ejpam-340	18	15	as	as	ADP
ejpam-340	18	16	generalised	generalised	ADJ
ejpam-340	18	17	structure	structure	NOUN
ejpam-340	18	18	manifold	manifold	ADJ
ejpam-340	18	19	of	of	ADP
ejpam-340	18	20	order	order	NOUN
ejpam-340	18	21	s	s	VERB
ejpam-340	18	22	where	where	SCONJ
ejpam-340	18	23	s	s	VERB
ejpam-340	18	24	<	<	X
ejpam-340	18	25	n.	n.	PROPN
ejpam-340	18	26	lemma	lemma	PROPN
ejpam-340	18	27	1	1	NUM
ejpam-340	18	28	.	.	PUNCT
ejpam-340	19	1	all	all	DET
ejpam-340	19	2	the	the	DET
ejpam-340	19	3	equations	equation	NOUN
ejpam-340	19	4	which	which	PRON
ejpam-340	19	5	follow	follow	VERB
ejpam-340	19	6	hold	hold	NOUN
ejpam-340	19	7	for	for	ADP
ejpam-340	19	8	arbitrary	arbitrary	ADJ
ejpam-340	19	9	vector	vector	NOUN
ejpam-340	19	10	fields	field	NOUN
ejpam-340	19	11	x	x	SYM
ejpam-340	19	12	,	,	PUNCT
ejpam-340	19	13	y	y	PROPN
ejpam-340	19	14	,	,	PUNCT
ejpam-340	19	15	z	z	NOUN
ejpam-340	19	16	,	,	PUNCT
ejpam-340	19	17	.	.	PUNCT
ejpam-340	19	18	.	.	PUNCT
ejpam-340	19	19	.	.	PUNCT
ejpam-340	20	1	etc	etc	X
ejpam-340	20	2	.	.	X
ejpam-340	21	1	now	now	ADV
ejpam-340	21	2	,	,	PUNCT
ejpam-340	21	3	replacing	replace	VERB
ejpam-340	21	4	x	x	PUNCT
ejpam-340	21	5	by	by	ADP
ejpam-340	21	6	x	x	SYM
ejpam-340	21	7	in	in	ADP
ejpam-340	21	8	(	(	PUNCT
ejpam-340	21	9	1),we	1),we	NUM
ejpam-340	21	10	get	get	VERB
ejpam-340	21	11	x	x	X
ejpam-340	21	12	=	=	PUNCT
ejpam-340	21	13	b2x	b2x	PROPN
ejpam-340	21	14	+	+	CCONJ
ejpam-340	21	15	c	c	NOUN
ejpam-340	21	16	ui(x	ui(x	PUNCT
ejpam-340	21	17	)	)	PUNCT
ejpam-340	22	1	ui	ui	NOUN
ejpam-340	22	2	(	(	PUNCT
ejpam-340	22	3	3	3	X
ejpam-340	22	4	)	)	PUNCT
ejpam-340	22	5	∗corresponding	∗corresponde	VERB
ejpam-340	22	6	author	author	NOUN
ejpam-340	22	7	.	.	PUNCT
ejpam-340	23	1	email	email	NOUN
ejpam-340	23	2	address	address	NOUN
ejpam-340	23	3	:	:	PUNCT
ejpam-340	23	4	rajabhaia	rajabhaia	PROPN
ejpam-340	23	5	�	�	PROPN
ejpam-340	23	6	gmail	gmail	NOUN
ejpam-340	23	7	.	.	PUNCT
ejpam-340	24	1	om	om	PROPN
ejpam-340	24	2	(	(	PUNCT
ejpam-340	24	3	r.	r.	PROPN
ejpam-340	24	4	singh	singh	PROPN
ejpam-340	24	5	)	)	PUNCT
ejpam-340	24	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-340	25	1	839	839	NUM
ejpam-340	25	2	c	c	NOUN
ejpam-340	25	3	©	©	PROPN
ejpam-340	25	4	2010	2010	NUM
ejpam-340	25	5	ejpam	ejpam	NOUN
ejpam-340	25	6	all	all	DET
ejpam-340	25	7	rights	right	NOUN
ejpam-340	25	8	reserved	reserve	VERB
ejpam-340	25	9	.	.	PUNCT
ejpam-340	26	1	r.	r.	PROPN
ejpam-340	26	2	singh	singh	PROPN
ejpam-340	26	3	and	and	CCONJ
ejpam-340	26	4	s.	s.	PROPN
ejpam-340	26	5	singh	singh	PROPN
ejpam-340	26	6	/	/	SYM
ejpam-340	26	7	eur	eur	PROPN
ejpam-340	26	8	.	.	PUNCT
ejpam-340	27	1	j.	j.	PROPN
ejpam-340	27	2	pure	pure	PROPN
ejpam-340	27	3	appl	appl	PROPN
ejpam-340	27	4	.	.	PROPN
ejpam-340	27	5	math	math	PROPN
ejpam-340	27	6	,	,	PUNCT
ejpam-340	27	7	3	3	NUM
ejpam-340	27	8	(	(	PUNCT
ejpam-340	27	9	2010	2010	NUM
ejpam-340	27	10	)	)	PUNCT
ejpam-340	27	11	,	,	PUNCT
ejpam-340	27	12	839	839	NUM
ejpam-340	27	13	-	-	SYM
ejpam-340	27	14	852	852	NUM
ejpam-340	27	15	840	840	NUM
ejpam-340	27	16	operating	operating	NOUN
ejpam-340	27	17	f	f	NOUN
ejpam-340	27	18	in	in	ADP
ejpam-340	27	19	(	(	PUNCT
ejpam-340	27	20	1	1	NUM
ejpam-340	27	21	)	)	PUNCT
ejpam-340	27	22	,	,	PUNCT
ejpam-340	27	23	we	we	PRON
ejpam-340	27	24	get	get	VERB
ejpam-340	27	25	x	x	X
ejpam-340	27	26	=	=	PUNCT
ejpam-340	27	27	b2x	b2x	PROPN
ejpam-340	27	28	+	+	CCONJ
ejpam-340	27	29	c	c	NOUN
ejpam-340	27	30	ui(x	ui(x	PUNCT
ejpam-340	27	31	)	)	PUNCT
ejpam-340	27	32	ui	ui	NOUN
ejpam-340	27	33	using	use	VERB
ejpam-340	27	34	(	(	PUNCT
ejpam-340	27	35	2	2	NUM
ejpam-340	27	36	)	)	PUNCT
ejpam-340	27	37	in	in	ADP
ejpam-340	27	38	above	above	ADV
ejpam-340	27	39	,	,	PUNCT
ejpam-340	27	40	we	we	PRON
ejpam-340	27	41	get	get	VERB
ejpam-340	27	42	x	x	X
ejpam-340	27	43	=	=	PUNCT
ejpam-340	27	44	b2x	b2x	PROPN
ejpam-340	27	45	+	+	CCONJ
ejpam-340	27	46	c	c	NOUN
ejpam-340	27	47	ui(x	ui(x	PUNCT
ejpam-340	27	48	)	)	PUNCT
ejpam-340	28	1	p	p	NOUN
ejpam-340	28	2	j	j	PROPN
ejpam-340	29	1	i	i	PRON
ejpam-340	29	2	u	u	VERB
ejpam-340	29	3	j	j	PROPN
ejpam-340	29	4	(	(	PUNCT
ejpam-340	29	5	4	4	NUM
ejpam-340	29	6	)	)	PUNCT
ejpam-340	29	7	from	from	ADP
ejpam-340	29	8	(	(	PUNCT
ejpam-340	29	9	3	3	NUM
ejpam-340	29	10	)	)	PUNCT
ejpam-340	29	11	and	and	CCONJ
ejpam-340	29	12	(	(	PUNCT
ejpam-340	29	13	4	4	NUM
ejpam-340	29	14	)	)	PUNCT
ejpam-340	29	15	,	,	PUNCT
ejpam-340	29	16	we	we	PRON
ejpam-340	29	17	have	have	VERB
ejpam-340	29	18	ui(x	ui(x	PUNCT
ejpam-340	29	19	)	)	PUNCT
ejpam-340	30	1	=	=	SYM
ejpam-340	30	2	pi	pi	PROPN
ejpam-340	30	3	ju	ju	PROPN
ejpam-340	30	4	j(x	j(x	PROPN
ejpam-340	30	5	)	)	PUNCT
ejpam-340	31	1	(	(	PUNCT
ejpam-340	31	2	5	5	X
ejpam-340	31	3	)	)	PUNCT
ejpam-340	31	4	further	far	ADV
ejpam-340	31	5	,	,	PUNCT
ejpam-340	31	6	operating	operate	VERB
ejpam-340	31	7	f	f	NOUN
ejpam-340	31	8	in	in	ADP
ejpam-340	31	9	(	(	PUNCT
ejpam-340	31	10	2	2	NUM
ejpam-340	31	11	)	)	PUNCT
ejpam-340	31	12	and	and	CCONJ
ejpam-340	31	13	using	use	VERB
ejpam-340	31	14	(	(	PUNCT
ejpam-340	31	15	1	1	NUM
ejpam-340	31	16	)	)	PUNCT
ejpam-340	31	17	,	,	PUNCT
ejpam-340	31	18	(	(	PUNCT
ejpam-340	31	19	2	2	X
ejpam-340	31	20	)	)	PUNCT
ejpam-340	31	21	we	we	PRON
ejpam-340	31	22	get	get	VERB
ejpam-340	31	23	(	(	PUNCT
ejpam-340	31	24	2)p	2)p	NUM
ejpam-340	31	25	j	j	NOUN
ejpam-340	32	1	i	i	PRON
ejpam-340	32	2	=	=	PUNCT
ejpam-340	32	3	b2δ	b2δ	PROPN
ejpam-340	33	1	j	j	X
ejpam-340	34	1	i	i	PRON
ejpam-340	34	2	+	+	CCONJ
ejpam-340	34	3	c	c	VERB
ejpam-340	34	4	u	u	PROPN
ejpam-340	34	5	j(ui	j(ui	PROPN
ejpam-340	34	6	)	)	PUNCT
ejpam-340	34	7	(	(	PUNCT
ejpam-340	34	8	6	6	NUM
ejpam-340	34	9	)	)	PUNCT
ejpam-340	34	10	where	where	SCONJ
ejpam-340	34	11	(	(	PUNCT
ejpam-340	34	12	r)pi	r)pi	NOUN
ejpam-340	34	13	j	j	NOUN
ejpam-340	34	14	=	=	PRON
ejpam-340	34	15	(	(	PUNCT
ejpam-340	34	16	r−1	r−1	PROPN
ejpam-340	34	17	)	)	PUNCT
ejpam-340	34	18	pi	pi	NOUN
ejpam-340	35	1	k	k	PROPN
ejpam-340	35	2	pk	pk	PROPN
ejpam-340	35	3	j	j	PROPN
ejpam-340	35	4	on	on	ADP
ejpam-340	35	5	generalised	generalised	ADJ
ejpam-340	35	6	structure	structure	NOUN
ejpam-340	35	7	manifold	manifold	PROPN
ejpam-340	35	8	vn	vn	NOUN
ejpam-340	35	9	,	,	PUNCT
ejpam-340	35	10	let	let	VERB
ejpam-340	35	11	us	we	PRON
ejpam-340	35	12	introduce	introduce	VERB
ejpam-340	35	13	a	a	DET
ejpam-340	35	14	metric	metric	ADJ
ejpam-340	35	15	tensor	tensor	NOUN
ejpam-340	35	16	g	g	PROPN
ejpam-340	35	17	such	such	ADJ
ejpam-340	35	18	that	that	SCONJ
ejpam-340	35	19	2	2	NUM
ejpam-340	35	20	-	-	PUNCT
ejpam-340	35	21	form	form	NOUN
ejpam-340	35	22	′f	′f	NOUN
ejpam-340	35	23	defined	define	VERB
ejpam-340	35	24	by	by	ADP
ejpam-340	35	25	′f(x	′f(x	PROPN
ejpam-340	35	26	,	,	PUNCT
ejpam-340	35	27	y	y	PROPN
ejpam-340	35	28	)	)	PUNCT
ejpam-340	35	29	de	de	PROPN
ejpam-340	35	30	f	f	PROPN
ejpam-340	35	31	=	=	SYM
ejpam-340	35	32	g(x	g(x	PROPN
ejpam-340	35	33	,	,	PUNCT
ejpam-340	35	34	y	y	PROPN
ejpam-340	35	35	)	)	PUNCT
ejpam-340	35	36	is	be	AUX
ejpam-340	35	37	skew	skew	ADJ
ejpam-340	35	38	-	-	PUNCT
ejpam-340	35	39	symmetric	symmetric	ADJ
ejpam-340	35	40	,	,	PUNCT
ejpam-340	35	41	then	then	ADV
ejpam-340	35	42	vn	vn	PROPN
ejpam-340	35	43	is	be	AUX
ejpam-340	35	44	called	call	VERB
ejpam-340	35	45	generalised	generalised	ADJ
ejpam-340	35	46	metric	metric	ADJ
ejpam-340	35	47	structure	structure	NOUN
ejpam-340	35	48	manifold	manifold	NOUN
ejpam-340	36	1	[	[	X
ejpam-340	36	2	8,12	8,12	NUM
ejpam-340	36	3	]	]	PUNCT
ejpam-340	36	4	.	.	PUNCT
ejpam-340	37	1	we	we	PRON
ejpam-340	37	2	have	have	VERB
ejpam-340	37	3	on	on	ADP
ejpam-340	37	4	a	a	DET
ejpam-340	37	5	generalised	generalise	VERB
ejpam-340	37	6	metric	metric	ADJ
ejpam-340	37	7	structure	structure	NOUN
ejpam-340	37	8	manifold	manifold	NOUN
ejpam-340	37	9	,	,	PUNCT
ejpam-340	37	10	g(x	g(x	PROPN
ejpam-340	37	11	,	,	PUNCT
ejpam-340	37	12	y	y	PROPN
ejpam-340	37	13	)	)	PUNCT
ejpam-340	38	1	+	+	CCONJ
ejpam-340	39	1	g(x	g(x	ADJ
ejpam-340	39	2	,	,	PUNCT
ejpam-340	39	3	y	y	PROPN
ejpam-340	39	4	)	)	PUNCT
ejpam-340	39	5	=	=	SYM
ejpam-340	39	6	0	0	PUNCT
ejpam-340	39	7	replacing	replace	VERB
ejpam-340	39	8	y	y	PRON
ejpam-340	39	9	by	by	ADP
ejpam-340	39	10	y	y	PROPN
ejpam-340	39	11	in	in	ADP
ejpam-340	39	12	above	above	ADP
ejpam-340	39	13	equation	equation	NOUN
ejpam-340	39	14	and	and	CCONJ
ejpam-340	39	15	using	use	VERB
ejpam-340	39	16	(	(	PUNCT
ejpam-340	39	17	1	1	NUM
ejpam-340	39	18	)	)	PUNCT
ejpam-340	39	19	,	,	PUNCT
ejpam-340	39	20	we	we	PRON
ejpam-340	39	21	obtain	obtain	VERB
ejpam-340	39	22	g(x	g(x	PROPN
ejpam-340	39	23	,	,	PUNCT
ejpam-340	39	24	y	y	PROPN
ejpam-340	39	25	)	)	PUNCT
ejpam-340	40	1	+	+	NUM
ejpam-340	40	2	b2	b2	NOUN
ejpam-340	40	3	g(x	g(x	PROPN
ejpam-340	40	4	,	,	PUNCT
ejpam-340	40	5	y	y	PROPN
ejpam-340	40	6	)	)	PUNCT
ejpam-340	41	1	+	+	CCONJ
ejpam-340	41	2	c	c	NOUN
ejpam-340	41	3	ui(x	ui(x	PUNCT
ejpam-340	41	4	)	)	PUNCT
ejpam-340	41	5	ui(y	ui(y	PUNCT
ejpam-340	41	6	)	)	PUNCT
ejpam-340	42	1	=	=	SYM
ejpam-340	42	2	0	0	PUNCT
ejpam-340	42	3	(	(	PUNCT
ejpam-340	42	4	7	7	NUM
ejpam-340	42	5	)	)	PUNCT
ejpam-340	42	6	where	where	SCONJ
ejpam-340	42	7	ui(x	ui(x	ADP
ejpam-340	42	8	)	)	PUNCT
ejpam-340	42	9	=	=	SYM
ejpam-340	42	10	g(ui	g(ui	PROPN
ejpam-340	42	11	,	,	PUNCT
ejpam-340	42	12	x	x	X
ejpam-340	42	13	)	)	PUNCT
ejpam-340	42	14	(	(	PUNCT
ejpam-340	42	15	8)	8)	NUM
ejpam-340	42	16	lemma	lemma	PROPN
ejpam-340	42	17	2	2	NUM
ejpam-340	42	18	.	.	PUNCT
ejpam-340	43	1	the	the	DET
ejpam-340	43	2	generalised	generalise	VERB
ejpam-340	43	3	metric	metric	ADJ
ejpam-340	43	4	structure	structure	NOUN
ejpam-340	43	5	manifold	manifold	NOUN
ejpam-340	43	6	always	always	ADV
ejpam-340	43	7	be	be	AUX
ejpam-340	43	8	denoted	denote	VERB
ejpam-340	43	9	by	by	ADP
ejpam-340	43	10	vn	vn	PROPN
ejpam-340	43	11	.	.	PROPN
ejpam-340	43	12	1.1	1.1	NUM
ejpam-340	43	13	.	.	PUNCT
ejpam-340	44	1	definitions	definition	NOUN
ejpam-340	44	2	this	this	DET
ejpam-340	44	3	section	section	NOUN
ejpam-340	44	4	consists	consist	VERB
ejpam-340	44	5	of	of	ADP
ejpam-340	44	6	well	well	ADV
ejpam-340	44	7	known	know	VERB
ejpam-340	44	8	definitions	definition	NOUN
ejpam-340	44	9	required	require	VERB
ejpam-340	44	10	to	to	PART
ejpam-340	44	11	go	go	VERB
ejpam-340	44	12	through	through	ADP
ejpam-340	44	13	the	the	DET
ejpam-340	44	14	insuring	insure	VERB
ejpam-340	44	15	sections	section	NOUN
ejpam-340	45	1	[	[	X
ejpam-340	45	2	1,6	1,6	NUM
ejpam-340	45	3	]	]	PUNCT
ejpam-340	45	4	.	.	PUNCT
ejpam-340	46	1	1	1	X
ejpam-340	46	2	.	.	X
ejpam-340	46	3	a	a	DET
ejpam-340	46	4	differentiable	differentiable	ADJ
ejpam-340	46	5	manifold	manifold	ADJ
ejpam-340	46	6	mn	mn	PROPN
ejpam-340	46	7	on	on	ADP
ejpam-340	46	8	which	which	PRON
ejpam-340	46	9	there	there	ADV
ejpam-340	46	10	a	a	DET
ejpam-340	46	11	vector	vector	NOUN
ejpam-340	46	12	valued	value	VERB
ejpam-340	46	13	linear	linear	NOUN
ejpam-340	46	14	function	function	NOUN
ejpam-340	46	15	f	f	PROPN
ejpam-340	46	16	,	,	PUNCT
ejpam-340	46	17	a	a	DET
ejpam-340	46	18	2	2	NUM
ejpam-340	46	19	-	-	PUNCT
ejpam-340	46	20	form	form	NOUN
ejpam-340	46	21	′f	′f	NOUN
ejpam-340	46	22	defined	define	VERB
ejpam-340	46	23	by	by	ADP
ejpam-340	46	24	′f(x	′f(x	PROPN
ejpam-340	46	25	,	,	PUNCT
ejpam-340	46	26	y	y	PROPN
ejpam-340	46	27	)	)	PUNCT
ejpam-340	46	28	de	de	PROPN
ejpam-340	46	29	f	f	PROPN
ejpam-340	46	30	=	=	SYM
ejpam-340	46	31	g(x	g(x	PROPN
ejpam-340	46	32	,	,	PUNCT
ejpam-340	46	33	y	y	PROPN
ejpam-340	46	34	)	)	PUNCT
ejpam-340	46	35	such	such	ADJ
ejpam-340	46	36	that	that	SCONJ
ejpam-340	46	37	•	•	NOUN
ejpam-340	46	38	f2	f2	PROPN
ejpam-340	46	39	=	=	SYM
ejpam-340	46	40	0	0	NUM
ejpam-340	46	41	and	and	CCONJ
ejpam-340	46	42	′f(x	′f(x	PROPN
ejpam-340	46	43	,	,	PUNCT
ejpam-340	46	44	y	y	PROPN
ejpam-340	46	45	)	)	PUNCT
ejpam-340	46	46	is	be	AUX
ejpam-340	46	47	skew	skew	ADJ
ejpam-340	46	48	-	-	PUNCT
ejpam-340	46	49	symmetric	symmetric	ADJ
ejpam-340	46	50	,	,	PUNCT
ejpam-340	46	51	then	then	ADV
ejpam-340	46	52	mn	mn	PROPN
ejpam-340	46	53	is	be	AUX
ejpam-340	46	54	called	call	VERB
ejpam-340	46	55	an	an	DET
ejpam-340	46	56	almost	almost	ADV
ejpam-340	46	57	tangent	tangent	ADJ
ejpam-340	46	58	metric	metric	ADJ
ejpam-340	46	59	manifold	manifold	NOUN
ejpam-340	46	60	.	.	PUNCT
ejpam-340	47	1	•	•	NOUN
ejpam-340	47	2	f2	f2	PROPN
ejpam-340	47	3	=	=	PUNCT
ejpam-340	47	4	−in	−in	PROPN
ejpam-340	47	5	and	and	CCONJ
ejpam-340	47	6	′f(x	′f(x	PROPN
ejpam-340	47	7	,	,	PUNCT
ejpam-340	47	8	y	y	PROPN
ejpam-340	47	9	)	)	PUNCT
ejpam-340	47	10	is	be	AUX
ejpam-340	47	11	skew	skew	ADJ
ejpam-340	47	12	-	-	PUNCT
ejpam-340	47	13	symmetric	symmetric	ADJ
ejpam-340	47	14	,	,	PUNCT
ejpam-340	47	15	then	then	ADV
ejpam-340	47	16	mn	mn	PROPN
ejpam-340	47	17	is	be	AUX
ejpam-340	47	18	called	call	VERB
ejpam-340	47	19	an	an	DET
ejpam-340	47	20	almost	almost	ADV
ejpam-340	47	21	hermite	hermite	ADJ
ejpam-340	47	22	manifold	manifold	ADJ
ejpam-340	47	23	.	.	PUNCT
ejpam-340	48	1	•	•	NOUN
ejpam-340	48	2	f2	f2	ADV
ejpam-340	48	3	=	=	NOUN
ejpam-340	48	4	λ2	λ2	NOUN
ejpam-340	48	5	in	in	ADP
ejpam-340	48	6	,	,	PUNCT
ejpam-340	48	7	where	where	SCONJ
ejpam-340	48	8	λ	λ	PROPN
ejpam-340	48	9	is	be	AUX
ejpam-340	48	10	a	a	DET
ejpam-340	48	11	non	non	ADJ
ejpam-340	48	12	-	-	ADJ
ejpam-340	48	13	zero	zero	ADJ
ejpam-340	48	14	complex	complex	ADJ
ejpam-340	48	15	constant	constant	ADJ
ejpam-340	48	16	and	and	CCONJ
ejpam-340	48	17	′f(x	′f(x	PROPN
ejpam-340	48	18	,	,	PUNCT
ejpam-340	48	19	y	y	PROPN
ejpam-340	48	20	)	)	PUNCT
ejpam-340	48	21	is	be	AUX
ejpam-340	48	22	skew	skew	ADJ
ejpam-340	48	23	-	-	PUNCT
ejpam-340	48	24	symmetric	symmetric	ADJ
ejpam-340	48	25	,	,	PUNCT
ejpam-340	48	26	then	then	ADV
ejpam-340	48	27	mn	mn	PROPN
ejpam-340	48	28	is	be	AUX
ejpam-340	48	29	called	call	VERB
ejpam-340	48	30	an	an	DET
ejpam-340	48	31	metric	metric	ADJ
ejpam-340	48	32	π	π	NOUN
ejpam-340	48	33	-	-	NOUN
ejpam-340	48	34	structure	structure	NOUN
ejpam-340	48	35	manifold	manifold	NOUN
ejpam-340	48	36	[	[	X
ejpam-340	48	37	13	13	NUM
ejpam-340	48	38	]	]	PUNCT
ejpam-340	48	39	.	.	PUNCT
ejpam-340	49	1	r.	r.	PROPN
ejpam-340	49	2	singh	singh	PROPN
ejpam-340	49	3	and	and	CCONJ
ejpam-340	49	4	s.	s.	PROPN
ejpam-340	49	5	singh	singh	PROPN
ejpam-340	49	6	/	/	SYM
ejpam-340	49	7	eur	eur	PROPN
ejpam-340	49	8	.	.	PUNCT
ejpam-340	50	1	j.	j.	PROPN
ejpam-340	50	2	pure	pure	PROPN
ejpam-340	50	3	appl	appl	PROPN
ejpam-340	50	4	.	.	PROPN
ejpam-340	50	5	math	math	PROPN
ejpam-340	50	6	,	,	PUNCT
ejpam-340	50	7	3	3	NUM
ejpam-340	50	8	(	(	PUNCT
ejpam-340	50	9	2010	2010	NUM
ejpam-340	50	10	)	)	PUNCT
ejpam-340	50	11	,	,	PUNCT
ejpam-340	50	12	839	839	NUM
ejpam-340	50	13	-	-	SYM
ejpam-340	50	14	852	852	NUM
ejpam-340	50	15	841	841	NUM
ejpam-340	50	16	•	•	NOUN
ejpam-340	50	17	f2	f2	ADV
ejpam-340	50	18	=	=	PUNCT
ejpam-340	50	19	λr	λr	NOUN
ejpam-340	50	20	in	in	ADP
ejpam-340	50	21	and	and	CCONJ
ejpam-340	50	22	′f(x	′f(x	PROPN
ejpam-340	50	23	,	,	PUNCT
ejpam-340	50	24	y	y	PROPN
ejpam-340	50	25	)	)	PUNCT
ejpam-340	50	26	is	be	AUX
ejpam-340	50	27	skew	skew	ADJ
ejpam-340	50	28	-	-	PUNCT
ejpam-340	50	29	symmetric	symmetric	ADJ
ejpam-340	50	30	,	,	PUNCT
ejpam-340	50	31	then	then	ADV
ejpam-340	50	32	mn	mn	PROPN
ejpam-340	50	33	is	be	AUX
ejpam-340	50	34	called	call	VERB
ejpam-340	50	35	an	an	DET
ejpam-340	50	36	hsu	hsu	NOUN
ejpam-340	50	37	-	-	PUNCT
ejpam-340	50	38	structure	structure	NOUN
ejpam-340	50	39	metric	metric	ADJ
ejpam-340	50	40	manifold	manifold	NOUN
ejpam-340	50	41	[	[	X
ejpam-340	50	42	4,5	4,5	NUM
ejpam-340	50	43	]	]	PUNCT
ejpam-340	50	44	.	.	PUNCT
ejpam-340	51	1	•	•	NOUN
ejpam-340	51	2	f2	f2	ADV
ejpam-340	51	3	=	=	PUNCT
ejpam-340	51	4	in	in	ADP
ejpam-340	51	5	and	and	CCONJ
ejpam-340	51	6	′f(x	′f(x	PROPN
ejpam-340	51	7	,	,	PUNCT
ejpam-340	51	8	y	y	PROPN
ejpam-340	51	9	)	)	PUNCT
ejpam-340	51	10	is	be	AUX
ejpam-340	51	11	symmetric	symmetric	ADJ
ejpam-340	51	12	,	,	PUNCT
ejpam-340	51	13	then	then	ADV
ejpam-340	51	14	mn	mn	PROPN
ejpam-340	51	15	is	be	AUX
ejpam-340	51	16	said	say	VERB
ejpam-340	51	17	to	to	PART
ejpam-340	51	18	be	be	AUX
ejpam-340	51	19	an	an	DET
ejpam-340	51	20	almost	almost	ADV
ejpam-340	51	21	product	product	NOUN
ejpam-340	51	22	riemannian	riemannian	NOUN
ejpam-340	51	23	manifold	manifold	NOUN
ejpam-340	52	1	[	[	X
ejpam-340	52	2	7	7	NUM
ejpam-340	52	3	]	]	SYM
ejpam-340	52	4	.	.	PUNCT
ejpam-340	53	1	2	2	X
ejpam-340	53	2	.	.	X
ejpam-340	53	3	let	let	VERB
ejpam-340	53	4	us	we	PRON
ejpam-340	53	5	consider	consider	VERB
ejpam-340	53	6	a	a	DET
ejpam-340	53	7	c∞-manifold	c∞-manifold	PROPN
ejpam-340	53	8	mn	mn	PROPN
ejpam-340	53	9	(	(	PUNCT
ejpam-340	53	10	n	n	NOUN
ejpam-340	53	11	=	=	SYM
ejpam-340	53	12	2m+	2m+	NUM
ejpam-340	53	13	1	1	NUM
ejpam-340	53	14	)	)	PUNCT
ejpam-340	53	15	.	.	PUNCT
ejpam-340	54	1	let	let	VERB
ejpam-340	54	2	there	there	PRON
ejpam-340	54	3	exist	exist	VERB
ejpam-340	54	4	in	in	ADP
ejpam-340	54	5	mn	mn	PROPN
ejpam-340	54	6	a	a	DET
ejpam-340	54	7	tensor	tensor	NOUN
ejpam-340	54	8	field	field	NOUN
ejpam-340	54	9	f	f	PROPN
ejpam-340	54	10	of	of	ADP
ejpam-340	54	11	the	the	DET
ejpam-340	54	12	type	type	NOUN
ejpam-340	54	13	(	(	PUNCT
ejpam-340	54	14	1,1	1,1	NUM
ejpam-340	54	15	)	)	PUNCT
ejpam-340	54	16	,	,	PUNCT
ejpam-340	54	17	a	a	DET
ejpam-340	54	18	1	1	NUM
ejpam-340	54	19	-	-	PUNCT
ejpam-340	54	20	form	form	NOUN
ejpam-340	54	21	u	u	NOUN
ejpam-340	54	22	,	,	PUNCT
ejpam-340	54	23	a	a	DET
ejpam-340	54	24	vector	vector	NOUN
ejpam-340	54	25	field	field	NOUN
ejpam-340	54	26	u	u	NOUN
ejpam-340	54	27	and	and	CCONJ
ejpam-340	54	28	a	a	DET
ejpam-340	54	29	riemannian	riemannian	ADJ
ejpam-340	54	30	metric	metric	NOUN
ejpam-340	54	31	g	g	NOUN
ejpam-340	54	32	satisfying	satisfy	VERB
ejpam-340	54	33	x	x	PUNCT
ejpam-340	54	34	=	=	PUNCT
ejpam-340	54	35	−x	−x	NOUN
ejpam-340	54	36	+	+	CCONJ
ejpam-340	54	37	u(x	u(x	PROPN
ejpam-340	54	38	)	)	PUNCT
ejpam-340	54	39	u	u	NOUN
ejpam-340	54	40	(	(	PUNCT
ejpam-340	54	41	9a	9a	NOUN
ejpam-340	54	42	)	)	PUNCT
ejpam-340	54	43	u	u	NOUN
ejpam-340	54	44	=	=	NOUN
ejpam-340	54	45	0	0	PROPN
ejpam-340	54	46	(	(	PUNCT
ejpam-340	54	47	9b	9b	NUM
ejpam-340	54	48	)	)	PUNCT
ejpam-340	54	49	g(x	g(x	NOUN
ejpam-340	54	50	,	,	PUNCT
ejpam-340	54	51	y	y	PROPN
ejpam-340	54	52	)	)	PUNCT
ejpam-340	55	1	=	=	PUNCT
ejpam-340	56	1	g(x	g(x	PROPN
ejpam-340	56	2	,	,	PUNCT
ejpam-340	56	3	y	y	PROPN
ejpam-340	56	4	)	)	PUNCT
ejpam-340	56	5	−	−	PROPN
ejpam-340	56	6	u(x	u(x	PROPN
ejpam-340	56	7	)	)	PUNCT
ejpam-340	56	8	u(x	u(x	PROPN
ejpam-340	56	9	)	)	PUNCT
ejpam-340	56	10	(	(	PUNCT
ejpam-340	56	11	9c	9c	NOUN
ejpam-340	56	12	)	)	PUNCT
ejpam-340	56	13	where	where	SCONJ
ejpam-340	56	14	g(x	g(x	PROPN
ejpam-340	56	15	,	,	PUNCT
ejpam-340	56	16	u	u	NOUN
ejpam-340	56	17	)	)	PUNCT
ejpam-340	56	18	=	=	SYM
ejpam-340	56	19	u(x	u(x	X
ejpam-340	56	20	)	)	PUNCT
ejpam-340	56	21	and	and	CCONJ
ejpam-340	56	22	f(x	f(x	PROPN
ejpam-340	56	23	)	)	PUNCT
ejpam-340	57	1	de	de	PROPN
ejpam-340	57	2	f	f	PROPN
ejpam-340	57	3	=	=	PUNCT
ejpam-340	57	4	x	x	PROPN
ejpam-340	57	5	then	then	ADV
ejpam-340	57	6	mn	mn	PROPN
ejpam-340	57	7	is	be	AUX
ejpam-340	57	8	called	call	VERB
ejpam-340	57	9	an	an	DET
ejpam-340	57	10	almost	almost	ADV
ejpam-340	57	11	contact	contact	NOUN
ejpam-340	57	12	metric	metric	ADJ
ejpam-340	57	13	manifold	manifold	NOUN
ejpam-340	57	14	or	or	CCONJ
ejpam-340	57	15	an	an	DET
ejpam-340	57	16	almost	almost	ADV
ejpam-340	57	17	grayan	grayan	ADJ
ejpam-340	57	18	manifold	manifold	NOUN
ejpam-340	58	1	[	[	X
ejpam-340	58	2	16,17	16,17	NUM
ejpam-340	58	3	]	]	PUNCT
ejpam-340	58	4	.	.	PUNCT
ejpam-340	59	1	3	3	X
ejpam-340	59	2	.	.	X
ejpam-340	59	3	we	we	PRON
ejpam-340	59	4	consider	consider	VERB
ejpam-340	59	5	a	a	DET
ejpam-340	59	6	manifold	manifold	ADJ
ejpam-340	59	7	mn	mn	PROPN
ejpam-340	59	8	of	of	ADP
ejpam-340	59	9	differentiability	differentiability	NOUN
ejpam-340	59	10	class	class	NOUN
ejpam-340	59	11	c∞.	c∞.	PROPN
ejpam-340	59	12	let	let	VERB
ejpam-340	59	13	there	there	PRON
ejpam-340	59	14	exist	exist	VERB
ejpam-340	59	15	in	in	ADP
ejpam-340	59	16	mn	mn	PROPN
ejpam-340	59	17	,	,	PUNCT
ejpam-340	59	18	a	a	DET
ejpam-340	59	19	tensor	tensor	NOUN
ejpam-340	59	20	field	field	NOUN
ejpam-340	59	21	f	f	PROPN
ejpam-340	59	22	of	of	ADP
ejpam-340	59	23	the	the	DET
ejpam-340	59	24	type	type	NOUN
ejpam-340	59	25	(	(	PUNCT
ejpam-340	59	26	1,1	1,1	NUM
ejpam-340	59	27	)	)	PUNCT
ejpam-340	59	28	and	and	CCONJ
ejpam-340	59	29	rank	rank	NOUN
ejpam-340	59	30	r	r	NOUN
ejpam-340	59	31	(	(	PUNCT
ejpam-340	59	32	1≤	1≤	INTJ
ejpam-340	59	33	r	r	NOUN
ejpam-340	59	34	≤	≤	NUM
ejpam-340	59	35	n	n	CCONJ
ejpam-340	59	36	)	)	PUNCT
ejpam-340	59	37	satisfying	satisfy	VERB
ejpam-340	59	38	f3	f3	PROPN
ejpam-340	60	1	+	+	CCONJ
ejpam-340	60	2	f	f	PROPN
ejpam-340	60	3	=	=	SYM
ejpam-340	60	4	0	0	NUM
ejpam-340	60	5	(	(	PUNCT
ejpam-340	60	6	10	10	NUM
ejpam-340	60	7	)	)	PUNCT
ejpam-340	60	8	then	then	ADV
ejpam-340	60	9	{	{	PUNCT
ejpam-340	60	10	f	f	X
ejpam-340	60	11	}	}	PUNCT
ejpam-340	60	12	is	be	AUX
ejpam-340	60	13	called	call	VERB
ejpam-340	60	14	f	f	PROPN
ejpam-340	60	15	-structure	-structure	NOUN
ejpam-340	60	16	and	and	CCONJ
ejpam-340	60	17	mn	mn	NOUN
ejpam-340	60	18	satisfying	satisfy	VERB
ejpam-340	60	19	(	(	PUNCT
ejpam-340	60	20	10	10	NUM
ejpam-340	60	21	)	)	PUNCT
ejpam-340	60	22	is	be	AUX
ejpam-340	60	23	called	call	VERB
ejpam-340	60	24	f	f	PROPN
ejpam-340	60	25	-structure	-structure	NOUN
ejpam-340	60	26	manifold	manifold	ADJ
ejpam-340	60	27	[	[	X
ejpam-340	60	28	2	2	NUM
ejpam-340	60	29	]	]	PUNCT
ejpam-340	60	30	.	.	PUNCT
ejpam-340	61	1	if	if	SCONJ
ejpam-340	61	2	we	we	PRON
ejpam-340	61	3	consider	consider	VERB
ejpam-340	61	4	′f(x	′f(x	PROPN
ejpam-340	61	5	,	,	PUNCT
ejpam-340	61	6	y	y	PROPN
ejpam-340	61	7	)	)	PUNCT
ejpam-340	61	8	de	de	PROPN
ejpam-340	61	9	f	f	PROPN
ejpam-340	61	10	=	=	SYM
ejpam-340	61	11	g(x	g(x	PROPN
ejpam-340	61	12	,	,	PUNCT
ejpam-340	61	13	y	y	PROPN
ejpam-340	61	14	)	)	PUNCT
ejpam-340	61	15	where	where	SCONJ
ejpam-340	61	16	g	g	PROPN
ejpam-340	61	17	is	be	AUX
ejpam-340	61	18	a	a	DET
ejpam-340	61	19	riemannian	riemannian	ADJ
ejpam-340	61	20	metric	metric	NOUN
ejpam-340	61	21	and	and	CCONJ
ejpam-340	61	22	′f	′f	PROPN
ejpam-340	61	23	is	be	AUX
ejpam-340	61	24	skewsymmetric	skewsymmetric	ADJ
ejpam-340	61	25	then	then	ADV
ejpam-340	61	26	,	,	PUNCT
ejpam-340	61	27	f	f	PROPN
ejpam-340	61	28	-structure	-structure	NOUN
ejpam-340	61	29	manifold	manifold	PROPN
ejpam-340	61	30	mn	mn	PROPN
ejpam-340	61	31	is	be	AUX
ejpam-340	61	32	called	call	VERB
ejpam-340	61	33	a	a	DET
ejpam-340	61	34	metric	metric	ADJ
ejpam-340	61	35	f	f	NOUN
ejpam-340	61	36	-structure	-structure	NOUN
ejpam-340	61	37	manifold	manifold	ADJ
ejpam-340	61	38	.	.	PUNCT
ejpam-340	62	1	4	4	X
ejpam-340	62	2	.	.	X
ejpam-340	62	3	the	the	DET
ejpam-340	62	4	tensor	tensor	NOUN
ejpam-340	62	5	k	k	PROPN
ejpam-340	62	6	of	of	ADP
ejpam-340	62	7	the	the	DET
ejpam-340	62	8	type	type	NOUN
ejpam-340	62	9	(	(	PUNCT
ejpam-340	62	10	1,3	1,3	NUM
ejpam-340	62	11	)	)	PUNCT
ejpam-340	62	12	defined	define	VERB
ejpam-340	62	13	by	by	ADP
ejpam-340	62	14	[	[	X
ejpam-340	62	15	14	14	NUM
ejpam-340	62	16	]	]	X
ejpam-340	62	17	k(x	k(x	PROPN
ejpam-340	62	18	,	,	PUNCT
ejpam-340	62	19	y	y	PROPN
ejpam-340	62	20	,	,	PUNCT
ejpam-340	62	21	z	z	NOUN
ejpam-340	62	22	)	)	PUNCT
ejpam-340	62	23	de	de	PROPN
ejpam-340	62	24	f	f	PROPN
ejpam-340	62	25	=	=	SYM
ejpam-340	62	26	dx	dx	PROPN
ejpam-340	62	27	dy	dy	NOUN
ejpam-340	62	28	z	z	PROPN
ejpam-340	62	29	−	−	PROPN
ejpam-340	62	30	dy	dy	NOUN
ejpam-340	62	31	dx	dx	PROPN
ejpam-340	62	32	z	z	PROPN
ejpam-340	63	1	−	−	PROPN
ejpam-340	63	2	d[x	d[x	PROPN
ejpam-340	63	3	,	,	PUNCT
ejpam-340	63	4	y]z	y]z	NOUN
ejpam-340	63	5	(	(	PUNCT
ejpam-340	63	6	11	11	NUM
ejpam-340	63	7	)	)	PUNCT
ejpam-340	63	8	is	be	AUX
ejpam-340	63	9	called	call	VERB
ejpam-340	63	10	the	the	DET
ejpam-340	63	11	curvature	curvature	NOUN
ejpam-340	63	12	tensor	tensor	NOUN
ejpam-340	63	13	of	of	ADP
ejpam-340	63	14	the	the	DET
ejpam-340	63	15	connexion	connexion	PROPN
ejpam-340	63	16	d.	d.	PROPN
ejpam-340	63	17	5	5	NUM
ejpam-340	63	18	.	.	PUNCT
ejpam-340	64	1	the	the	DET
ejpam-340	64	2	vector	vector	NOUN
ejpam-340	64	3	field	field	NOUN
ejpam-340	64	4	ui	ui	NOUN
ejpam-340	64	5	in	in	ADP
ejpam-340	64	6	generalised	generalised	ADJ
ejpam-340	64	7	structure	structure	NOUN
ejpam-340	64	8	metric	metric	ADJ
ejpam-340	64	9	manifold	manifold	ADJ
ejpam-340	64	10	vn	vn	PROPN
ejpam-340	64	11	is	be	AUX
ejpam-340	64	12	called	call	VERB
ejpam-340	64	13	a	a	DET
ejpam-340	64	14	killing	kill	VERB
ejpam-340	64	15	vector	vector	NOUN
ejpam-340	64	16	if	if	SCONJ
ejpam-340	64	17	it	it	PRON
ejpam-340	64	18	satisfies	satisfy	VERB
ejpam-340	64	19	[	[	X
ejpam-340	64	20	11	11	NUM
ejpam-340	64	21	]	]	X
ejpam-340	64	22	dx	dx	PROPN
ejpam-340	64	23	ui)(y	ui)(y	PROPN
ejpam-340	64	24	)	)	PUNCT
ejpam-340	65	1	+	+	CCONJ
ejpam-340	65	2	(	(	PUNCT
ejpam-340	65	3	dy	dy	NOUN
ejpam-340	65	4	ui)(x	ui)(x	PROPN
ejpam-340	65	5	)	)	PUNCT
ejpam-340	66	1	=	=	PUNCT
ejpam-340	66	2	0	0	NUM
ejpam-340	67	1	6	6	NUM
ejpam-340	67	2	.	.	PUNCT
ejpam-340	68	1	a	a	DET
ejpam-340	68	2	connection	connection	NOUN
ejpam-340	68	3	d	d	X
ejpam-340	68	4	which	which	PRON
ejpam-340	68	5	satisfies	satisfy	VERB
ejpam-340	68	6	(	(	PUNCT
ejpam-340	68	7	dx	dx	PROPN
ejpam-340	68	8	f)(y	f)(y	NUM
ejpam-340	68	9	)	)	PUNCT
ejpam-340	69	1	=	=	PUNCT
ejpam-340	69	2	0	0	NUM
ejpam-340	69	3	,	,	PUNCT
ejpam-340	69	4	(	(	PUNCT
ejpam-340	69	5	dx	dx	PROPN
ejpam-340	69	6	ui)(y	ui)(y	PROPN
ejpam-340	69	7	)	)	PUNCT
ejpam-340	70	1	=	=	SYM
ejpam-340	70	2	0	0	NUM
ejpam-340	70	3	,	,	PUNCT
ejpam-340	70	4	dx	dx	PROPN
ejpam-340	70	5	ui	ui	PROPN
ejpam-340	71	1	=	=	NOUN
ejpam-340	71	2	0	0	PUNCT
ejpam-340	71	3	(	(	PUNCT
ejpam-340	71	4	12	12	NUM
ejpam-340	71	5	)	)	PUNCT
ejpam-340	71	6	is	be	AUX
ejpam-340	71	7	called	call	VERB
ejpam-340	71	8	an	an	DET
ejpam-340	71	9	(	(	PUNCT
ejpam-340	71	10	f	f	NOUN
ejpam-340	71	11	,	,	PUNCT
ejpam-340	71	12	ui	ui	PROPN
ejpam-340	71	13	,	,	PUNCT
ejpam-340	71	14	u	u	NOUN
ejpam-340	71	15	i)-connexion	i)-connexion	NOUN
ejpam-340	71	16	.	.	PUNCT
ejpam-340	72	1	7	7	X
ejpam-340	72	2	.	.	X
ejpam-340	72	3	a	a	DET
ejpam-340	72	4	connection	connection	NOUN
ejpam-340	73	1	d	d	NOUN
ejpam-340	73	2	is	be	AUX
ejpam-340	73	3	called	call	VERB
ejpam-340	73	4	an	an	DET
ejpam-340	73	5	f	f	PROPN
ejpam-340	73	6	-connexion	-connexion	NOUN
ejpam-340	73	7	if	if	SCONJ
ejpam-340	73	8	it	it	PRON
ejpam-340	73	9	satisfies	satisfy	VERB
ejpam-340	73	10	(	(	PUNCT
ejpam-340	73	11	dx	dx	PROPN
ejpam-340	73	12	f)(y	f)(y	NUM
ejpam-340	73	13	)	)	PUNCT
ejpam-340	74	1	=	=	SYM
ejpam-340	74	2	0	0	PUNCT
ejpam-340	75	1	i.e.	i.e.	X
ejpam-340	75	2	,	,	PUNCT
ejpam-340	75	3	dx	dx	PROPN
ejpam-340	75	4	y	y	PROPN
ejpam-340	75	5	=	=	PUNCT
ejpam-340	75	6	dx	dx	PROPN
ejpam-340	75	7	y	y	PROPN
ejpam-340	75	8	(	(	PUNCT
ejpam-340	75	9	13	13	NUM
ejpam-340	75	10	)	)	PUNCT
ejpam-340	75	11	r.	r.	PROPN
ejpam-340	75	12	singh	singh	PROPN
ejpam-340	75	13	and	and	CCONJ
ejpam-340	75	14	s.	s.	PROPN
ejpam-340	75	15	singh	singh	PROPN
ejpam-340	75	16	/	/	SYM
ejpam-340	75	17	eur	eur	PROPN
ejpam-340	75	18	.	.	PUNCT
ejpam-340	76	1	j.	j.	PROPN
ejpam-340	76	2	pure	pure	PROPN
ejpam-340	76	3	appl	appl	PROPN
ejpam-340	76	4	.	.	PROPN
ejpam-340	76	5	math	math	PROPN
ejpam-340	76	6	,	,	PUNCT
ejpam-340	76	7	3	3	NUM
ejpam-340	76	8	(	(	PUNCT
ejpam-340	76	9	2010	2010	NUM
ejpam-340	76	10	)	)	PUNCT
ejpam-340	76	11	,	,	PUNCT
ejpam-340	76	12	839	839	NUM
ejpam-340	76	13	-	-	SYM
ejpam-340	76	14	852	852	NUM
ejpam-340	76	15	842	842	NUM
ejpam-340	76	16	8	8	NUM
ejpam-340	76	17	.	.	PUNCT
ejpam-340	77	1	nijenhuis	nijenhuis	ADJ
ejpam-340	77	2	tensor	tensor	NOUN
ejpam-340	77	3	is	be	AUX
ejpam-340	77	4	a	a	DET
ejpam-340	77	5	vector	vector	NOUN
ejpam-340	77	6	valued	value	VERB
ejpam-340	77	7	bilinear	bilinear	NOUN
ejpam-340	77	8	function	function	NOUN
ejpam-340	77	9	n	n	PROPN
ejpam-340	77	10	,	,	PUNCT
ejpam-340	77	11	given	give	VERB
ejpam-340	77	12	by	by	ADP
ejpam-340	77	13	n(x	n(x	PROPN
ejpam-340	77	14	,	,	PUNCT
ejpam-340	77	15	y	y	PROPN
ejpam-340	77	16	)	)	PUNCT
ejpam-340	77	17	de	de	PROPN
ejpam-340	77	18	f	f	X
ejpam-340	77	19	=	=	PUNCT
ejpam-340	78	1	[	[	PUNCT
ejpam-340	78	2	x	x	X
ejpam-340	78	3	,	,	PUNCT
ejpam-340	78	4	y	y	PROPN
ejpam-340	78	5	]	]	PUNCT
ejpam-340	78	6	+	+	CCONJ
ejpam-340	78	7	[	[	X
ejpam-340	78	8	x	x	X
ejpam-340	78	9	,	,	PUNCT
ejpam-340	78	10	y	y	PROPN
ejpam-340	78	11	]	]	PUNCT
ejpam-340	78	12	−	−	X
ejpam-340	79	1	[	[	X
ejpam-340	79	2	x	x	X
ejpam-340	79	3	,	,	PUNCT
ejpam-340	79	4	y	y	PROPN
ejpam-340	79	5	]	]	PUNCT
ejpam-340	79	6	−	−	X
ejpam-340	80	1	[	[	X
ejpam-340	80	2	x	x	X
ejpam-340	80	3	,	,	PUNCT
ejpam-340	80	4	y	y	PROPN
ejpam-340	80	5	]	]	PUNCT
ejpam-340	80	6	(	(	PUNCT
ejpam-340	80	7	14	14	NUM
ejpam-340	80	8	)	)	PUNCT
ejpam-340	80	9	9	9	NUM
ejpam-340	80	10	.	.	X
ejpam-340	80	11	a	a	DET
ejpam-340	80	12	vector	vector	NOUN
ejpam-340	80	13	valued	value	VERB
ejpam-340	80	14	,	,	PUNCT
ejpam-340	80	15	skew	skew	NOUN
ejpam-340	80	16	-	-	PUNCT
ejpam-340	80	17	symmetric	symmetric	ADJ
ejpam-340	80	18	,	,	PUNCT
ejpam-340	80	19	bilinear	bilinear	NOUN
ejpam-340	80	20	function	function	NOUN
ejpam-340	80	21	s	s	AUX
ejpam-340	80	22	defined	define	VERB
ejpam-340	80	23	by	by	ADP
ejpam-340	80	24	s(x	s(x	NOUN
ejpam-340	80	25	,	,	PUNCT
ejpam-340	80	26	y	y	PROPN
ejpam-340	80	27	)	)	PUNCT
ejpam-340	81	1	de	de	PROPN
ejpam-340	81	2	f	f	PROPN
ejpam-340	81	3	=	=	SYM
ejpam-340	81	4	dx	dx	PROPN
ejpam-340	81	5	y	y	PROPN
ejpam-340	81	6	−	−	PROPN
ejpam-340	81	7	dy	dy	NOUN
ejpam-340	81	8	x	x	X
ejpam-340	81	9	−	−	PROPN
ejpam-340	82	1	[	[	X
ejpam-340	82	2	x	x	X
ejpam-340	82	3	,	,	PUNCT
ejpam-340	82	4	y	y	PROPN
ejpam-340	82	5	]	]	PUNCT
ejpam-340	82	6	(	(	PUNCT
ejpam-340	82	7	15	15	NUM
ejpam-340	82	8	)	)	PUNCT
ejpam-340	82	9	is	be	AUX
ejpam-340	82	10	called	call	VERB
ejpam-340	82	11	torsion	torsion	NOUN
ejpam-340	82	12	tensor	tensor	NOUN
ejpam-340	82	13	of	of	ADP
ejpam-340	82	14	a	a	DET
ejpam-340	82	15	connexion	connexion	PROPN
ejpam-340	82	16	d.	d.	NOUN
ejpam-340	82	17	for	for	ADP
ejpam-340	82	18	symmetric	symmetric	ADJ
ejpam-340	82	19	or	or	CCONJ
ejpam-340	82	20	torsion	torsion	NOUN
ejpam-340	82	21	free	free	ADJ
ejpam-340	82	22	connexion	connexion	NOUN
ejpam-340	82	23	d	d	NOUN
ejpam-340	82	24	,	,	PUNCT
ejpam-340	82	25	the	the	DET
ejpam-340	82	26	torsion	torsion	NOUN
ejpam-340	82	27	tensor	tensor	NOUN
ejpam-340	82	28	vanishes	vanish	VERB
ejpam-340	82	29	,	,	PUNCT
ejpam-340	82	30	i.e.	i.e.	X
ejpam-340	82	31	dx	dx	X
ejpam-340	82	32	y	y	PROPN
ejpam-340	82	33	−	−	PROPN
ejpam-340	82	34	dy	dy	X
ejpam-340	82	35	x	x	PUNCT
ejpam-340	83	1	=	=	PUNCT
ejpam-340	84	1	[	[	X
ejpam-340	84	2	x	x	X
ejpam-340	84	3	,	,	PUNCT
ejpam-340	84	4	y	y	PROPN
ejpam-340	84	5	]	]	PUNCT
ejpam-340	84	6	(	(	PUNCT
ejpam-340	84	7	16	16	NUM
ejpam-340	84	8	)	)	PUNCT
ejpam-340	84	9	10	10	NUM
ejpam-340	84	10	.	.	PUNCT
ejpam-340	85	1	lie	lie	VERB
ejpam-340	85	2	derivative	derivative	NOUN
ejpam-340	85	3	along	along	ADP
ejpam-340	85	4	any	any	DET
ejpam-340	85	5	vector	vector	NOUN
ejpam-340	85	6	v	v	NOUN
ejpam-340	85	7	in	in	ADP
ejpam-340	85	8	a	a	DET
ejpam-340	85	9	c∞-manifold	c∞-manifold	PROPN
ejpam-340	85	10	mn	mn	PROPN
ejpam-340	85	11	is	be	AUX
ejpam-340	85	12	a	a	DET
ejpam-340	85	13	type	type	NOUN
ejpam-340	85	14	preserving	preserve	VERB
ejpam-340	85	15	mapping	mapping	NOUN
ejpam-340	85	16	such	such	ADJ
ejpam-340	85	17	that	that	SCONJ
ejpam-340	85	18	[	[	X
ejpam-340	85	19	3	3	X
ejpam-340	85	20	]	]	X
ejpam-340	85	21	lv	lv	PROPN
ejpam-340	85	22	f	f	PROPN
ejpam-340	85	23	=	=	SYM
ejpam-340	85	24	v	v	PROPN
ejpam-340	85	25	f	f	NOUN
ejpam-340	85	26	;	;	PUNCT
ejpam-340	85	27	f	f	PROPN
ejpam-340	85	28	is	be	AUX
ejpam-340	85	29	a	a	DET
ejpam-340	85	30	c∞–function	c∞–function	NOUN
ejpam-340	85	31	(	(	PUNCT
ejpam-340	85	32	17a	17a	X
ejpam-340	85	33	)	)	PUNCT
ejpam-340	85	34	lv	lv	PROPN
ejpam-340	86	1	x	x	PUNCT
ejpam-340	87	1	=	=	PUNCT
ejpam-340	88	1	[	[	X
ejpam-340	88	2	v	v	NOUN
ejpam-340	88	3	,	,	PUNCT
ejpam-340	88	4	x	x	X
ejpam-340	88	5	]	]	X
ejpam-340	88	6	(	(	PUNCT
ejpam-340	88	7	17b	17b	NUM
ejpam-340	88	8	)	)	PUNCT
ejpam-340	88	9	lv	lv	PROPN
ejpam-340	88	10	b(x	b(x	PROPN
ejpam-340	88	11	)	)	PUNCT
ejpam-340	88	12	=	=	SYM
ejpam-340	88	13	v	v	X
ejpam-340	88	14	(	(	PUNCT
ejpam-340	88	15	b(x	b(x	NOUN
ejpam-340	88	16	)	)	PUNCT
ejpam-340	88	17	)	)	PUNCT
ejpam-340	88	18	−	−	PROPN
ejpam-340	89	1	b([v	b([v	ADJ
ejpam-340	89	2	,	,	PUNCT
ejpam-340	89	3	x	x	X
ejpam-340	89	4	]	]	X
ejpam-340	89	5	)	)	PUNCT
ejpam-340	89	6	(	(	PUNCT
ejpam-340	89	7	17c	17c	NUM
ejpam-340	89	8	)	)	PUNCT
ejpam-340	89	9	where	where	SCONJ
ejpam-340	89	10	b	b	NOUN
ejpam-340	89	11	is	be	AUX
ejpam-340	89	12	an	an	DET
ejpam-340	89	13	arbitrary	arbitrary	ADJ
ejpam-340	89	14	1	1	NUM
ejpam-340	89	15	-	-	PUNCT
ejpam-340	89	16	form	form	NOUN
ejpam-340	89	17	.	.	PUNCT
ejpam-340	90	1	remark	remark	NOUN
ejpam-340	90	2	1	1	NUM
ejpam-340	90	3	.	.	PUNCT
ejpam-340	91	1	it	it	PRON
ejpam-340	91	2	may	may	AUX
ejpam-340	91	3	be	be	AUX
ejpam-340	91	4	noted	note	VERB
ejpam-340	91	5	that	that	SCONJ
ejpam-340	91	6	vn	vn	PROPN
ejpam-340	91	7	gives	give	VERB
ejpam-340	91	8	an	an	DET
ejpam-340	91	9	almost	almost	ADV
ejpam-340	91	10	tangent	tangent	ADJ
ejpam-340	91	11	metric	metric	ADJ
ejpam-340	91	12	manifold	manifold	NOUN
ejpam-340	91	13	,	,	PUNCT
ejpam-340	91	14	an	an	DET
ejpam-340	91	15	almost	almost	ADV
ejpam-340	91	16	hermite	hermite	ADJ
ejpam-340	91	17	manifold	manifold	ADJ
ejpam-340	91	18	,	,	PUNCT
ejpam-340	91	19	metric	metric	ADJ
ejpam-340	91	20	π	π	NOUN
ejpam-340	91	21	-	-	ADJ
ejpam-340	91	22	structure	structure	ADJ
ejpam-340	91	23	manifold	manifold	NOUN
ejpam-340	91	24	,	,	PUNCT
ejpam-340	91	25	hsu	hsu	NOUN
ejpam-340	91	26	-	-	PUNCT
ejpam-340	91	27	structure	structure	NOUN
ejpam-340	91	28	manifold	manifold	NOUN
ejpam-340	91	29	,	,	PUNCT
ejpam-340	91	30	f	f	NOUN
ejpam-340	91	31	-	-	PUNCT
ejpam-340	91	32	structure	structure	NOUN
ejpam-340	91	33	manifold	manifold	NOUN
ejpam-340	91	34	,	,	PUNCT
ejpam-340	91	35	an	an	DET
ejpam-340	91	36	almost	almost	ADV
ejpam-340	91	37	product	product	NOUN
ejpam-340	91	38	riemannian	riemannian	NOUN
ejpam-340	91	39	manifold	manifold	NOUN
ejpam-340	91	40	,	,	PUNCT
ejpam-340	91	41	an	an	DET
ejpam-340	91	42	almost	almost	ADV
ejpam-340	91	43	grayan	grayan	ADJ
ejpam-340	91	44	manifold	manifold	NOUN
ejpam-340	91	45	and	and	CCONJ
ejpam-340	91	46	{	{	PUNCT
ejpam-340	91	47	f	f	X
ejpam-340	91	48	,	,	PUNCT
ejpam-340	91	49	g	g	PROPN
ejpam-340	91	50	,	,	PUNCT
ejpam-340	91	51	u1,u2	u1,u2	PROPN
ejpam-340	91	52	,	,	PUNCT
ejpam-340	91	53	u1	u1	NOUN
ejpam-340	91	54	,	,	PUNCT
ejpam-340	91	55	u2	u2	NOUN
ejpam-340	91	56	}	}	PUNCT
ejpam-340	91	57	structure	structure	NOUN
ejpam-340	91	58	manifold	manifold	ADJ
ejpam-340	91	59	according	accord	VERB
ejpam-340	91	60	as	as	ADP
ejpam-340	91	61	(	(	PUNCT
ejpam-340	91	62	b2	b2	NOUN
ejpam-340	91	63	=	=	SYM
ejpam-340	91	64	0	0	NUM
ejpam-340	91	65	,	,	PUNCT
ejpam-340	91	66	c	c	NOUN
ejpam-340	91	67	=	=	SYM
ejpam-340	91	68	0	0	NUM
ejpam-340	91	69	)	)	PUNCT
ejpam-340	91	70	;	;	PUNCT
ejpam-340	91	71	(	(	PUNCT
ejpam-340	91	72	b2	b2	NOUN
ejpam-340	91	73	=	=	SYM
ejpam-340	91	74	−1	−1	NOUN
ejpam-340	91	75	,	,	PUNCT
ejpam-340	91	76	c	c	NOUN
ejpam-340	91	77	=	=	SYM
ejpam-340	91	78	0	0	NUM
ejpam-340	91	79	)	)	PUNCT
ejpam-340	91	80	;	;	PUNCT
ejpam-340	91	81	(	(	PUNCT
ejpam-340	91	82	c	c	X
ejpam-340	91	83	=	=	SYM
ejpam-340	91	84	0	0	NUM
ejpam-340	91	85	)	)	PUNCT
ejpam-340	91	86	;	;	PUNCT
ejpam-340	91	87	(	(	PUNCT
ejpam-340	91	88	b2	b2	NOUN
ejpam-340	91	89	=	=	SYM
ejpam-340	91	90	λr	λr	NOUN
ejpam-340	91	91	,	,	PUNCT
ejpam-340	91	92	c	c	NOUN
ejpam-340	91	93	=	=	SYM
ejpam-340	91	94	0	0	NUM
ejpam-340	91	95	)	)	PUNCT
ejpam-340	91	96	;	;	PUNCT
ejpam-340	91	97	(	(	PUNCT
ejpam-340	91	98	b2	b2	NOUN
ejpam-340	91	99	=	=	SYM
ejpam-340	91	100	−1	−1	NOUN
ejpam-340	91	101	,	,	PUNCT
ejpam-340	91	102	p	p	NOUN
ejpam-340	91	103	j	j	PROPN
ejpam-340	91	104	i	i	NOUN
ejpam-340	91	105	=	=	NOUN
ejpam-340	91	106	0	0	NUM
ejpam-340	91	107	)	)	PUNCT
ejpam-340	91	108	;	;	PUNCT
ejpam-340	91	109	(	(	PUNCT
ejpam-340	91	110	b2	b2	NOUN
ejpam-340	91	111	=	=	SYM
ejpam-340	91	112	1	1	NUM
ejpam-340	91	113	,	,	PUNCT
ejpam-340	91	114	c	c	NOUN
ejpam-340	91	115	=	=	SYM
ejpam-340	91	116	0	0	NUM
ejpam-340	91	117	)	)	PUNCT
ejpam-340	91	118	;	;	PUNCT
ejpam-340	91	119	(	(	PUNCT
ejpam-340	91	120	b2	b2	NOUN
ejpam-340	91	121	=	=	SYM
ejpam-340	91	122	−1	−1	NOUN
ejpam-340	91	123	,	,	PUNCT
ejpam-340	91	124	c	c	NOUN
ejpam-340	91	125	=	=	SYM
ejpam-340	91	126	1	1	NUM
ejpam-340	91	127	,	,	PUNCT
ejpam-340	91	128	p1	p1	NOUN
ejpam-340	91	129	1	1	NUM
ejpam-340	91	130	=	=	SYM
ejpam-340	91	131	0	0	NUM
ejpam-340	91	132	:	:	PUNCT
ejpam-340	91	133	i	i	PRON
ejpam-340	91	134	,	,	PUNCT
ejpam-340	91	135	j	j	PROPN
ejpam-340	91	136	=	=	NOUN
ejpam-340	91	137	1	1	NUM
ejpam-340	91	138	)	)	PUNCT
ejpam-340	91	139	;	;	PUNCT
ejpam-340	91	140	and	and	CCONJ
ejpam-340	91	141	(	(	PUNCT
ejpam-340	91	142	b2	b2	NOUN
ejpam-340	91	143	=	=	SYM
ejpam-340	91	144	−1	−1	NOUN
ejpam-340	91	145	,	,	PUNCT
ejpam-340	91	146	c	c	NOUN
ejpam-340	91	147	=	=	SYM
ejpam-340	91	148	1	1	NUM
ejpam-340	91	149	,	,	PUNCT
ejpam-340	91	150	p	p	NOUN
ejpam-340	91	151	j	j	PROPN
ejpam-340	92	1	i	i	PRON
ejpam-340	92	2	+	+	CCONJ
ejpam-340	92	3	pi	pi	NOUN
ejpam-340	92	4	j	j	PROPN
ejpam-340	92	5	=	=	NOUN
ejpam-340	92	6	0	0	NUM
ejpam-340	92	7	:	:	PUNCT
ejpam-340	92	8	i	i	PRON
ejpam-340	92	9	,	,	PUNCT
ejpam-340	92	10	j	j	PROPN
ejpam-340	92	11	=	=	SYM
ejpam-340	92	12	1,2	1,2	NUM
ejpam-340	92	13	)	)	PUNCT
ejpam-340	92	14	respectively	respectively	ADV
ejpam-340	92	15	.	.	PUNCT
ejpam-340	93	1	1.2	1.2	NUM
ejpam-340	93	2	.	.	PUNCT
ejpam-340	94	1	some	some	DET
ejpam-340	94	2	basic	basic	ADJ
ejpam-340	94	3	results	result	NOUN
ejpam-340	94	4	1	1	NUM
ejpam-340	94	5	.	.	PUNCT
ejpam-340	95	1	if	if	SCONJ
ejpam-340	95	2	we	we	PRON
ejpam-340	95	3	put	put	VERB
ejpam-340	95	4	,	,	PUNCT
ejpam-340	95	5	ρf	ρf	PRON
ejpam-340	95	6	′	′	NOUN
ejpam-340	96	1	=	=	NOUN
ejpam-340	96	2	fρ	fρ	PROPN
ejpam-340	96	3	,	,	PUNCT
ejpam-340	96	4	u	u	NOUN
ejpam-340	96	5	′i	′i	NOUN
ejpam-340	96	6	=	=	PUNCT
ejpam-340	96	7	−1	−1	NOUN
ejpam-340	96	8	ρui	ρui	NOUN
ejpam-340	96	9	and	and	CCONJ
ejpam-340	96	10	u′i	u′i	ADJ
ejpam-340	96	11	=	=	PUNCT
ejpam-340	96	12	ui	ui	PROPN
ejpam-340	97	1	◦	◦	NOUN
ejpam-340	97	2	ρ	ρ	PROPN
ejpam-340	97	3	,	,	PUNCT
ejpam-340	97	4	where	where	SCONJ
ejpam-340	97	5	ρ	ρ	PROPN
ejpam-340	97	6	is	be	AUX
ejpam-340	97	7	a	a	DET
ejpam-340	97	8	non	non	ADJ
ejpam-340	97	9	-	-	ADJ
ejpam-340	97	10	singular	singular	ADJ
ejpam-340	97	11	tensor	tensor	NOUN
ejpam-340	97	12	of	of	ADP
ejpam-340	97	13	the	the	DET
ejpam-340	97	14	type	type	NOUN
ejpam-340	97	15	(	(	PUNCT
ejpam-340	97	16	1,1	1,1	NUM
ejpam-340	97	17	)	)	PUNCT
ejpam-340	97	18	,	,	PUNCT
ejpam-340	97	19	then	then	ADV
ejpam-340	97	20	it	it	PRON
ejpam-340	97	21	can	can	AUX
ejpam-340	97	22	be	be	AUX
ejpam-340	97	23	easily	easily	ADV
ejpam-340	97	24	seen	see	VERB
ejpam-340	97	25	that	that	SCONJ
ejpam-340	97	26	{	{	PUNCT
ejpam-340	97	27	f	f	PROPN
ejpam-340	97	28	′,u′i	′,u′i	PROPN
ejpam-340	97	29	,	,	PUNCT
ejpam-340	97	30	u	u	NOUN
ejpam-340	97	31	′i	′i	NOUN
ejpam-340	97	32	,	,	PUNCT
ejpam-340	97	33	p	p	X
ejpam-340	97	34	j	j	X
ejpam-340	97	35	i	i	PRON
ejpam-340	97	36	;	;	PUNCT
ejpam-340	97	37	i	i	PRON
ejpam-340	97	38	,	,	PUNCT
ejpam-340	97	39	j	j	PROPN
ejpam-340	97	40	=	=	SYM
ejpam-340	97	41	1,2	1,2	NUM
ejpam-340	97	42	,	,	PUNCT
ejpam-340	97	43	.	.	PUNCT
ejpam-340	97	44	.	.	PUNCT
ejpam-340	98	1	.	.	PUNCT
ejpam-340	99	1	,	,	PUNCT
ejpam-340	99	2	s	s	X
ejpam-340	99	3	}	}	PUNCT
ejpam-340	99	4	is	be	AUX
ejpam-340	99	5	also	also	ADV
ejpam-340	99	6	a	a	DET
ejpam-340	99	7	generalised	generalised	ADJ
ejpam-340	99	8	structure	structure	NOUN
ejpam-340	99	9	.	.	PUNCT
ejpam-340	100	1	2	2	X
ejpam-340	100	2	.	.	X
ejpam-340	100	3	the	the	DET
ejpam-340	100	4	eigen	eigen	PROPN
ejpam-340	100	5	values	value	NOUN
ejpam-340	100	6	of	of	ADP
ejpam-340	100	7	f	f	PROPN
ejpam-340	100	8	are	be	AUX
ejpam-340	100	9	given	give	VERB
ejpam-340	100	10	by	by	ADP
ejpam-340	100	11	b,−b	b,−b	NOUN
ejpam-340	100	12	,	,	PUNCT
ejpam-340	100	13	p	p	NOUN
ejpam-340	100	14	ai,−	ai,−	PROPN
ejpam-340	100	15	p	p	PROPN
ejpam-340	100	16	ai	ai	VERB
ejpam-340	100	17	where	where	SCONJ
ejpam-340	100	18	ai	ai	VERB
ejpam-340	100	19	are	be	AUX
ejpam-340	100	20	the	the	DET
ejpam-340	100	21	roots	root	NOUN
ejpam-340	100	22	of	of	ADP
ejpam-340	100	23	the	the	DET
ejpam-340	100	24	equation	equation	NOUN
ejpam-340	100	25	|λ2δ	|λ2δ	PROPN
ejpam-340	101	1	j	j	NOUN
ejpam-340	102	1	i	i	PRON
ejpam-340	102	2	−	−	PROPN
ejpam-340	102	3	(	(	PUNCT
ejpam-340	102	4	2	2	NUM
ejpam-340	102	5	)	)	PUNCT
ejpam-340	102	6	p	p	NOUN
ejpam-340	102	7	j	j	NOUN
ejpam-340	103	1	i	i	PRON
ejpam-340	103	2	|	|	ADV
ejpam-340	103	3	=	=	NOUN
ejpam-340	103	4	0	0	X
ejpam-340	103	5	.	.	PUNCT
ejpam-340	104	1	the	the	DET
ejpam-340	104	2	multiplicity	multiplicity	NOUN
ejpam-340	104	3	of	of	ADP
ejpam-340	104	4	the	the	DET
ejpam-340	104	5	eigen	eigen	PROPN
ejpam-340	104	6	values	value	NOUN
ejpam-340	104	7	depends	depend	VERB
ejpam-340	104	8	on	on	ADP
ejpam-340	104	9	rank((f	rank((f	NOUN
ejpam-340	104	10	)	)	PUNCT
ejpam-340	104	11	)	)	PUNCT
ejpam-340	104	12	,	,	PUNCT
ejpam-340	104	13	on	on	ADP
ejpam-340	104	14	p	p	PROPN
ejpam-340	104	15	j	j	PROPN
ejpam-340	104	16	i	i	PROPN
ejpam-340	104	17	and	and	CCONJ
ejpam-340	104	18	the	the	DET
ejpam-340	104	19	nature	nature	NOUN
ejpam-340	104	20	of	of	ADP
ejpam-340	104	21	b2	b2	NOUN
ejpam-340	104	22	,	,	PUNCT
ejpam-340	104	23	c.	c.	PROPN
ejpam-340	104	24	r.	r.	PROPN
ejpam-340	104	25	singh	singh	PROPN
ejpam-340	104	26	and	and	CCONJ
ejpam-340	104	27	s.	s.	PROPN
ejpam-340	104	28	singh	singh	PROPN
ejpam-340	104	29	/	/	SYM
ejpam-340	104	30	eur	eur	PROPN
ejpam-340	104	31	.	.	PUNCT
ejpam-340	105	1	j.	j.	PROPN
ejpam-340	105	2	pure	pure	PROPN
ejpam-340	105	3	appl	appl	PROPN
ejpam-340	105	4	.	.	PROPN
ejpam-340	105	5	math	math	PROPN
ejpam-340	105	6	,	,	PUNCT
ejpam-340	105	7	3	3	NUM
ejpam-340	105	8	(	(	PUNCT
ejpam-340	105	9	2010	2010	NUM
ejpam-340	105	10	)	)	PUNCT
ejpam-340	105	11	,	,	PUNCT
ejpam-340	105	12	839	839	NUM
ejpam-340	105	13	-	-	SYM
ejpam-340	105	14	852	852	NUM
ejpam-340	105	15	843	843	NUM
ejpam-340	105	16	2	2	NUM
ejpam-340	105	17	.	.	PUNCT
ejpam-340	106	1	an	an	DET
ejpam-340	106	2	affine	affine	NOUN
ejpam-340	106	3	connexion	connexion	NOUN
ejpam-340	106	4	i	i	PRON
ejpam-340	106	5	in	in	ADP
ejpam-340	106	6	this	this	DET
ejpam-340	106	7	section	section	NOUN
ejpam-340	106	8	an	an	DET
ejpam-340	106	9	affine	affine	NOUN
ejpam-340	106	10	connexion	connexion	NOUN
ejpam-340	106	11	in	in	ADP
ejpam-340	106	12	a	a	DET
ejpam-340	106	13	generalised	generalise	VERB
ejpam-340	106	14	structure	structure	NOUN
ejpam-340	106	15	manifold	manifold	ADJ
ejpam-340	106	16	vn	vn	PROPN
ejpam-340	106	17	is	be	AUX
ejpam-340	106	18	defined	define	VERB
ejpam-340	106	19	and	and	CCONJ
ejpam-340	106	20	its	its	PRON
ejpam-340	106	21	properties	property	NOUN
ejpam-340	106	22	have	have	AUX
ejpam-340	106	23	been	be	AUX
ejpam-340	106	24	studied	study	VERB
ejpam-340	107	1	[	[	X
ejpam-340	107	2	9,10,15	9,10,15	NUM
ejpam-340	107	3	]	]	PUNCT
ejpam-340	107	4	.	.	PUNCT
ejpam-340	108	1	let	let	VERB
ejpam-340	108	2	us	we	PRON
ejpam-340	108	3	define	define	VERB
ejpam-340	108	4	an	an	DET
ejpam-340	108	5	affine	affine	NOUN
ejpam-340	108	6	connexion	connexion	NOUN
ejpam-340	108	7	d	d	X
ejpam-340	108	8	such	such	ADJ
ejpam-340	108	9	that	that	PRON
ejpam-340	108	10	ui(y	ui(y	PUNCT
ejpam-340	108	11	)	)	PUNCT
ejpam-340	108	12	(	(	PUNCT
ejpam-340	108	13	dx	dx	PROPN
ejpam-340	108	14	ui	ui	PROPN
ejpam-340	108	15	)	)	PUNCT
ejpam-340	108	16	+	+	CCONJ
ejpam-340	108	17	(	(	PUNCT
ejpam-340	108	18	dx	dx	PROPN
ejpam-340	108	19	ui)(y	ui)(y	PROPN
ejpam-340	108	20	)	)	PUNCT
ejpam-340	108	21	ui	ui	PROPN
ejpam-340	109	1	=	=	NOUN
ejpam-340	109	2	0	0	PROPN
ejpam-340	109	3	(	(	PUNCT
ejpam-340	109	4	18	18	NUM
ejpam-340	109	5	)	)	PUNCT
ejpam-340	109	6	where	where	SCONJ
ejpam-340	109	7	d	d	NOUN
ejpam-340	109	8	is	be	AUX
ejpam-340	109	9	an	an	DET
ejpam-340	109	10	f	f	PROPN
ejpam-340	109	11	-connexion	-connexion	NOUN
ejpam-340	109	12	given	give	VERB
ejpam-340	109	13	by	by	ADP
ejpam-340	109	14	(	(	PUNCT
ejpam-340	109	15	13	13	NUM
ejpam-340	109	16	)	)	PUNCT
ejpam-340	109	17	.	.	PUNCT
ejpam-340	110	1	it	it	PRON
ejpam-340	110	2	can	can	AUX
ejpam-340	110	3	be	be	AUX
ejpam-340	110	4	easily	easily	ADV
ejpam-340	110	5	seen	see	VERB
ejpam-340	110	6	that	that	SCONJ
ejpam-340	110	7	,	,	PUNCT
ejpam-340	110	8	ui(dx	ui(dx	PROPN
ejpam-340	110	9	ui	ui	NOUN
ejpam-340	110	10	)	)	PUNCT
ejpam-340	110	11	=	=	SYM
ejpam-340	110	12	−(dx	−(dx	PROPN
ejpam-340	110	13	ui)(y	ui)(y	PROPN
ejpam-340	110	14	)	)	PUNCT
ejpam-340	110	15	(	(	PUNCT
ejpam-340	110	16	19a	19a	NUM
ejpam-340	110	17	)	)	PUNCT
ejpam-340	110	18	(	(	PUNCT
ejpam-340	110	19	(	(	PUNCT
ejpam-340	110	20	2)pi	2)pi	NUM
ejpam-340	110	21	j	j	PROPN
ejpam-340	110	22	−	−	PROPN
ejpam-340	110	23	b2δi	b2δi	PROPN
ejpam-340	110	24	j)(dx	j)(dx	X
ejpam-340	110	25	ui	ui	PROPN
ejpam-340	110	26	)	)	PUNCT
ejpam-340	111	1	=	=	SYM
ejpam-340	111	2	ui(dx	ui(dx	PROPN
ejpam-340	112	1	ui)u	ui)u	PROPN
ejpam-340	112	2	j	j	PROPN
ejpam-340	112	3	(	(	PUNCT
ejpam-340	112	4	19b	19b	NOUN
ejpam-340	112	5	)	)	PUNCT
ejpam-340	112	6	(	(	PUNCT
ejpam-340	112	7	dx	dx	PROPN
ejpam-340	112	8	ui)(y	ui)(y	PROPN
ejpam-340	112	9	)	)	PUNCT
ejpam-340	112	10	(	(	PUNCT
ejpam-340	112	11	ui	ui	NOUN
ejpam-340	112	12	)	)	PUNCT
ejpam-340	112	13	=	=	SYM
ejpam-340	112	14	−pi	−pi	PROPN
ejpam-340	112	15	ju	ju	NOUN
ejpam-340	112	16	j(y	j(y	PROPN
ejpam-340	112	17	)	)	PUNCT
ejpam-340	112	18	(	(	PUNCT
ejpam-340	112	19	dx	dx	PROPN
ejpam-340	112	20	ui	ui	PROPN
ejpam-340	112	21	)	)	PUNCT
ejpam-340	112	22	(	(	PUNCT
ejpam-340	112	23	19c	19c	NUM
ejpam-340	112	24	)	)	PUNCT
ejpam-340	112	25	(	(	PUNCT
ejpam-340	112	26	(	(	PUNCT
ejpam-340	112	27	2)pi	2)pi	NUM
ejpam-340	112	28	j	j	PROPN
ejpam-340	112	29	−	−	PROPN
ejpam-340	112	30	b2δi	b2δi	PROPN
ejpam-340	112	31	j	j	NOUN
ejpam-340	112	32	)	)	PUNCT
ejpam-340	112	33	div	div	X
ejpam-340	112	34	u	u	NOUN
ejpam-340	112	35	j	j	PROPN
ejpam-340	112	36	=	=	SYM
ejpam-340	112	37	c	c	PROPN
ejpam-340	112	38	u	u	PROPN
ejpam-340	112	39	j(du	j(du	PROPN
ejpam-340	112	40	j	j	PROPN
ejpam-340	112	41	ui	ui	PROPN
ejpam-340	112	42	)	)	PUNCT
ejpam-340	112	43	(	(	PUNCT
ejpam-340	112	44	19d	19d	NOUN
ejpam-340	112	45	)	)	PUNCT
ejpam-340	112	46	where	where	SCONJ
ejpam-340	112	47	div(x	div(x	X
ejpam-340	112	48	)	)	PUNCT
ejpam-340	112	49	de	de	PROPN
ejpam-340	112	50	f	f	PROPN
ejpam-340	112	51	=	=	PUNCT
ejpam-340	112	52	(	(	PUNCT
ejpam-340	112	53	c1	c1	PROPN
ejpam-340	112	54	1∇x	1∇x	NUM
ejpam-340	112	55	)	)	PUNCT
ejpam-340	112	56	and	and	CCONJ
ejpam-340	112	57	(	(	PUNCT
ejpam-340	112	58	∇x	∇x	PROPN
ejpam-340	112	59	)	)	PUNCT
ejpam-340	112	60	(	(	PUNCT
ejpam-340	112	61	y	y	NOUN
ejpam-340	112	62	)	)	PUNCT
ejpam-340	112	63	=	=	PUNCT
ejpam-340	112	64	(	(	PUNCT
ejpam-340	112	65	dy	dy	NOUN
ejpam-340	112	66	x	x	PROPN
ejpam-340	112	67	)	)	PUNCT
ejpam-340	112	68	.	.	PUNCT
ejpam-340	113	1	theorem	theorem	NOUN
ejpam-340	113	2	1	1	NUM
ejpam-340	113	3	.	.	PUNCT
ejpam-340	114	1	in	in	ADP
ejpam-340	114	2	vn	vn	PROPN
ejpam-340	114	3	,	,	PUNCT
ejpam-340	114	4	let	let	VERB
ejpam-340	114	5	us	we	PRON
ejpam-340	114	6	put	put	VERB
ejpam-340	114	7	m(x	m(x	PROPN
ejpam-340	114	8	,	,	PUNCT
ejpam-340	114	9	y	y	PROPN
ejpam-340	114	10	)	)	PUNCT
ejpam-340	115	1	de	de	PROPN
ejpam-340	115	2	f	f	PROPN
ejpam-340	115	3	=	=	SYM
ejpam-340	115	4	dx	dx	PROPN
ejpam-340	115	5	y	y	PROPN
ejpam-340	116	1	+	+	CCONJ
ejpam-340	116	2	dx	dx	PROPN
ejpam-340	116	3	y	y	PROPN
ejpam-340	116	4	−	−	PROPN
ejpam-340	116	5	dx	dx	PROPN
ejpam-340	116	6	y	y	PROPN
ejpam-340	116	7	−	−	PROPN
ejpam-340	117	1	dx	dx	PROPN
ejpam-340	117	2	y	y	PROPN
ejpam-340	117	3	(	(	PUNCT
ejpam-340	117	4	20	20	NUM
ejpam-340	117	5	)	)	PUNCT
ejpam-340	117	6	then	then	ADV
ejpam-340	117	7	,	,	PUNCT
ejpam-340	117	8	m(x	m(x	PROPN
ejpam-340	117	9	,	,	PUNCT
ejpam-340	117	10	y	y	PROPN
ejpam-340	117	11	)	)	PUNCT
ejpam-340	118	1	=	=	SYM
ejpam-340	118	2	0	0	PUNCT
ejpam-340	118	3	(	(	PUNCT
ejpam-340	118	4	21	21	NUM
ejpam-340	118	5	)	)	PUNCT
ejpam-340	118	6	proof	proof	NOUN
ejpam-340	118	7	.	.	PUNCT
ejpam-340	119	1	using	use	VERB
ejpam-340	119	2	(	(	PUNCT
ejpam-340	119	3	13	13	NUM
ejpam-340	119	4	)	)	PUNCT
ejpam-340	119	5	in	in	ADP
ejpam-340	119	6	(	(	PUNCT
ejpam-340	119	7	20	20	NUM
ejpam-340	119	8	)	)	PUNCT
ejpam-340	119	9	,	,	PUNCT
ejpam-340	119	10	we	we	PRON
ejpam-340	119	11	get	get	VERB
ejpam-340	119	12	(	(	PUNCT
ejpam-340	119	13	21	21	NUM
ejpam-340	119	14	)	)	PUNCT
ejpam-340	119	15	.	.	PUNCT
ejpam-340	120	1	theorem	theorem	NOUN
ejpam-340	120	2	2	2	NUM
ejpam-340	120	3	.	.	PUNCT
ejpam-340	121	1	if	if	SCONJ
ejpam-340	121	2	connexion	connexion	PROPN
ejpam-340	121	3	d	d	PROPN
ejpam-340	121	4	is	be	AUX
ejpam-340	121	5	torsion	torsion	NOUN
ejpam-340	121	6	free	free	ADJ
ejpam-340	121	7	in	in	ADP
ejpam-340	121	8	vn	vn	PROPN
ejpam-340	121	9	,	,	PUNCT
ejpam-340	121	10	then	then	ADV
ejpam-340	121	11	we	we	PRON
ejpam-340	121	12	have	have	VERB
ejpam-340	121	13	n(x	n(x	PROPN
ejpam-340	121	14	,	,	PUNCT
ejpam-340	121	15	y	y	PROPN
ejpam-340	121	16	)	)	PUNCT
ejpam-340	122	1	=	=	SYM
ejpam-340	122	2	0	0	PUNCT
ejpam-340	122	3	(	(	PUNCT
ejpam-340	122	4	22	22	NUM
ejpam-340	122	5	)	)	PUNCT
ejpam-340	122	6	where	where	SCONJ
ejpam-340	122	7	n(x	n(x	PROPN
ejpam-340	122	8	,	,	PUNCT
ejpam-340	122	9	y	y	PROPN
ejpam-340	122	10	)	)	PUNCT
ejpam-340	122	11	is	be	AUX
ejpam-340	122	12	nijenhuis	nijenhuis	NOUN
ejpam-340	122	13	tensor	tensor	NOUN
ejpam-340	122	14	.	.	PUNCT
ejpam-340	123	1	proof	proof	NOUN
ejpam-340	123	2	.	.	PUNCT
ejpam-340	124	1	using	use	VERB
ejpam-340	124	2	(	(	PUNCT
ejpam-340	124	3	16	16	NUM
ejpam-340	124	4	)	)	PUNCT
ejpam-340	124	5	and	and	CCONJ
ejpam-340	124	6	(	(	PUNCT
ejpam-340	124	7	13	13	NUM
ejpam-340	124	8	)	)	PUNCT
ejpam-340	124	9	in	in	ADP
ejpam-340	124	10	(	(	PUNCT
ejpam-340	124	11	14	14	NUM
ejpam-340	124	12	)	)	PUNCT
ejpam-340	124	13	,	,	PUNCT
ejpam-340	124	14	we	we	PRON
ejpam-340	124	15	get	get	VERB
ejpam-340	124	16	(	(	PUNCT
ejpam-340	124	17	22	22	NUM
ejpam-340	124	18	)	)	PUNCT
ejpam-340	124	19	.	.	PUNCT
ejpam-340	125	1	now	now	ADV
ejpam-340	125	2	,	,	PUNCT
ejpam-340	125	3	corresponding	correspond	VERB
ejpam-340	125	4	to	to	ADP
ejpam-340	125	5	the	the	DET
ejpam-340	125	6	nijenhuis	nijenhuis	PROPN
ejpam-340	125	7	tensor	tensor	NOUN
ejpam-340	125	8	of	of	ADP
ejpam-340	125	9	an	an	DET
ejpam-340	125	10	almost	almost	ADV
ejpam-340	125	11	complex	complex	ADJ
ejpam-340	125	12	manifold	manifold	ADJ
ejpam-340	125	13	,	,	PUNCT
ejpam-340	125	14	we	we	PRON
ejpam-340	125	15	have	have	VERB
ejpam-340	125	16	three	three	NUM
ejpam-340	125	17	tensors	tensor	NOUN
ejpam-340	125	18	µ,ν	µ,ν	ADV
ejpam-340	125	19	and	and	CCONJ
ejpam-340	125	20	σ	σ	NOUN
ejpam-340	125	21	given	give	VERB
ejpam-340	125	22	by	by	ADP
ejpam-340	125	23	µ(x	µ(x	NOUN
ejpam-340	125	24	,	,	PUNCT
ejpam-340	125	25	y	y	PROPN
ejpam-340	125	26	)	)	PUNCT
ejpam-340	125	27	de	de	PROPN
ejpam-340	125	28	f	f	PROPN
ejpam-340	125	29	=	=	PUNCT
ejpam-340	125	30	(	(	PUNCT
ejpam-340	125	31	dy	dy	NOUN
ejpam-340	125	32	ui)(x	ui)(x	PROPN
ejpam-340	125	33	)	)	PUNCT
ejpam-340	125	34	−	−	PROPN
ejpam-340	126	1	(	(	PUNCT
ejpam-340	126	2	dx	dx	PROPN
ejpam-340	126	3	ui)(y	ui)(y	PROPN
ejpam-340	126	4	)	)	PUNCT
ejpam-340	127	1	+	+	CCONJ
ejpam-340	127	2	(	(	PUNCT
ejpam-340	127	3	dy	dy	NOUN
ejpam-340	127	4	ui)(x	ui)(x	PROPN
ejpam-340	127	5	)	)	PUNCT
ejpam-340	127	6	−	−	PROPN
ejpam-340	127	7	(	(	PUNCT
ejpam-340	127	8	dx	dx	PROPN
ejpam-340	127	9	ui)(y	ui)(y	PROPN
ejpam-340	127	10	)	)	PUNCT
ejpam-340	127	11	(	(	PUNCT
ejpam-340	127	12	23	23	NUM
ejpam-340	127	13	)	)	PUNCT
ejpam-340	127	14	ν(x	ν(x	PROPN
ejpam-340	127	15	)	)	PUNCT
ejpam-340	128	1	de	de	PROPN
ejpam-340	128	2	f	f	PROPN
ejpam-340	128	3	=	=	PUNCT
ejpam-340	128	4	(	(	PUNCT
ejpam-340	128	5	dui	dui	PROPN
ejpam-340	128	6	f)(x	f)(x	PROPN
ejpam-340	128	7	)	)	PUNCT
ejpam-340	128	8	−	−	PROPN
ejpam-340	128	9	(	(	PUNCT
ejpam-340	128	10	dx	dx	PROPN
ejpam-340	128	11	f)(ui)−	f)(ui)−	NUM
ejpam-340	128	12	dx	dx	PROPN
ejpam-340	128	13	ui	ui	PROPN
ejpam-340	128	14	(	(	PUNCT
ejpam-340	128	15	24	24	NUM
ejpam-340	128	16	)	)	PUNCT
ejpam-340	128	17	σ(x	σ(x	PROPN
ejpam-340	128	18	)	)	PUNCT
ejpam-340	128	19	de	de	PROPN
ejpam-340	128	20	f	f	PROPN
ejpam-340	128	21	=	=	PUNCT
ejpam-340	128	22	(	(	PUNCT
ejpam-340	128	23	dx	dx	PROPN
ejpam-340	128	24	u	u	PROPN
ejpam-340	128	25	j)(ui)−	j)(ui)−	PROPN
ejpam-340	128	26	(	(	PUNCT
ejpam-340	128	27	dui	dui	PROPN
ejpam-340	128	28	u	u	PROPN
ejpam-340	128	29	j)(x	j)(x	PROPN
ejpam-340	128	30	)	)	PUNCT
ejpam-340	128	31	(	(	PUNCT
ejpam-340	128	32	25	25	NUM
ejpam-340	128	33	)	)	PUNCT
ejpam-340	128	34	respectively	respectively	ADV
ejpam-340	128	35	.	.	PUNCT
ejpam-340	129	1	r.	r.	PROPN
ejpam-340	129	2	singh	singh	PROPN
ejpam-340	129	3	and	and	CCONJ
ejpam-340	129	4	s.	s.	PROPN
ejpam-340	129	5	singh	singh	PROPN
ejpam-340	129	6	/	/	SYM
ejpam-340	129	7	eur	eur	PROPN
ejpam-340	129	8	.	.	PUNCT
ejpam-340	130	1	j.	j.	PROPN
ejpam-340	130	2	pure	pure	PROPN
ejpam-340	130	3	appl	appl	PROPN
ejpam-340	130	4	.	.	PROPN
ejpam-340	130	5	math	math	PROPN
ejpam-340	130	6	,	,	PUNCT
ejpam-340	130	7	3	3	NUM
ejpam-340	130	8	(	(	PUNCT
ejpam-340	130	9	2010	2010	NUM
ejpam-340	130	10	)	)	PUNCT
ejpam-340	130	11	,	,	PUNCT
ejpam-340	130	12	839	839	NUM
ejpam-340	130	13	-	-	SYM
ejpam-340	130	14	852	852	NUM
ejpam-340	130	15	844	844	NUM
ejpam-340	130	16	theorem	theorem	NOUN
ejpam-340	130	17	3	3	NUM
ejpam-340	130	18	.	.	PUNCT
ejpam-340	131	1	if	if	SCONJ
ejpam-340	131	2	connexion	connexion	PROPN
ejpam-340	131	3	d	d	PROPN
ejpam-340	131	4	is	be	AUX
ejpam-340	131	5	torsion	torsion	NOUN
ejpam-340	131	6	free	free	ADJ
ejpam-340	131	7	in	in	ADP
ejpam-340	131	8	vn	vn	PROPN
ejpam-340	131	9	,	,	PUNCT
ejpam-340	131	10	then	then	ADV
ejpam-340	131	11	we	we	PRON
ejpam-340	131	12	have	have	VERB
ejpam-340	131	13	µ(x	µ(x	NOUN
ejpam-340	131	14	,	,	PUNCT
ejpam-340	131	15	y	y	PROPN
ejpam-340	131	16	)	)	PUNCT
ejpam-340	131	17	ui	ui	PROPN
ejpam-340	132	1	=	=	PUNCT
ejpam-340	132	2	(	(	PUNCT
ejpam-340	132	3	dx	dx	PROPN
ejpam-340	132	4	ui	ui	PROPN
ejpam-340	132	5	)	)	PUNCT
ejpam-340	133	1	[	[	X
ejpam-340	133	2	u	u	NOUN
ejpam-340	133	3	i(y	i(y	NOUN
ejpam-340	133	4	)	)	PUNCT
ejpam-340	134	1	+	+	NUM
ejpam-340	134	2	ui(y	ui(y	NUM
ejpam-340	134	3	)	)	PUNCT
ejpam-340	134	4	]	]	PUNCT
ejpam-340	135	1	−	−	PROPN
ejpam-340	135	2	(	(	PUNCT
ejpam-340	135	3	dy	dy	NOUN
ejpam-340	135	4	ui	ui	PROPN
ejpam-340	135	5	)	)	PUNCT
ejpam-340	136	1	[	[	X
ejpam-340	136	2	u	u	X
ejpam-340	136	3	i(x	i(x	PROPN
ejpam-340	136	4	)	)	PUNCT
ejpam-340	136	5	+	+	NUM
ejpam-340	136	6	ui(x	ui(x	X
ejpam-340	136	7	)	)	PUNCT
ejpam-340	136	8	]	]	PUNCT
ejpam-340	136	9	(	(	PUNCT
ejpam-340	136	10	26	26	NUM
ejpam-340	136	11	)	)	PUNCT
ejpam-340	136	12	ν(x	ν(x	PROPN
ejpam-340	136	13	)	)	PUNCT
ejpam-340	137	1	=	=	PUNCT
ejpam-340	137	2	−(dx	−(dx	PROPN
ejpam-340	137	3	ui	ui	PROPN
ejpam-340	137	4	)	)	PUNCT
ejpam-340	137	5	(	(	PUNCT
ejpam-340	137	6	27	27	NUM
ejpam-340	137	7	)	)	PUNCT
ejpam-340	137	8	σ(x	σ(x	PROPN
ejpam-340	137	9	)	)	PUNCT
ejpam-340	138	1	=	=	SYM
ejpam-340	139	1	−u	−u	PROPN
ejpam-340	139	2	j(dx	j(dx	NOUN
ejpam-340	139	3	ui)−	ui)−	NUM
ejpam-340	140	1	(	(	PUNCT
ejpam-340	140	2	dui	dui	PROPN
ejpam-340	140	3	u	u	PROPN
ejpam-340	140	4	j)(x	j)(x	PROPN
ejpam-340	140	5	)	)	PUNCT
ejpam-340	140	6	(	(	PUNCT
ejpam-340	140	7	28	28	X
ejpam-340	140	8	)	)	PUNCT
ejpam-340	140	9	proof	proof	NOUN
ejpam-340	140	10	.	.	PUNCT
ejpam-340	141	1	using	use	VERB
ejpam-340	141	2	(	(	PUNCT
ejpam-340	141	3	5	5	NUM
ejpam-340	141	4	)	)	PUNCT
ejpam-340	141	5	,	,	PUNCT
ejpam-340	141	6	(	(	PUNCT
ejpam-340	141	7	18	18	NUM
ejpam-340	141	8	)	)	PUNCT
ejpam-340	141	9	and	and	CCONJ
ejpam-340	141	10	(	(	PUNCT
ejpam-340	141	11	19c	19c	NUM
ejpam-340	141	12	)	)	PUNCT
ejpam-340	141	13	in	in	ADP
ejpam-340	141	14	(	(	PUNCT
ejpam-340	141	15	23	23	NUM
ejpam-340	141	16	)	)	PUNCT
ejpam-340	141	17	,	,	PUNCT
ejpam-340	141	18	we	we	PRON
ejpam-340	141	19	get	get	VERB
ejpam-340	141	20	(	(	PUNCT
ejpam-340	141	21	26	26	NUM
ejpam-340	141	22	)	)	PUNCT
ejpam-340	141	23	.	.	PUNCT
ejpam-340	142	1	the	the	DET
ejpam-340	142	2	equation	equation	NOUN
ejpam-340	142	3	(	(	PUNCT
ejpam-340	142	4	24	24	NUM
ejpam-340	142	5	)	)	PUNCT
ejpam-340	142	6	yields	yield	NOUN
ejpam-340	142	7	(	(	PUNCT
ejpam-340	142	8	27	27	NUM
ejpam-340	142	9	)	)	PUNCT
ejpam-340	142	10	on	on	ADP
ejpam-340	142	11	use	use	NOUN
ejpam-340	142	12	of	of	ADP
ejpam-340	142	13	(	(	PUNCT
ejpam-340	142	14	13	13	NUM
ejpam-340	142	15	)	)	PUNCT
ejpam-340	142	16	.	.	PUNCT
ejpam-340	143	1	(	(	PUNCT
ejpam-340	143	2	28	28	NUM
ejpam-340	143	3	)	)	PUNCT
ejpam-340	143	4	is	be	AUX
ejpam-340	143	5	obtained	obtain	VERB
ejpam-340	143	6	on	on	ADP
ejpam-340	143	7	the	the	DET
ejpam-340	143	8	use	use	NOUN
ejpam-340	143	9	of	of	ADP
ejpam-340	143	10	(	(	PUNCT
ejpam-340	143	11	19a	19a	NUM
ejpam-340	143	12	)	)	PUNCT
ejpam-340	143	13	in	in	ADP
ejpam-340	143	14	(	(	PUNCT
ejpam-340	143	15	25	25	NUM
ejpam-340	143	16	)	)	PUNCT
ejpam-340	143	17	.	.	PUNCT
ejpam-340	144	1	theorem	theorem	ADJ
ejpam-340	144	2	4	4	NUM
ejpam-340	144	3	.	.	PUNCT
ejpam-340	145	1	in	in	ADP
ejpam-340	145	2	vn	vn	PROPN
ejpam-340	145	3	,	,	PUNCT
ejpam-340	145	4	let	let	VERB
ejpam-340	145	5	us	we	PRON
ejpam-340	145	6	put	put	VERB
ejpam-340	145	7	c(x	c(x	NOUN
ejpam-340	145	8	,	,	PUNCT
ejpam-340	145	9	y	y	PROPN
ejpam-340	145	10	)	)	PUNCT
ejpam-340	146	1	=	=	PUNCT
ejpam-340	146	2	(	(	PUNCT
ejpam-340	146	3	dx	dx	PROPN
ejpam-340	146	4	ui)(y	ui)(y	PROPN
ejpam-340	146	5	)	)	PUNCT
ejpam-340	146	6	−	−	PROPN
ejpam-340	147	1	(	(	PUNCT
ejpam-340	147	2	dy	dy	X
ejpam-340	147	3	ui)(x	ui)(x	PROPN
ejpam-340	147	4	)	)	PUNCT
ejpam-340	147	5	(	(	PUNCT
ejpam-340	147	6	29	29	NUM
ejpam-340	147	7	)	)	PUNCT
ejpam-340	147	8	then	then	ADV
ejpam-340	147	9	,	,	PUNCT
ejpam-340	147	10	we	we	PRON
ejpam-340	147	11	have	have	VERB
ejpam-340	147	12	c(x	c(x	NOUN
ejpam-340	147	13	,	,	PUNCT
ejpam-340	147	14	y	y	PROPN
ejpam-340	147	15	)	)	PUNCT
ejpam-340	148	1	+	+	CCONJ
ejpam-340	148	2	c(x	c(x	NOUN
ejpam-340	148	3	,	,	PUNCT
ejpam-340	148	4	y	y	PROPN
ejpam-340	148	5	)	)	PUNCT
ejpam-340	149	1	=	=	SYM
ejpam-340	149	2	−µ(x	−µ(x	PROPN
ejpam-340	149	3	,	,	PUNCT
ejpam-340	149	4	y	y	PROPN
ejpam-340	149	5	)	)	PUNCT
ejpam-340	149	6	(	(	PUNCT
ejpam-340	149	7	30	30	NUM
ejpam-340	149	8	)	)	PUNCT
ejpam-340	149	9	c(x	c(x	NOUN
ejpam-340	149	10	,	,	PUNCT
ejpam-340	149	11	y	y	PROPN
ejpam-340	149	12	)	)	PUNCT
ejpam-340	149	13	ui	ui	PROPN
ejpam-340	150	1	=	=	NOUN
ejpam-340	150	2	ui(y	ui(y	PRON
ejpam-340	150	3	)	)	PUNCT
ejpam-340	151	1	ν(x	ν(x	PROPN
ejpam-340	151	2	)	)	PUNCT
ejpam-340	151	3	−	−	PROPN
ejpam-340	151	4	ui(x	ui(x	PUNCT
ejpam-340	151	5	)	)	PUNCT
ejpam-340	151	6	ν(y	ν(y	PROPN
ejpam-340	151	7	)	)	PUNCT
ejpam-340	151	8	(	(	PUNCT
ejpam-340	151	9	31	31	NUM
ejpam-340	151	10	)	)	PUNCT
ejpam-340	151	11	proof	proof	NOUN
ejpam-340	151	12	.	.	PUNCT
ejpam-340	152	1	replacing	replace	VERB
ejpam-340	152	2	y	y	PRON
ejpam-340	152	3	by	by	ADP
ejpam-340	152	4	y	y	PROPN
ejpam-340	152	5	and	and	CCONJ
ejpam-340	152	6	x	x	PUNCT
ejpam-340	152	7	by	by	ADP
ejpam-340	152	8	x	x	SYM
ejpam-340	152	9	in	in	ADP
ejpam-340	152	10	(	(	PUNCT
ejpam-340	152	11	29	29	NUM
ejpam-340	152	12	)	)	PUNCT
ejpam-340	152	13	separately	separately	ADV
ejpam-340	152	14	and	and	CCONJ
ejpam-340	152	15	adding	add	VERB
ejpam-340	152	16	resulting	result	VERB
ejpam-340	152	17	these	these	DET
ejpam-340	152	18	two	two	NUM
ejpam-340	152	19	equations	equation	NOUN
ejpam-340	152	20	,	,	PUNCT
ejpam-340	152	21	we	we	PRON
ejpam-340	152	22	get	get	VERB
ejpam-340	152	23	(	(	PUNCT
ejpam-340	152	24	30	30	NUM
ejpam-340	152	25	)	)	PUNCT
ejpam-340	152	26	.	.	PUNCT
ejpam-340	153	1	further	far	ADV
ejpam-340	153	2	,	,	PUNCT
ejpam-340	153	3	replacing	replace	VERB
ejpam-340	153	4	x	x	SYM
ejpam-340	153	5	by	by	ADP
ejpam-340	153	6	x	x	X
ejpam-340	153	7	,	,	PUNCT
ejpam-340	153	8	y	y	PROPN
ejpam-340	153	9	by	by	ADP
ejpam-340	153	10	y	y	PROPN
ejpam-340	153	11	and	and	CCONJ
ejpam-340	153	12	multiplying	multiply	VERB
ejpam-340	153	13	with	with	ADP
ejpam-340	153	14	ui	ui	NOUN
ejpam-340	153	15	in	in	ADP
ejpam-340	153	16	(	(	PUNCT
ejpam-340	153	17	29	29	NUM
ejpam-340	153	18	)	)	PUNCT
ejpam-340	153	19	,	,	PUNCT
ejpam-340	153	20	we	we	PRON
ejpam-340	153	21	get	get	VERB
ejpam-340	153	22	(	(	PUNCT
ejpam-340	153	23	31	31	NUM
ejpam-340	153	24	)	)	PUNCT
ejpam-340	153	25	on	on	ADP
ejpam-340	153	26	use	use	NOUN
ejpam-340	153	27	of	of	ADP
ejpam-340	153	28	(	(	PUNCT
ejpam-340	153	29	5	5	NUM
ejpam-340	153	30	)	)	PUNCT
ejpam-340	153	31	,	,	PUNCT
ejpam-340	153	32	(	(	PUNCT
ejpam-340	153	33	19c	19c	NUM
ejpam-340	153	34	)	)	PUNCT
ejpam-340	153	35	and	and	CCONJ
ejpam-340	153	36	(	(	PUNCT
ejpam-340	153	37	27	27	NUM
ejpam-340	153	38	)	)	PUNCT
ejpam-340	153	39	.	.	PUNCT
ejpam-340	154	1	corollary	corollary	ADJ
ejpam-340	154	2	1	1	NUM
ejpam-340	154	3	.	.	PUNCT
ejpam-340	155	1	in	in	ADP
ejpam-340	155	2	vn	vn	PROPN
ejpam-340	155	3	,	,	PUNCT
ejpam-340	155	4	we	we	PRON
ejpam-340	155	5	have	have	VERB
ejpam-340	155	6	c(x	c(x	NOUN
ejpam-340	155	7	,	,	PUNCT
ejpam-340	155	8	ui	ui	NOUN
ejpam-340	155	9	)	)	PUNCT
ejpam-340	155	10	=	=	SYM
ejpam-340	156	1	σ(x	σ(x	PROPN
ejpam-340	156	2	)	)	PUNCT
ejpam-340	156	3	(	(	PUNCT
ejpam-340	156	4	32	32	NUM
ejpam-340	156	5	)	)	PUNCT
ejpam-340	156	6	c(x	c(x	NOUN
ejpam-340	156	7	,	,	PUNCT
ejpam-340	156	8	ui	ui	NOUN
ejpam-340	156	9	)	)	PUNCT
ejpam-340	156	10	=	=	PUNCT
ejpam-340	156	11	(	(	PUNCT
ejpam-340	156	12	dx	dx	PROPN
ejpam-340	156	13	u	u	NOUN
ejpam-340	156	14	j)(x	j)(x	PROPN
ejpam-340	156	15	)	)	PUNCT
ejpam-340	156	16	−	−	PROPN
ejpam-340	157	1	u	u	NOUN
ejpam-340	157	2	j(ν(x	j(ν(x	PROPN
ejpam-340	157	3	)	)	PUNCT
ejpam-340	157	4	)	)	PUNCT
ejpam-340	157	5	(	(	PUNCT
ejpam-340	157	6	33	33	NUM
ejpam-340	157	7	)	)	PUNCT
ejpam-340	157	8	proof	proof	NOUN
ejpam-340	157	9	.	.	PUNCT
ejpam-340	158	1	by	by	ADP
ejpam-340	158	2	replacing	replace	VERB
ejpam-340	158	3	i	i	PRON
ejpam-340	158	4	by	by	ADP
ejpam-340	158	5	j	j	PROPN
ejpam-340	158	6	and	and	CCONJ
ejpam-340	158	7	y	y	PROPN
ejpam-340	158	8	by	by	ADP
ejpam-340	158	9	ui	ui	PROPN
ejpam-340	158	10	in	in	ADP
ejpam-340	158	11	(	(	PUNCT
ejpam-340	158	12	29	29	NUM
ejpam-340	158	13	)	)	PUNCT
ejpam-340	158	14	,	,	PUNCT
ejpam-340	158	15	we	we	PRON
ejpam-340	158	16	get	get	VERB
ejpam-340	158	17	(	(	PUNCT
ejpam-340	158	18	32	32	NUM
ejpam-340	158	19	)	)	PUNCT
ejpam-340	158	20	.	.	PUNCT
ejpam-340	159	1	further	far	ADV
ejpam-340	159	2	,	,	PUNCT
ejpam-340	159	3	by	by	ADP
ejpam-340	159	4	replacing	replace	VERB
ejpam-340	159	5	x	x	PUNCT
ejpam-340	159	6	by	by	ADP
ejpam-340	159	7	x	x	SYM
ejpam-340	159	8	in	in	ADP
ejpam-340	159	9	(	(	PUNCT
ejpam-340	159	10	32	32	NUM
ejpam-340	159	11	)	)	PUNCT
ejpam-340	159	12	and	and	CCONJ
ejpam-340	159	13	using	use	VERB
ejpam-340	159	14	(	(	PUNCT
ejpam-340	159	15	19c	19c	NUM
ejpam-340	159	16	)	)	PUNCT
ejpam-340	159	17	&	&	CCONJ
ejpam-340	159	18	(	(	PUNCT
ejpam-340	159	19	27	27	NUM
ejpam-340	159	20	)	)	PUNCT
ejpam-340	159	21	,	,	PUNCT
ejpam-340	159	22	we	we	PRON
ejpam-340	159	23	obtain	obtain	VERB
ejpam-340	159	24	(	(	PUNCT
ejpam-340	159	25	33	33	NUM
ejpam-340	159	26	)	)	PUNCT
ejpam-340	159	27	.	.	PUNCT
ejpam-340	160	1	theorem	theorem	ADJ
ejpam-340	160	2	5	5	NUM
ejpam-340	160	3	.	.	PUNCT
ejpam-340	161	1	in	in	ADP
ejpam-340	161	2	vn	vn	PROPN
ejpam-340	161	3	,	,	PUNCT
ejpam-340	161	4	with	with	ADP
ejpam-340	161	5	ui	ui	PROPN
ejpam-340	161	6	as	as	ADP
ejpam-340	161	7	a	a	DET
ejpam-340	161	8	killing	killing	NOUN
ejpam-340	161	9	vector	vector	NOUN
ejpam-340	161	10	,	,	PUNCT
ejpam-340	161	11	we	we	PRON
ejpam-340	161	12	have	have	VERB
ejpam-340	161	13	c(x	c(x	NOUN
ejpam-340	161	14	,	,	PUNCT
ejpam-340	161	15	ui	ui	NOUN
ejpam-340	161	16	)	)	PUNCT
ejpam-340	162	1	=	=	NOUN
ejpam-340	162	2	−2ui(dx	−2ui(dx	PROPN
ejpam-340	162	3	ui	ui	PROPN
ejpam-340	162	4	)	)	PUNCT
ejpam-340	162	5	(	(	PUNCT
ejpam-340	162	6	34	34	NUM
ejpam-340	162	7	)	)	PUNCT
ejpam-340	162	8	proof	proof	NOUN
ejpam-340	162	9	.	.	PUNCT
ejpam-340	163	1	considering	consider	VERB
ejpam-340	163	2	ui	ui	PROPN
ejpam-340	163	3	as	as	ADP
ejpam-340	163	4	a	a	DET
ejpam-340	163	5	killing	kill	VERB
ejpam-340	163	6	vector	vector	NOUN
ejpam-340	163	7	with	with	ADP
ejpam-340	163	8	respect	respect	NOUN
ejpam-340	163	9	to	to	ADP
ejpam-340	163	10	connexion	connexion	NOUN
ejpam-340	163	11	d	d	PROPN
ejpam-340	163	12	and	and	CCONJ
ejpam-340	163	13	using	use	VERB
ejpam-340	163	14	(	(	PUNCT
ejpam-340	163	15	19a	19a	NUM
ejpam-340	163	16	)	)	PUNCT
ejpam-340	163	17	in	in	ADP
ejpam-340	163	18	(	(	PUNCT
ejpam-340	163	19	29	29	NUM
ejpam-340	163	20	)	)	PUNCT
ejpam-340	163	21	after	after	ADP
ejpam-340	163	22	putting	put	VERB
ejpam-340	163	23	ui	ui	NOUN
ejpam-340	163	24	for	for	ADP
ejpam-340	163	25	y	y	PROPN
ejpam-340	163	26	,	,	PUNCT
ejpam-340	163	27	we	we	PRON
ejpam-340	163	28	get	get	VERB
ejpam-340	163	29	(	(	PUNCT
ejpam-340	163	30	34	34	NUM
ejpam-340	163	31	)	)	PUNCT
ejpam-340	163	32	.	.	PUNCT
ejpam-340	164	1	theorem	theorem	VERB
ejpam-340	164	2	6	6	NUM
ejpam-340	164	3	.	.	PUNCT
ejpam-340	165	1	in	in	ADP
ejpam-340	165	2	vn	vn	PROPN
ejpam-340	165	3	,	,	PUNCT
ejpam-340	165	4	we	we	PRON
ejpam-340	165	5	have	have	VERB
ejpam-340	165	6	(	(	PUNCT
ejpam-340	165	7	lx	lx	ADP
ejpam-340	165	8	ui)(y	ui)(y	PROPN
ejpam-340	165	9	)	)	PUNCT
ejpam-340	165	10	−	−	PROPN
ejpam-340	166	1	(	(	PUNCT
ejpam-340	166	2	ly	ly	ADP
ejpam-340	166	3	ui)(x	ui)(x	PROPN
ejpam-340	166	4	)	)	PUNCT
ejpam-340	167	1	=	=	PUNCT
ejpam-340	167	2	c(x	c(x	NOUN
ejpam-340	167	3	,	,	PUNCT
ejpam-340	167	4	y	y	PROPN
ejpam-340	167	5	)	)	PUNCT
ejpam-340	167	6	−	−	PROPN
ejpam-340	168	1	ui(lx	ui(lx	NOUN
ejpam-340	168	2	y	y	PROPN
ejpam-340	168	3	)	)	PUNCT
ejpam-340	168	4	(	(	PUNCT
ejpam-340	168	5	35	35	NUM
ejpam-340	168	6	)	)	PUNCT
ejpam-340	168	7	proof	proof	NOUN
ejpam-340	168	8	.	.	PUNCT
ejpam-340	169	1	lie	lie	VERB
ejpam-340	169	2	derivative	derivative	NOUN
ejpam-340	169	3	of	of	ADP
ejpam-340	169	4	ui	ui	PROPN
ejpam-340	169	5	is	be	AUX
ejpam-340	169	6	given	give	VERB
ejpam-340	169	7	by	by	ADP
ejpam-340	169	8	(	(	PUNCT
ejpam-340	169	9	lx	lx	ADP
ejpam-340	169	10	ui)(y	ui)(y	PROPN
ejpam-340	169	11	)	)	PUNCT
ejpam-340	170	1	=	=	PUNCT
ejpam-340	170	2	(	(	PUNCT
ejpam-340	170	3	dx	dx	PROPN
ejpam-340	170	4	ui)(y	ui)(y	PROPN
ejpam-340	170	5	)	)	PUNCT
ejpam-340	171	1	+	+	CCONJ
ejpam-340	171	2	ui(dy	ui(dy	ADJ
ejpam-340	171	3	x	x	X
ejpam-340	171	4	)	)	PUNCT
ejpam-340	171	5	(	(	PUNCT
ejpam-340	171	6	36	36	NUM
ejpam-340	171	7	)	)	PUNCT
ejpam-340	171	8	interchanging	interchange	VERB
ejpam-340	171	9	x	x	X
ejpam-340	171	10	and	and	CCONJ
ejpam-340	171	11	y	y	PROPN
ejpam-340	171	12	in	in	ADP
ejpam-340	171	13	the	the	DET
ejpam-340	171	14	above	above	ADJ
ejpam-340	171	15	equation	equation	NOUN
ejpam-340	171	16	and	and	CCONJ
ejpam-340	171	17	subtracting	subtract	VERB
ejpam-340	171	18	the	the	DET
ejpam-340	171	19	resulting	result	VERB
ejpam-340	171	20	equation	equation	NOUN
ejpam-340	171	21	from	from	ADP
ejpam-340	171	22	above	above	ADP
ejpam-340	171	23	equation	equation	NOUN
ejpam-340	171	24	,	,	PUNCT
ejpam-340	171	25	we	we	PRON
ejpam-340	171	26	get	get	VERB
ejpam-340	171	27	(	(	PUNCT
ejpam-340	171	28	35	35	NUM
ejpam-340	171	29	)	)	PUNCT
ejpam-340	171	30	on	on	ADP
ejpam-340	171	31	the	the	DET
ejpam-340	171	32	use	use	NOUN
ejpam-340	171	33	of	of	ADP
ejpam-340	171	34	(	(	PUNCT
ejpam-340	171	35	29	29	NUM
ejpam-340	171	36	)	)	PUNCT
ejpam-340	171	37	and	and	CCONJ
ejpam-340	171	38	(	(	PUNCT
ejpam-340	171	39	17b	17b	NUM
ejpam-340	171	40	)	)	PUNCT
ejpam-340	171	41	.	.	PUNCT
ejpam-340	172	1	r.	r.	PROPN
ejpam-340	172	2	singh	singh	PROPN
ejpam-340	172	3	and	and	CCONJ
ejpam-340	172	4	s.	s.	PROPN
ejpam-340	172	5	singh	singh	PROPN
ejpam-340	172	6	/	/	SYM
ejpam-340	172	7	eur	eur	PROPN
ejpam-340	172	8	.	.	PUNCT
ejpam-340	173	1	j.	j.	PROPN
ejpam-340	173	2	pure	pure	PROPN
ejpam-340	173	3	appl	appl	PROPN
ejpam-340	173	4	.	.	PROPN
ejpam-340	173	5	math	math	PROPN
ejpam-340	173	6	,	,	PUNCT
ejpam-340	173	7	3	3	NUM
ejpam-340	173	8	(	(	PUNCT
ejpam-340	173	9	2010	2010	NUM
ejpam-340	173	10	)	)	PUNCT
ejpam-340	173	11	,	,	PUNCT
ejpam-340	173	12	839	839	NUM
ejpam-340	173	13	-	-	SYM
ejpam-340	173	14	852	852	NUM
ejpam-340	173	15	845	845	NUM
ejpam-340	173	16	corollary	corollary	ADJ
ejpam-340	173	17	2	2	NUM
ejpam-340	173	18	.	.	PUNCT
ejpam-340	174	1	in	in	ADP
ejpam-340	174	2	vn	vn	PROPN
ejpam-340	174	3	,	,	PUNCT
ejpam-340	174	4	we	we	PRON
ejpam-340	174	5	have	have	AUX
ejpam-340	174	6	(	(	PUNCT
ejpam-340	174	7	lx	lx	NOUN
ejpam-340	174	8	ui)(ui)−	ui)(ui)−	NOUN
ejpam-340	174	9	(	(	PUNCT
ejpam-340	174	10	lui	lui	X
ejpam-340	174	11	ui)(x	ui)(x	PROPN
ejpam-340	174	12	)	)	PUNCT
ejpam-340	175	1	=	=	PUNCT
ejpam-340	176	1	σ(x	σ(x	PROPN
ejpam-340	176	2	)	)	PUNCT
ejpam-340	176	3	−	−	PROPN
ejpam-340	177	1	ui(lx	ui(lx	NOUN
ejpam-340	177	2	ui	ui	PROPN
ejpam-340	177	3	)	)	PUNCT
ejpam-340	177	4	(	(	PUNCT
ejpam-340	177	5	37	37	NUM
ejpam-340	177	6	)	)	PUNCT
ejpam-340	177	7	(	(	PUNCT
ejpam-340	177	8	lx	lx	NOUN
ejpam-340	177	9	ui)(ui)−	ui)(ui)−	NOUN
ejpam-340	177	10	(	(	PUNCT
ejpam-340	177	11	lui	lui	X
ejpam-340	177	12	ui)(x	ui)(x	PROPN
ejpam-340	177	13	)	)	PUNCT
ejpam-340	178	1	=	=	PUNCT
ejpam-340	178	2	(	(	PUNCT
ejpam-340	178	3	dui	dui	PROPN
ejpam-340	178	4	u	u	PROPN
ejpam-340	178	5	j)(x	j)(x	PROPN
ejpam-340	178	6	)	)	PUNCT
ejpam-340	179	1	−	−	PROPN
ejpam-340	179	2	u	u	NOUN
ejpam-340	179	3	j(ν(x	j(ν(x	PROPN
ejpam-340	179	4	)	)	PUNCT
ejpam-340	179	5	)	)	PUNCT
ejpam-340	179	6	−	−	PROPN
ejpam-340	180	1	ui(lx	ui(lx	NOUN
ejpam-340	180	2	ui	ui	PROPN
ejpam-340	180	3	)	)	PUNCT
ejpam-340	180	4	(	(	PUNCT
ejpam-340	180	5	38	38	NUM
ejpam-340	180	6	)	)	PUNCT
ejpam-340	180	7	theorem	theorem	VERB
ejpam-340	180	8	7	7	NUM
ejpam-340	180	9	.	.	PUNCT
ejpam-340	181	1	in	in	ADP
ejpam-340	181	2	vn	vn	PROPN
ejpam-340	181	3	,	,	PUNCT
ejpam-340	181	4	we	we	PRON
ejpam-340	181	5	have	have	VERB
ejpam-340	181	6	(	(	PUNCT
ejpam-340	181	7	lx	lx	ADP
ejpam-340	181	8	ui)(y	ui)(y	PROPN
ejpam-340	181	9	)	)	PUNCT
ejpam-340	181	10	−	−	PROPN
ejpam-340	182	1	(	(	PUNCT
ejpam-340	182	2	ly	ly	ADP
ejpam-340	182	3	ui)(x	ui)(x	PROPN
ejpam-340	182	4	)	)	PUNCT
ejpam-340	183	1	+	+	VERB
ejpam-340	183	2	µ(x	µ(x	NOUN
ejpam-340	183	3	,	,	PUNCT
ejpam-340	183	4	y	y	AUX
ejpam-340	183	5	)	)	PUNCT
ejpam-340	183	6	=	=	PUNCT
ejpam-340	183	7	(	(	PUNCT
ejpam-340	183	8	dy	dy	X
ejpam-340	183	9	ui)(x	ui)(x	PROPN
ejpam-340	183	10	)	)	PUNCT
ejpam-340	183	11	−	−	PROPN
ejpam-340	184	1	(	(	PUNCT
ejpam-340	184	2	dx	dx	PROPN
ejpam-340	184	3	ui)(y	ui)(y	PROPN
ejpam-340	184	4	)	)	PUNCT
ejpam-340	185	1	+	+	NUM
ejpam-340	185	2	pi	pi	NOUN
ejpam-340	185	3	ju	ju	PROPN
ejpam-340	185	4	j([x	j([x	PROPN
ejpam-340	185	5	,	,	PUNCT
ejpam-340	185	6	y	y	PROPN
ejpam-340	185	7	]	]	X
ejpam-340	185	8	)	)	PUNCT
ejpam-340	185	9	(	(	PUNCT
ejpam-340	185	10	39	39	NUM
ejpam-340	185	11	)	)	PUNCT
ejpam-340	185	12	proof	proof	NOUN
ejpam-340	185	13	.	.	PUNCT
ejpam-340	186	1	replacing	replace	VERB
ejpam-340	186	2	x	x	PUNCT
ejpam-340	186	3	by	by	ADP
ejpam-340	186	4	x	x	SYM
ejpam-340	186	5	in	in	ADP
ejpam-340	186	6	(	(	PUNCT
ejpam-340	186	7	36	36	NUM
ejpam-340	186	8	)	)	PUNCT
ejpam-340	186	9	and	and	CCONJ
ejpam-340	186	10	using	use	VERB
ejpam-340	186	11	(	(	PUNCT
ejpam-340	186	12	13	13	NUM
ejpam-340	186	13	)	)	PUNCT
ejpam-340	186	14	&	&	CCONJ
ejpam-340	186	15	(	(	PUNCT
ejpam-340	186	16	5	5	NUM
ejpam-340	186	17	)	)	PUNCT
ejpam-340	186	18	,	,	PUNCT
ejpam-340	186	19	we	we	PRON
ejpam-340	186	20	get	get	VERB
ejpam-340	186	21	(	(	PUNCT
ejpam-340	186	22	lx	lx	ADP
ejpam-340	186	23	ui)(y	ui)(y	PROPN
ejpam-340	186	24	)	)	PUNCT
ejpam-340	187	1	=	=	PUNCT
ejpam-340	187	2	(	(	PUNCT
ejpam-340	187	3	dx	dx	PROPN
ejpam-340	187	4	ui)(y	ui)(y	PROPN
ejpam-340	187	5	)	)	PUNCT
ejpam-340	188	1	+	+	NUM
ejpam-340	188	2	pi	pi	NOUN
ejpam-340	188	3	ju	ju	PROPN
ejpam-340	188	4	j(dy	j(dy	PROPN
ejpam-340	188	5	x	x	X
ejpam-340	188	6	)	)	PUNCT
ejpam-340	188	7	(	(	PUNCT
ejpam-340	188	8	40a	40a	NUM
ejpam-340	188	9	)	)	PUNCT
ejpam-340	188	10	similarly	similarly	ADV
ejpam-340	188	11	,	,	PUNCT
ejpam-340	188	12	we	we	PRON
ejpam-340	188	13	can	can	AUX
ejpam-340	188	14	get	get	VERB
ejpam-340	188	15	(	(	PUNCT
ejpam-340	188	16	ly	ly	ADP
ejpam-340	188	17	ui)(x	ui)(x	PROPN
ejpam-340	188	18	)	)	PUNCT
ejpam-340	189	1	=	=	PUNCT
ejpam-340	189	2	(	(	PUNCT
ejpam-340	189	3	dy	dy	X
ejpam-340	189	4	ui)(x	ui)(x	PROPN
ejpam-340	189	5	)	)	PUNCT
ejpam-340	190	1	+	+	NUM
ejpam-340	190	2	pi	pi	NOUN
ejpam-340	190	3	ju	ju	PROPN
ejpam-340	190	4	j(dx	j(dx	PROPN
ejpam-340	190	5	y	y	PROPN
ejpam-340	190	6	)	)	PUNCT
ejpam-340	190	7	(	(	PUNCT
ejpam-340	190	8	40b	40b	X
ejpam-340	190	9	)	)	PUNCT
ejpam-340	190	10	subtracting	subtracting	NOUN
ejpam-340	190	11	(	(	PUNCT
ejpam-340	190	12	40b	40b	NOUN
ejpam-340	190	13	)	)	PUNCT
ejpam-340	190	14	from	from	ADP
ejpam-340	190	15	(	(	PUNCT
ejpam-340	190	16	40a	40a	NUM
ejpam-340	190	17	)	)	PUNCT
ejpam-340	190	18	and	and	CCONJ
ejpam-340	190	19	using	use	VERB
ejpam-340	190	20	(	(	PUNCT
ejpam-340	190	21	16	16	NUM
ejpam-340	190	22	)	)	PUNCT
ejpam-340	190	23	and	and	CCONJ
ejpam-340	190	24	(	(	PUNCT
ejpam-340	190	25	23	23	NUM
ejpam-340	190	26	)	)	PUNCT
ejpam-340	190	27	,	,	PUNCT
ejpam-340	190	28	we	we	PRON
ejpam-340	190	29	get	get	VERB
ejpam-340	190	30	the	the	DET
ejpam-340	190	31	required	require	VERB
ejpam-340	190	32	result	result	NOUN
ejpam-340	190	33	.	.	PUNCT
ejpam-340	191	1	3	3	X
ejpam-340	191	2	.	.	X
ejpam-340	191	3	an	an	DET
ejpam-340	191	4	affine	affine	PROPN
ejpam-340	191	5	connexion	connexion	PROPN
ejpam-340	191	6	ii	ii	PROPN
ejpam-340	191	7	in	in	ADP
ejpam-340	191	8	this	this	DET
ejpam-340	191	9	section	section	NOUN
ejpam-340	191	10	an	an	DET
ejpam-340	191	11	affine	affine	NOUN
ejpam-340	191	12	connexion	connexion	NOUN
ejpam-340	191	13	e	e	PROPN
ejpam-340	191	14	has	have	AUX
ejpam-340	191	15	been	be	AUX
ejpam-340	191	16	defined	define	VERB
ejpam-340	191	17	in	in	ADP
ejpam-340	191	18	terms	term	NOUN
ejpam-340	191	19	of	of	ADP
ejpam-340	191	20	another	another	DET
ejpam-340	191	21	affine	affine	NOUN
ejpam-340	191	22	connexion	connexion	NOUN
ejpam-340	191	23	d	d	X
ejpam-340	191	24	such	such	ADJ
ejpam-340	191	25	that	that	SCONJ
ejpam-340	191	26	their	their	PRON
ejpam-340	191	27	torsions	torsion	NOUN
ejpam-340	191	28	are	be	AUX
ejpam-340	191	29	equal	equal	ADJ
ejpam-340	191	30	but	but	CCONJ
ejpam-340	191	31	opposite	opposite	ADJ
ejpam-340	191	32	in	in	ADP
ejpam-340	191	33	sign	sign	NOUN
ejpam-340	191	34	.	.	PUNCT
ejpam-340	192	1	the	the	DET
ejpam-340	192	2	properties	property	NOUN
ejpam-340	192	3	of	of	ADP
ejpam-340	192	4	this	this	DET
ejpam-340	192	5	affine	affine	NOUN
ejpam-340	192	6	connexion	connexion	NOUN
ejpam-340	192	7	e	e	PROPN
ejpam-340	192	8	have	have	AUX
ejpam-340	192	9	been	be	AUX
ejpam-340	192	10	studied	study	VERB
ejpam-340	192	11	in	in	ADP
ejpam-340	192	12	a	a	DET
ejpam-340	192	13	generalised	generalise	VERB
ejpam-340	192	14	structure	structure	NOUN
ejpam-340	192	15	manifold	manifold	NOUN
ejpam-340	192	16	vn	vn	PROPN
ejpam-340	193	1	[	[	X
ejpam-340	193	2	18	18	NUM
ejpam-340	193	3	]	]	PUNCT
ejpam-340	193	4	.	.	PUNCT
ejpam-340	194	1	let	let	VERB
ejpam-340	194	2	us	we	PRON
ejpam-340	194	3	define	define	VERB
ejpam-340	194	4	an	an	DET
ejpam-340	194	5	affine	affine	NOUN
ejpam-340	194	6	connexion	connexion	NOUN
ejpam-340	194	7	e	e	PROPN
ejpam-340	194	8	in	in	ADP
ejpam-340	194	9	vn	vn	PROPN
ejpam-340	194	10	by	by	ADP
ejpam-340	194	11	the	the	DET
ejpam-340	194	12	relation	relation	NOUN
ejpam-340	194	13	ex	ex	ADJ
ejpam-340	194	14	y	y	PROPN
ejpam-340	194	15	de	de	PROPN
ejpam-340	194	16	f	f	PROPN
ejpam-340	195	1	=	=	SYM
ejpam-340	195	2	−dx	−dx	PROPN
ejpam-340	195	3	y	y	PROPN
ejpam-340	195	4	+	+	PUNCT
ejpam-340	196	1	[	[	X
ejpam-340	196	2	x	x	X
ejpam-340	196	3	,	,	PUNCT
ejpam-340	196	4	y	y	PROPN
ejpam-340	196	5	]	]	PUNCT
ejpam-340	196	6	(	(	PUNCT
ejpam-340	196	7	41	41	NUM
ejpam-340	196	8	)	)	PUNCT
ejpam-340	196	9	where	where	SCONJ
ejpam-340	196	10	d	d	NOUN
ejpam-340	196	11	is	be	AUX
ejpam-340	196	12	an	an	DET
ejpam-340	196	13	(	(	PUNCT
ejpam-340	196	14	f	f	NOUN
ejpam-340	196	15	,	,	PUNCT
ejpam-340	196	16	ui	ui	PROPN
ejpam-340	196	17	,	,	PUNCT
ejpam-340	196	18	u	u	NOUN
ejpam-340	196	19	i)-connexion	i)-connexion	NOUN
ejpam-340	196	20	given	give	VERB
ejpam-340	196	21	by	by	ADP
ejpam-340	196	22	(	(	PUNCT
ejpam-340	196	23	12	12	NUM
ejpam-340	196	24	)	)	PUNCT
ejpam-340	196	25	and	and	CCONJ
ejpam-340	196	26	the	the	DET
ejpam-340	196	27	torsions	torsion	NOUN
ejpam-340	196	28	of	of	ADP
ejpam-340	196	29	e	e	PROPN
ejpam-340	196	30	and	and	CCONJ
ejpam-340	196	31	d	d	NOUN
ejpam-340	196	32	are	be	AUX
ejpam-340	196	33	equal	equal	ADJ
ejpam-340	196	34	but	but	CCONJ
ejpam-340	196	35	opposite	opposite	ADJ
ejpam-340	196	36	in	in	ADP
ejpam-340	196	37	sign	sign	NOUN
ejpam-340	196	38	.	.	PUNCT
ejpam-340	197	1	we	we	PRON
ejpam-340	197	2	shall	shall	AUX
ejpam-340	197	3	study	study	VERB
ejpam-340	197	4	◦	◦	NOUN
ejpam-340	197	5	n	n	CCONJ
ejpam-340	197	6	,	,	PUNCT
ejpam-340	197	7	◦	◦	NOUN
ejpam-340	197	8	m	m	ADJ
ejpam-340	197	9	and	and	CCONJ
ejpam-340	197	10	curvature	curvature	VERB
ejpam-340	197	11	tensors	tensor	NOUN
ejpam-340	197	12	of	of	ADP
ejpam-340	197	13	connexion	connexion	PROPN
ejpam-340	197	14	e.	e.	PROPN
ejpam-340	197	15	remark	remark	PROPN
ejpam-340	197	16	2	2	NUM
ejpam-340	197	17	.	.	PUNCT
ejpam-340	198	1	since	since	SCONJ
ejpam-340	198	2	the	the	DET
ejpam-340	198	3	torsions	torsion	NOUN
ejpam-340	198	4	of	of	ADP
ejpam-340	198	5	the	the	DET
ejpam-340	198	6	connexions	connexion	NOUN
ejpam-340	198	7	d	d	NOUN
ejpam-340	198	8	and	and	CCONJ
ejpam-340	198	9	e	e	NOUN
ejpam-340	198	10	are	be	AUX
ejpam-340	198	11	equal	equal	ADJ
ejpam-340	198	12	and	and	CCONJ
ejpam-340	198	13	opposite	opposite	ADJ
ejpam-340	198	14	to	to	ADP
ejpam-340	198	15	each	each	DET
ejpam-340	198	16	other	other	ADJ
ejpam-340	198	17	,	,	PUNCT
ejpam-340	198	18	therefore	therefore	ADV
ejpam-340	198	19	,	,	PUNCT
ejpam-340	198	20	if	if	SCONJ
ejpam-340	198	21	d	d	NOUN
ejpam-340	198	22	is	be	AUX
ejpam-340	198	23	half	half	ADV
ejpam-340	198	24	symmetric	symmetric	ADJ
ejpam-340	198	25	,	,	PUNCT
ejpam-340	198	26	semi	semi	ADJ
ejpam-340	198	27	-	-	ADJ
ejpam-340	198	28	symmetric	symmetric	ADJ
ejpam-340	198	29	and	and	CCONJ
ejpam-340	198	30	almost	almost	ADV
ejpam-340	198	31	symmetric	symmetric	ADJ
ejpam-340	198	32	,	,	PUNCT
ejpam-340	198	33	e	e	X
ejpam-340	198	34	is	be	AUX
ejpam-340	198	35	also	also	ADV
ejpam-340	198	36	half	half	ADV
ejpam-340	198	37	symmetric	symmetric	ADJ
ejpam-340	198	38	,	,	PUNCT
ejpam-340	198	39	semi	semi	ADJ
ejpam-340	198	40	-	-	ADJ
ejpam-340	198	41	symmetric	symmetric	ADJ
ejpam-340	198	42	and	and	CCONJ
ejpam-340	198	43	almost	almost	ADV
ejpam-340	198	44	symmetric	symmetric	ADJ
ejpam-340	198	45	respectively	respectively	ADV
ejpam-340	198	46	.	.	PUNCT
ejpam-340	199	1	theorem	theorem	VERB
ejpam-340	199	2	8	8	NUM
ejpam-340	199	3	.	.	PUNCT
ejpam-340	200	1	in	in	ADP
ejpam-340	200	2	vn	vn	PROPN
ejpam-340	200	3	,	,	PUNCT
ejpam-340	200	4	we	we	PRON
ejpam-340	200	5	have	have	VERB
ejpam-340	200	6	ex	ex	PRON
ejpam-340	200	7	y	y	NOUN
ejpam-340	200	8	−	−	NOUN
ejpam-340	200	9	ey	ey	INTJ
ejpam-340	200	10	x	x	SYM
ejpam-340	200	11	=	=	PUNCT
ejpam-340	200	12	dy	dy	NOUN
ejpam-340	200	13	x	x	NOUN
ejpam-340	200	14	−	−	PROPN
ejpam-340	200	15	dx	dx	PROPN
ejpam-340	200	16	y	y	PROPN
ejpam-340	200	17	+	+	CCONJ
ejpam-340	200	18	2[x	2[x	NUM
ejpam-340	200	19	,	,	PUNCT
ejpam-340	200	20	y	y	PROPN
ejpam-340	200	21	]	]	PUNCT
ejpam-340	200	22	(	(	PUNCT
ejpam-340	200	23	42a	42a	NOUN
ejpam-340	200	24	)	)	PUNCT
ejpam-340	200	25	ex	ex	PRON
ejpam-340	200	26	ui	ui	ADV
ejpam-340	200	27	−	−	PROPN
ejpam-340	200	28	eui	eui	NOUN
ejpam-340	201	1	x	x	X
ejpam-340	201	2	=	=	PUNCT
ejpam-340	201	3	dui	dui	PROPN
ejpam-340	201	4	x	x	PROPN
ejpam-340	202	1	+	+	CCONJ
ejpam-340	202	2	2[x	2[x	NUM
ejpam-340	202	3	,	,	PUNCT
ejpam-340	202	4	ui	ui	PROPN
ejpam-340	202	5	]	]	X
ejpam-340	202	6	(	(	PUNCT
ejpam-340	202	7	42b	42b	NOUN
ejpam-340	202	8	)	)	PUNCT
ejpam-340	202	9	ex	ex	VERB
ejpam-340	202	10	y	y	PROPN
ejpam-340	202	11	−	−	NOUN
ejpam-340	202	12	ey	ey	INTJ
ejpam-340	202	13	x	x	SYM
ejpam-340	202	14	=	=	PUNCT
ejpam-340	202	15	dy	dy	NOUN
ejpam-340	202	16	x	x	NOUN
ejpam-340	202	17	−	−	PROPN
ejpam-340	202	18	dx	dx	PROPN
ejpam-340	202	19	y	y	PROPN
ejpam-340	203	1	+	+	CCONJ
ejpam-340	203	2	2[x	2[x	NUM
ejpam-340	203	3	,	,	PUNCT
ejpam-340	203	4	y	y	PROPN
ejpam-340	203	5	]	]	PUNCT
ejpam-340	203	6	(	(	PUNCT
ejpam-340	203	7	42c	42c	NOUN
ejpam-340	203	8	)	)	PUNCT
ejpam-340	203	9	ex	ex	NOUN
ejpam-340	203	10	y	y	PROPN
ejpam-340	203	11	−	−	NOUN
ejpam-340	203	12	ey	ey	INTJ
ejpam-340	203	13	x	x	SYM
ejpam-340	203	14	=	=	SYM
ejpam-340	203	15	b2(dy	b2(dy	PROPN
ejpam-340	203	16	x	x	PUNCT
ejpam-340	204	1	−	−	PROPN
ejpam-340	204	2	dx	dx	PROPN
ejpam-340	204	3	y	y	PROPN
ejpam-340	204	4	)	)	PUNCT
ejpam-340	205	1	+	+	CCONJ
ejpam-340	205	2	cui(dy	cui(dy	NOUN
ejpam-340	205	3	x	x	PUNCT
ejpam-340	205	4	−	−	PROPN
ejpam-340	205	5	dx	dx	PROPN
ejpam-340	205	6	y	y	PROPN
ejpam-340	205	7	)	)	PUNCT
ejpam-340	205	8	ui	ui	PROPN
ejpam-340	206	1	+	+	NUM
ejpam-340	207	1	[	[	X
ejpam-340	207	2	x	x	X
ejpam-340	207	3	,	,	PUNCT
ejpam-340	207	4	y	y	PROPN
ejpam-340	207	5	]	]	PUNCT
ejpam-340	207	6	−	−	PROPN
ejpam-340	208	1	[	[	X
ejpam-340	208	2	y	y	PROPN
ejpam-340	208	3	,	,	PUNCT
ejpam-340	208	4	x	x	X
ejpam-340	208	5	]	]	X
ejpam-340	208	6	(	(	PUNCT
ejpam-340	208	7	42d	42d	NOUN
ejpam-340	208	8	)	)	PUNCT
ejpam-340	208	9	ex	ex	NOUN
ejpam-340	208	10	y	y	PROPN
ejpam-340	208	11	−	−	NOUN
ejpam-340	208	12	ey	ey	INTJ
ejpam-340	208	13	x	x	SYM
ejpam-340	208	14	=	=	PUNCT
ejpam-340	208	15	dy	dy	NOUN
ejpam-340	208	16	x	x	NOUN
ejpam-340	208	17	−	−	PROPN
ejpam-340	209	1	dx	dx	PROPN
ejpam-340	210	1	y	y	PROPN
ejpam-340	211	1	+	+	PROPN
ejpam-340	212	1	[	[	X
ejpam-340	212	2	x	x	X
ejpam-340	212	3	,	,	PUNCT
ejpam-340	212	4	y	y	PROPN
ejpam-340	212	5	]	]	PUNCT
ejpam-340	212	6	−	−	PROPN
ejpam-340	213	1	[	[	X
ejpam-340	213	2	y	y	INTJ
ejpam-340	213	3	,	,	PUNCT
ejpam-340	213	4	x	x	X
ejpam-340	213	5	]	]	X
ejpam-340	213	6	(	(	PUNCT
ejpam-340	213	7	42e	42e	NOUN
ejpam-340	213	8	)	)	PUNCT
ejpam-340	213	9	r.	r.	PROPN
ejpam-340	213	10	singh	singh	PROPN
ejpam-340	213	11	and	and	CCONJ
ejpam-340	213	12	s.	s.	PROPN
ejpam-340	213	13	singh	singh	PROPN
ejpam-340	213	14	/	/	SYM
ejpam-340	213	15	eur	eur	PROPN
ejpam-340	213	16	.	.	PUNCT
ejpam-340	214	1	j.	j.	PROPN
ejpam-340	214	2	pure	pure	PROPN
ejpam-340	214	3	appl	appl	PROPN
ejpam-340	214	4	.	.	PROPN
ejpam-340	214	5	math	math	PROPN
ejpam-340	214	6	,	,	PUNCT
ejpam-340	214	7	3	3	NUM
ejpam-340	214	8	(	(	PUNCT
ejpam-340	214	9	2010	2010	NUM
ejpam-340	214	10	)	)	PUNCT
ejpam-340	214	11	,	,	PUNCT
ejpam-340	214	12	839	839	NUM
ejpam-340	214	13	-	-	SYM
ejpam-340	214	14	852	852	NUM
ejpam-340	214	15	846	846	NUM
ejpam-340	214	16	proof	proof	NOUN
ejpam-340	214	17	.	.	PUNCT
ejpam-340	215	1	the	the	DET
ejpam-340	215	2	equation	equation	NOUN
ejpam-340	215	3	(	(	PUNCT
ejpam-340	215	4	41	41	NUM
ejpam-340	215	5	)	)	PUNCT
ejpam-340	215	6	yields	yield	NOUN
ejpam-340	215	7	(	(	PUNCT
ejpam-340	215	8	42a	42a	NOUN
ejpam-340	215	9	)	)	PUNCT
ejpam-340	215	10	.	.	PUNCT
ejpam-340	216	1	putting	put	VERB
ejpam-340	216	2	ui	ui	NOUN
ejpam-340	216	3	for	for	ADP
ejpam-340	216	4	y	y	PROPN
ejpam-340	216	5	in	in	ADP
ejpam-340	216	6	(	(	PUNCT
ejpam-340	216	7	42a	42a	NOUN
ejpam-340	216	8	)	)	PUNCT
ejpam-340	216	9	and	and	CCONJ
ejpam-340	216	10	using	use	VERB
ejpam-340	216	11	(	(	PUNCT
ejpam-340	216	12	12	12	NUM
ejpam-340	216	13	)	)	PUNCT
ejpam-340	216	14	,	,	PUNCT
ejpam-340	216	15	we	we	PRON
ejpam-340	216	16	get	get	VERB
ejpam-340	216	17	(	(	PUNCT
ejpam-340	216	18	42b	42b	NOUN
ejpam-340	216	19	)	)	PUNCT
ejpam-340	216	20	.	.	PUNCT
ejpam-340	217	1	replacing	replace	VERB
ejpam-340	217	2	x	x	PUNCT
ejpam-340	217	3	by	by	ADP
ejpam-340	217	4	x	x	PUNCT
ejpam-340	217	5	and	and	CCONJ
ejpam-340	217	6	y	y	PROPN
ejpam-340	217	7	by	by	ADP
ejpam-340	217	8	y	y	PROPN
ejpam-340	217	9	in	in	ADP
ejpam-340	217	10	(	(	PUNCT
ejpam-340	217	11	42a	42a	NOUN
ejpam-340	217	12	)	)	PUNCT
ejpam-340	217	13	,	,	PUNCT
ejpam-340	217	14	we	we	PRON
ejpam-340	217	15	get	get	VERB
ejpam-340	217	16	(	(	PUNCT
ejpam-340	217	17	42c	42c	NOUN
ejpam-340	217	18	)	)	PUNCT
ejpam-340	217	19	on	on	ADP
ejpam-340	217	20	the	the	DET
ejpam-340	217	21	use	use	NOUN
ejpam-340	217	22	of	of	ADP
ejpam-340	217	23	(	(	PUNCT
ejpam-340	217	24	12	12	NUM
ejpam-340	217	25	)	)	PUNCT
ejpam-340	217	26	.	.	PUNCT
ejpam-340	218	1	the	the	DET
ejpam-340	218	2	value	value	NOUN
ejpam-340	218	3	of	of	ADP
ejpam-340	218	4	(	(	PUNCT
ejpam-340	218	5	ex	ex	X
ejpam-340	218	6	y	y	NOUN
ejpam-340	218	7	−	−	PROPN
ejpam-340	218	8	ey	ey	PROPN
ejpam-340	218	9	x	x	X
ejpam-340	218	10	)	)	PUNCT
ejpam-340	218	11	is	be	AUX
ejpam-340	218	12	obtained	obtain	VERB
ejpam-340	218	13	by	by	ADP
ejpam-340	218	14	making	make	VERB
ejpam-340	218	15	use	use	NOUN
ejpam-340	218	16	of	of	ADP
ejpam-340	218	17	(	(	PUNCT
ejpam-340	218	18	41	41	NUM
ejpam-340	218	19	)	)	PUNCT
ejpam-340	218	20	and	and	CCONJ
ejpam-340	218	21	operating	operate	VERB
ejpam-340	218	22	f	f	PROPN
ejpam-340	218	23	on	on	ADP
ejpam-340	218	24	the	the	DET
ejpam-340	218	25	resulting	result	VERB
ejpam-340	218	26	equation	equation	NOUN
ejpam-340	218	27	and	and	CCONJ
ejpam-340	218	28	using	use	VERB
ejpam-340	218	29	(	(	PUNCT
ejpam-340	218	30	1	1	NUM
ejpam-340	218	31	)	)	PUNCT
ejpam-340	218	32	&	&	CCONJ
ejpam-340	218	33	(	(	PUNCT
ejpam-340	218	34	12	12	NUM
ejpam-340	218	35	)	)	PUNCT
ejpam-340	218	36	,	,	PUNCT
ejpam-340	218	37	we	we	PRON
ejpam-340	218	38	get	get	VERB
ejpam-340	218	39	(	(	PUNCT
ejpam-340	218	40	42d	42d	NOUN
ejpam-340	218	41	)	)	PUNCT
ejpam-340	218	42	.	.	PUNCT
ejpam-340	219	1	similarly	similarly	ADV
ejpam-340	219	2	,	,	PUNCT
ejpam-340	219	3	we	we	PRON
ejpam-340	219	4	can	can	AUX
ejpam-340	219	5	get	get	VERB
ejpam-340	219	6	(	(	PUNCT
ejpam-340	219	7	42e	42e	NOUN
ejpam-340	219	8	)	)	PUNCT
ejpam-340	219	9	.	.	PUNCT
ejpam-340	220	1	theorem	theorem	VERB
ejpam-340	220	2	9	9	NUM
ejpam-340	220	3	.	.	PUNCT
ejpam-340	221	1	in	in	ADP
ejpam-340	221	2	vn	vn	PROPN
ejpam-340	221	3	,	,	PUNCT
ejpam-340	221	4	we	we	PRON
ejpam-340	221	5	have	have	VERB
ejpam-340	221	6	(	(	PUNCT
ejpam-340	221	7	ex	ex	X
ejpam-340	221	8	f)(y	f)(y	NUM
ejpam-340	221	9	)	)	PUNCT
ejpam-340	222	1	=	=	PUNCT
ejpam-340	223	1	[	[	X
ejpam-340	223	2	x	x	X
ejpam-340	223	3	,	,	PUNCT
ejpam-340	223	4	y	y	PROPN
ejpam-340	223	5	]	]	PUNCT
ejpam-340	223	6	−	−	X
ejpam-340	224	1	[	[	X
ejpam-340	224	2	x	x	X
ejpam-340	224	3	,	,	PUNCT
ejpam-340	224	4	y	y	PROPN
ejpam-340	224	5	]	]	PUNCT
ejpam-340	224	6	(	(	PUNCT
ejpam-340	224	7	43a	43a	NOUN
ejpam-340	224	8	)	)	PUNCT
ejpam-340	224	9	(	(	PUNCT
ejpam-340	224	10	ex	ex	X
ejpam-340	224	11	f)(ui	f)(ui	NOUN
ejpam-340	224	12	)	)	PUNCT
ejpam-340	224	13	=	=	SYM
ejpam-340	225	1	pi	pi	NOUN
ejpam-340	225	2	j[x	j[x	NOUN
ejpam-340	225	3	,	,	PUNCT
ejpam-340	225	4	u	u	NOUN
ejpam-340	225	5	j]−	j]−	X
ejpam-340	226	1	[	[	X
ejpam-340	226	2	x	x	X
ejpam-340	226	3	,	,	PUNCT
ejpam-340	226	4	ui	ui	PROPN
ejpam-340	226	5	]	]	X
ejpam-340	226	6	(	(	PUNCT
ejpam-340	226	7	43b	43b	ADJ
ejpam-340	226	8	)	)	PUNCT
ejpam-340	226	9	proof	proof	NOUN
ejpam-340	226	10	.	.	PUNCT
ejpam-340	227	1	replacing	replace	VERB
ejpam-340	227	2	y	y	PRON
ejpam-340	227	3	by	by	ADP
ejpam-340	227	4	y	y	PROPN
ejpam-340	227	5	in	in	ADP
ejpam-340	227	6	(	(	PUNCT
ejpam-340	227	7	41	41	NUM
ejpam-340	227	8	)	)	PUNCT
ejpam-340	227	9	,	,	PUNCT
ejpam-340	227	10	we	we	PRON
ejpam-340	227	11	have	have	VERB
ejpam-340	227	12	ex	ex	PRON
ejpam-340	227	13	y	y	NOUN
ejpam-340	227	14	=	=	PUNCT
ejpam-340	227	15	−dx	−dx	PROPN
ejpam-340	227	16	y	y	PROPN
ejpam-340	228	1	+	+	PUNCT
ejpam-340	229	1	[	[	X
ejpam-340	229	2	x	x	X
ejpam-340	229	3	,	,	PUNCT
ejpam-340	229	4	y	y	PROPN
ejpam-340	229	5	]	]	PUNCT
ejpam-340	229	6	(	(	PUNCT
ejpam-340	229	7	44	44	NUM
ejpam-340	229	8	)	)	PUNCT
ejpam-340	229	9	which	which	PRON
ejpam-340	229	10	on	on	ADP
ejpam-340	229	11	use	use	NOUN
ejpam-340	229	12	of	of	ADP
ejpam-340	229	13	(	(	PUNCT
ejpam-340	229	14	41	41	NUM
ejpam-340	229	15	)	)	PUNCT
ejpam-340	229	16	yields	yield	NOUN
ejpam-340	229	17	(	(	PUNCT
ejpam-340	229	18	43a	43a	NOUN
ejpam-340	229	19	)	)	PUNCT
ejpam-340	229	20	and	and	CCONJ
ejpam-340	229	21	by	by	ADP
ejpam-340	229	22	replacing	replace	VERB
ejpam-340	229	23	y	y	PRON
ejpam-340	229	24	by	by	ADP
ejpam-340	229	25	ui	ui	PROPN
ejpam-340	229	26	and	and	CCONJ
ejpam-340	229	27	using	use	VERB
ejpam-340	229	28	(	(	PUNCT
ejpam-340	229	29	5	5	NUM
ejpam-340	229	30	)	)	PUNCT
ejpam-340	229	31	,	,	PUNCT
ejpam-340	229	32	we	we	PRON
ejpam-340	229	33	get	get	VERB
ejpam-340	229	34	(	(	PUNCT
ejpam-340	229	35	43b	43b	NUM
ejpam-340	229	36	)	)	PUNCT
ejpam-340	229	37	.	.	PUNCT
ejpam-340	230	1	theorem	theorem	ADJ
ejpam-340	230	2	10	10	NUM
ejpam-340	230	3	.	.	PUNCT
ejpam-340	231	1	in	in	ADP
ejpam-340	231	2	vn	vn	PROPN
ejpam-340	231	3	,	,	PUNCT
ejpam-340	231	4	we	we	PRON
ejpam-340	231	5	have	have	VERB
ejpam-340	231	6	c{(ex	c{(ex	VERB
ejpam-340	231	7	ui)(y	ui)(y	PROPN
ejpam-340	231	8	)	)	PUNCT
ejpam-340	232	1	+	+	CCONJ
ejpam-340	232	2	ui([x	ui([x	ADJ
ejpam-340	232	3	,	,	PUNCT
ejpam-340	232	4	y	y	PROPN
ejpam-340	232	5	]	]	X
ejpam-340	232	6	)	)	PUNCT
ejpam-340	232	7	}	}	PUNCT
ejpam-340	232	8	=	=	SYM
ejpam-340	232	9	0	0	PUNCT
ejpam-340	232	10	(	(	PUNCT
ejpam-340	232	11	45	45	NUM
ejpam-340	232	12	)	)	PUNCT
ejpam-340	232	13	proof	proof	NOUN
ejpam-340	232	14	.	.	PUNCT
ejpam-340	233	1	replacing	replace	VERB
ejpam-340	233	2	y	y	PRON
ejpam-340	233	3	by	by	ADP
ejpam-340	233	4	y	y	PROPN
ejpam-340	233	5	in	in	ADP
ejpam-340	233	6	(	(	PUNCT
ejpam-340	233	7	41	41	NUM
ejpam-340	233	8	)	)	PUNCT
ejpam-340	233	9	and	and	CCONJ
ejpam-340	233	10	using	use	VERB
ejpam-340	233	11	(	(	PUNCT
ejpam-340	233	12	1	1	NUM
ejpam-340	233	13	)	)	PUNCT
ejpam-340	233	14	,	,	PUNCT
ejpam-340	233	15	we	we	PRON
ejpam-340	233	16	get	get	VERB
ejpam-340	233	17	ex	ex	X
ejpam-340	233	18	(	(	PUNCT
ejpam-340	233	19	b	b	NOUN
ejpam-340	233	20	2y	2y	PROPN
ejpam-340	233	21	+	+	CCONJ
ejpam-340	233	22	cui(y	cui(y	ADJ
ejpam-340	233	23	)	)	PUNCT
ejpam-340	233	24	ui	ui	NOUN
ejpam-340	233	25	)	)	PUNCT
ejpam-340	233	26	=	=	SYM
ejpam-340	233	27	−dx	−dx	NOUN
ejpam-340	233	28	(	(	PUNCT
ejpam-340	233	29	b	b	NOUN
ejpam-340	233	30	2y	2y	PROPN
ejpam-340	233	31	+	+	CCONJ
ejpam-340	233	32	cui(y	cui(y	ADJ
ejpam-340	233	33	)	)	PUNCT
ejpam-340	233	34	ui	ui	PROPN
ejpam-340	233	35	)	)	PUNCT
ejpam-340	234	1	+	+	CCONJ
ejpam-340	234	2	b2[x	b2[x	NOUN
ejpam-340	234	3	,	,	PUNCT
ejpam-340	234	4	y	y	PROPN
ejpam-340	234	5	]	]	PUNCT
ejpam-340	235	1	+	+	CCONJ
ejpam-340	235	2	cui(y	cui(y	NOUN
ejpam-340	235	3	)	)	PUNCT
ejpam-340	236	1	[	[	X
ejpam-340	236	2	x	x	X
ejpam-340	236	3	,	,	PUNCT
ejpam-340	236	4	ui	ui	PROPN
ejpam-340	236	5	]	]	X
ejpam-340	236	6	(	(	PUNCT
ejpam-340	236	7	46a	46a	NOUN
ejpam-340	236	8	)	)	PUNCT
ejpam-340	236	9	using	use	VERB
ejpam-340	236	10	(	(	PUNCT
ejpam-340	236	11	1.12	1.12	NUM
ejpam-340	236	12	)	)	PUNCT
ejpam-340	236	13	and	and	CCONJ
ejpam-340	236	14	(	(	PUNCT
ejpam-340	236	15	3.1	3.1	NUM
ejpam-340	236	16	)	)	PUNCT
ejpam-340	236	17	in	in	ADP
ejpam-340	236	18	above	above	ADV
ejpam-340	236	19	,	,	PUNCT
ejpam-340	236	20	we	we	PRON
ejpam-340	236	21	get	get	VERB
ejpam-340	236	22	c	c	NOUN
ejpam-340	236	23	ui(ex	ui(ex	ADJ
ejpam-340	236	24	ui)(y	ui)(y	PROPN
ejpam-340	236	25	)	)	PUNCT
ejpam-340	237	1	=	=	PUNCT
ejpam-340	237	2	−c	−c	NOUN
ejpam-340	237	3	uiu	uiu	PROPN
ejpam-340	238	1	i([x	i([x	PROPN
ejpam-340	238	2	,	,	PUNCT
ejpam-340	238	3	y	y	PROPN
ejpam-340	238	4	]	]	X
ejpam-340	238	5	)	)	PUNCT
ejpam-340	238	6	(	(	PUNCT
ejpam-340	238	7	46b	46b	NUM
ejpam-340	238	8	)	)	PUNCT
ejpam-340	238	9	which	which	PRON
ejpam-340	238	10	implies(45	implies(45	VERB
ejpam-340	238	11	)	)	PUNCT
ejpam-340	238	12	.	.	PUNCT
ejpam-340	239	1	now	now	ADV
ejpam-340	239	2	,	,	PUNCT
ejpam-340	239	3	let	let	VERB
ejpam-340	239	4	us	we	PRON
ejpam-340	239	5	consider	consider	VERB
ejpam-340	239	6	nijenhuis	nijenhuis	ADJ
ejpam-340	239	7	tensor	tensor	NOUN
ejpam-340	239	8	n(x	n(x	PROPN
ejpam-340	239	9	,	,	PUNCT
ejpam-340	239	10	y	y	PROPN
ejpam-340	239	11	)	)	PUNCT
ejpam-340	239	12	in	in	ADP
ejpam-340	239	13	vn	vn	PROPN
ejpam-340	239	14	,	,	PUNCT
ejpam-340	239	15	which	which	PRON
ejpam-340	239	16	is	be	AUX
ejpam-340	239	17	given	give	VERB
ejpam-340	239	18	by	by	ADP
ejpam-340	239	19	(	(	PUNCT
ejpam-340	239	20	14	14	NUM
ejpam-340	239	21	)	)	PUNCT
ejpam-340	239	22	.	.	PUNCT
ejpam-340	240	1	for	for	ADP
ejpam-340	240	2	the	the	DET
ejpam-340	240	3	symmetric	symmetric	ADJ
ejpam-340	240	4	connexion	connexion	NOUN
ejpam-340	240	5	d	d	NOUN
ejpam-340	240	6	,	,	PUNCT
ejpam-340	240	7	it	it	PRON
ejpam-340	240	8	takes	take	VERB
ejpam-340	240	9	the	the	DET
ejpam-340	240	10	following	follow	VERB
ejpam-340	240	11	form	form	NOUN
ejpam-340	240	12	:	:	PUNCT
ejpam-340	240	13	n(x	n(x	PROPN
ejpam-340	240	14	,	,	PUNCT
ejpam-340	240	15	y	y	PROPN
ejpam-340	240	16	)	)	PUNCT
ejpam-340	241	1	=	=	PUNCT
ejpam-340	241	2	dx	dx	PROPN
ejpam-340	241	3	y	y	PROPN
ejpam-340	241	4	−	−	PROPN
ejpam-340	241	5	dy	dy	NOUN
ejpam-340	241	6	x	x	PUNCT
ejpam-340	242	1	+	+	NUM
ejpam-340	242	2	dx	dx	PROPN
ejpam-340	242	3	y	y	PROPN
ejpam-340	242	4	−	−	PROPN
ejpam-340	242	5	dy	dy	NOUN
ejpam-340	242	6	x	x	PUNCT
ejpam-340	242	7	−	−	PROPN
ejpam-340	242	8	dx	dx	PROPN
ejpam-340	242	9	y	y	PROPN
ejpam-340	243	1	+	+	CCONJ
ejpam-340	243	2	dy	dy	X
ejpam-340	243	3	x	x	PUNCT
ejpam-340	243	4	−	−	PROPN
ejpam-340	243	5	dx	dx	PROPN
ejpam-340	243	6	y	y	PROPN
ejpam-340	244	1	+	+	CCONJ
ejpam-340	244	2	dy	dy	X
ejpam-340	244	3	x	x	X
ejpam-340	244	4	(	(	PUNCT
ejpam-340	244	5	47	47	NUM
ejpam-340	244	6	)	)	PUNCT
ejpam-340	244	7	using	use	VERB
ejpam-340	244	8	(	(	PUNCT
ejpam-340	244	9	1	1	NUM
ejpam-340	244	10	)	)	PUNCT
ejpam-340	244	11	in	in	ADP
ejpam-340	244	12	above	above	ADV
ejpam-340	244	13	,	,	PUNCT
ejpam-340	244	14	we	we	PRON
ejpam-340	244	15	get	get	VERB
ejpam-340	244	16	n(x	n(x	PROPN
ejpam-340	244	17	,	,	PUNCT
ejpam-340	244	18	y	y	PROPN
ejpam-340	244	19	)	)	PUNCT
ejpam-340	245	1	=	=	PUNCT
ejpam-340	245	2	dx	dx	PROPN
ejpam-340	245	3	y	y	PROPN
ejpam-340	245	4	−	−	PROPN
ejpam-340	246	1	dy	dy	NOUN
ejpam-340	246	2	x	x	PUNCT
ejpam-340	246	3	+	+	PROPN
ejpam-340	247	1	b2(dx	b2(dx	PROPN
ejpam-340	247	2	y	y	PROPN
ejpam-340	247	3	−	−	NOUN
ejpam-340	247	4	dy	dy	X
ejpam-340	247	5	x	x	PROPN
ejpam-340	247	6	)	)	PUNCT
ejpam-340	248	1	+	+	CCONJ
ejpam-340	249	1	c	c	NOUN
ejpam-340	249	2	ui(dx	ui(dx	NOUN
ejpam-340	249	3	y	y	NOUN
ejpam-340	249	4	−	−	NOUN
ejpam-340	249	5	dy	dy	X
ejpam-340	249	6	x	x	PROPN
ejpam-340	249	7	)	)	PUNCT
ejpam-340	249	8	ui	ui	PROPN
ejpam-340	249	9	−dx	−dx	PROPN
ejpam-340	249	10	y	y	PROPN
ejpam-340	250	1	+	+	CCONJ
ejpam-340	250	2	dy	dy	X
ejpam-340	250	3	x	x	PUNCT
ejpam-340	250	4	−	−	PROPN
ejpam-340	250	5	dx	dx	PROPN
ejpam-340	250	6	y	y	PROPN
ejpam-340	251	1	+	+	CCONJ
ejpam-340	251	2	dy	dy	X
ejpam-340	251	3	x	x	SYM
ejpam-340	251	4	(	(	PUNCT
ejpam-340	251	5	48	48	NUM
ejpam-340	251	6	)	)	PUNCT
ejpam-340	251	7	similar	similar	ADJ
ejpam-340	251	8	to	to	ADP
ejpam-340	251	9	nijenhuis	nijenhuis	PROPN
ejpam-340	251	10	tensor	tensor	NOUN
ejpam-340	251	11	for	for	ADP
ejpam-340	251	12	connexion	connexion	NOUN
ejpam-340	251	13	d	d	NOUN
ejpam-340	251	14	,	,	PUNCT
ejpam-340	251	15	let	let	VERB
ejpam-340	251	16	us	we	PRON
ejpam-340	251	17	introduce	introduce	VERB
ejpam-340	251	18	a	a	DET
ejpam-340	251	19	tensor	tensor	NOUN
ejpam-340	251	20	◦	◦	NOUN
ejpam-340	252	1	n	n	CCONJ
ejpam-340	252	2	(	(	PUNCT
ejpam-340	252	3	x	x	X
ejpam-340	252	4	,	,	PUNCT
ejpam-340	252	5	y	y	PROPN
ejpam-340	252	6	)	)	PUNCT
ejpam-340	252	7	for	for	ADP
ejpam-340	252	8	the	the	DET
ejpam-340	252	9	connexion	connexion	PROPN
ejpam-340	252	10	e	e	NOUN
ejpam-340	252	11	,	,	PUNCT
ejpam-340	252	12	given	give	VERB
ejpam-340	252	13	by	by	ADP
ejpam-340	252	14	◦	◦	NOUN
ejpam-340	252	15	n	n	CCONJ
ejpam-340	252	16	(	(	PUNCT
ejpam-340	252	17	x	x	X
ejpam-340	252	18	,	,	PUNCT
ejpam-340	252	19	y	y	PROPN
ejpam-340	252	20	)	)	PUNCT
ejpam-340	252	21	de	de	PROPN
ejpam-340	252	22	f	f	X
ejpam-340	252	23	=	=	PUNCT
ejpam-340	252	24	ex	ex	ADJ
ejpam-340	252	25	y	y	PROPN
ejpam-340	252	26	−	−	NOUN
ejpam-340	252	27	ey	ey	INTJ
ejpam-340	252	28	x	x	SYM
ejpam-340	252	29	+	+	PROPN
ejpam-340	252	30	b2(ex	b2(ex	PROPN
ejpam-340	252	31	y	y	PROPN
ejpam-340	252	32	−	−	NOUN
ejpam-340	252	33	ey	ey	INTJ
ejpam-340	252	34	x	x	PUNCT
ejpam-340	252	35	)	)	PUNCT
ejpam-340	252	36	+	+	NUM
ejpam-340	252	37	c	c	NOUN
ejpam-340	252	38	ui(ex	ui(ex	ADJ
ejpam-340	252	39	y	y	PROPN
ejpam-340	252	40	−	−	PROPN
ejpam-340	252	41	ey	ey	INTJ
ejpam-340	252	42	x	x	X
ejpam-340	252	43	)	)	PUNCT
ejpam-340	252	44	ui	ui	NOUN
ejpam-340	252	45	−ex	−ex	NOUN
ejpam-340	252	46	y	y	PROPN
ejpam-340	252	47	+	+	CCONJ
ejpam-340	252	48	ey	ey	PROPN
ejpam-340	252	49	x	x	SYM
ejpam-340	252	50	−	−	X
ejpam-340	252	51	ex	ex	X
ejpam-340	252	52	y	y	NOUN
ejpam-340	252	53	+	+	CCONJ
ejpam-340	252	54	ey	ey	PROPN
ejpam-340	252	55	x	x	SYM
ejpam-340	252	56	(	(	PUNCT
ejpam-340	252	57	49	49	NUM
ejpam-340	252	58	)	)	PUNCT
ejpam-340	252	59	r.	r.	PROPN
ejpam-340	252	60	singh	singh	PROPN
ejpam-340	252	61	and	and	CCONJ
ejpam-340	252	62	s.	s.	PROPN
ejpam-340	252	63	singh	singh	PROPN
ejpam-340	252	64	/	/	SYM
ejpam-340	252	65	eur	eur	PROPN
ejpam-340	252	66	.	.	PUNCT
ejpam-340	253	1	j.	j.	PROPN
ejpam-340	253	2	pure	pure	PROPN
ejpam-340	253	3	appl	appl	PROPN
ejpam-340	253	4	.	.	PROPN
ejpam-340	253	5	math	math	PROPN
ejpam-340	253	6	,	,	PUNCT
ejpam-340	253	7	3	3	NUM
ejpam-340	253	8	(	(	PUNCT
ejpam-340	253	9	2010	2010	NUM
ejpam-340	253	10	)	)	PUNCT
ejpam-340	253	11	,	,	PUNCT
ejpam-340	253	12	839	839	NUM
ejpam-340	253	13	-	-	SYM
ejpam-340	253	14	852	852	NUM
ejpam-340	253	15	847	847	NUM
ejpam-340	253	16	theorem	theorem	VERB
ejpam-340	253	17	11	11	NUM
ejpam-340	253	18	.	.	PUNCT
ejpam-340	254	1	in	in	ADP
ejpam-340	254	2	vn	vn	PROPN
ejpam-340	254	3	,	,	PUNCT
ejpam-340	254	4	we	we	PRON
ejpam-340	254	5	have	have	VERB
ejpam-340	254	6	◦	◦	NOUN
ejpam-340	254	7	n	n	PROPN
ejpam-340	254	8	(	(	PUNCT
ejpam-340	254	9	x	x	INTJ
ejpam-340	254	10	,	,	PUNCT
ejpam-340	254	11	y	y	PROPN
ejpam-340	254	12	)	)	PUNCT
ejpam-340	255	1	=	=	SYM
ejpam-340	255	2	2	2	NUM
ejpam-340	255	3	(	(	PUNCT
ejpam-340	255	4	[	[	PUNCT
ejpam-340	255	5	x	x	X
ejpam-340	255	6	,	,	PUNCT
ejpam-340	255	7	y	y	PROPN
ejpam-340	255	8	]	]	PUNCT
ejpam-340	256	1	+	+	CCONJ
ejpam-340	257	1	[	[	X
ejpam-340	257	2	x	x	X
ejpam-340	257	3	,	,	PUNCT
ejpam-340	257	4	y	y	PROPN
ejpam-340	257	5	]	]	PUNCT
ejpam-340	257	6	−	−	X
ejpam-340	258	1	[	[	X
ejpam-340	258	2	x	x	X
ejpam-340	258	3	,	,	PUNCT
ejpam-340	258	4	y	y	PROPN
ejpam-340	258	5	]	]	PUNCT
ejpam-340	258	6	−	−	X
ejpam-340	259	1	[	[	X
ejpam-340	259	2	x	x	X
ejpam-340	259	3	,	,	PUNCT
ejpam-340	259	4	y	y	PROPN
ejpam-340	259	5	]	]	PUNCT
ejpam-340	259	6	)	)	PUNCT
ejpam-340	259	7	=	=	SYM
ejpam-340	259	8	2n(x	2n(x	NUM
ejpam-340	259	9	,	,	PUNCT
ejpam-340	259	10	y	y	PROPN
ejpam-340	259	11	)	)	PUNCT
ejpam-340	259	12	(	(	PUNCT
ejpam-340	259	13	50	50	X
ejpam-340	259	14	)	)	PUNCT
ejpam-340	259	15	proof	proof	NOUN
ejpam-340	259	16	.	.	PUNCT
ejpam-340	260	1	using	use	VERB
ejpam-340	260	2	(	(	PUNCT
ejpam-340	260	3	42a	42a	NOUN
ejpam-340	260	4	)	)	PUNCT
ejpam-340	260	5	,	,	PUNCT
ejpam-340	260	6	(	(	PUNCT
ejpam-340	260	7	42c	42c	NOUN
ejpam-340	260	8	)	)	PUNCT
ejpam-340	260	9	,	,	PUNCT
ejpam-340	260	10	(	(	PUNCT
ejpam-340	260	11	42d	42d	NOUN
ejpam-340	260	12	)	)	PUNCT
ejpam-340	260	13	and	and	CCONJ
ejpam-340	260	14	(	(	PUNCT
ejpam-340	260	15	42e	42e	NOUN
ejpam-340	260	16	)	)	PUNCT
ejpam-340	260	17	in	in	ADP
ejpam-340	260	18	(	(	PUNCT
ejpam-340	260	19	49	49	NUM
ejpam-340	260	20	)	)	PUNCT
ejpam-340	260	21	,	,	PUNCT
ejpam-340	260	22	we	we	PRON
ejpam-340	260	23	obtain	obtain	VERB
ejpam-340	260	24	◦	◦	NOUN
ejpam-340	261	1	n	n	CCONJ
ejpam-340	261	2	(	(	PUNCT
ejpam-340	261	3	x	x	INTJ
ejpam-340	261	4	,	,	PUNCT
ejpam-340	261	5	y	y	PROPN
ejpam-340	261	6	)	)	PUNCT
ejpam-340	261	7	=	=	PUNCT
ejpam-340	262	1	(	(	PUNCT
ejpam-340	262	2	dy	dy	X
ejpam-340	262	3	x	x	NOUN
ejpam-340	262	4	−	−	PROPN
ejpam-340	262	5	dx	dx	PROPN
ejpam-340	262	6	y	y	PROPN
ejpam-340	263	1	+	+	PROPN
ejpam-340	263	2	2	2	NUM
ejpam-340	263	3	[	[	PUNCT
ejpam-340	263	4	x	x	X
ejpam-340	263	5	,	,	PUNCT
ejpam-340	263	6	y	y	PROPN
ejpam-340	263	7	]	]	PUNCT
ejpam-340	263	8	)	)	PUNCT
ejpam-340	264	1	+	+	CCONJ
ejpam-340	264	2	b2(dy	b2(dy	PROPN
ejpam-340	264	3	x	x	PUNCT
ejpam-340	265	1	−	−	PROPN
ejpam-340	265	2	dx	dx	PROPN
ejpam-340	265	3	y	y	PROPN
ejpam-340	265	4	+	+	CCONJ
ejpam-340	265	5	2[x	2[x	NUM
ejpam-340	265	6	,	,	PUNCT
ejpam-340	265	7	y	y	PROPN
ejpam-340	265	8	]	]	PUNCT
ejpam-340	265	9	)	)	PUNCT
ejpam-340	266	1	+	+	CCONJ
ejpam-340	266	2	c	c	PROPN
ejpam-340	266	3	ui(dy	ui(dy	PROPN
ejpam-340	266	4	x	x	PUNCT
ejpam-340	267	1	−	−	PROPN
ejpam-340	267	2	dx	dx	PROPN
ejpam-340	267	3	y	y	PROPN
ejpam-340	267	4	+	+	CCONJ
ejpam-340	267	5	2[x	2[x	NUM
ejpam-340	267	6	,	,	PUNCT
ejpam-340	267	7	y	y	PROPN
ejpam-340	267	8	]	]	PUNCT
ejpam-340	267	9	)	)	PUNCT
ejpam-340	267	10	ui	ui	PROPN
ejpam-340	268	1	−	−	PROPN
ejpam-340	268	2	b2(dy	b2(dy	PROPN
ejpam-340	268	3	x	x	PUNCT
ejpam-340	269	1	−	−	PROPN
ejpam-340	269	2	dx	dx	PROPN
ejpam-340	269	3	y	y	PROPN
ejpam-340	269	4	)	)	PUNCT
ejpam-340	270	1	−	−	PROPN
ejpam-340	270	2	c	c	PROPN
ejpam-340	270	3	ui(dy	ui(dy	PROPN
ejpam-340	270	4	x	x	PROPN
ejpam-340	271	1	−	−	PROPN
ejpam-340	271	2	dx	dx	PROPN
ejpam-340	271	3	y	y	PROPN
ejpam-340	271	4	)	)	PUNCT
ejpam-340	271	5	ui	ui	NOUN
ejpam-340	272	1	−	−	PROPN
ejpam-340	273	1	[	[	X
ejpam-340	273	2	x	x	X
ejpam-340	273	3	,	,	PUNCT
ejpam-340	273	4	y	y	PROPN
ejpam-340	273	5	]	]	PUNCT
ejpam-340	274	1	+	+	CCONJ
ejpam-340	274	2	[	[	X
ejpam-340	274	3	y	y	X
ejpam-340	274	4	,	,	PUNCT
ejpam-340	274	5	x	x	X
ejpam-340	274	6	]	]	X
ejpam-340	274	7	−	−	X
ejpam-340	274	8	dy	dy	NOUN
ejpam-340	274	9	x	x	PUNCT
ejpam-340	275	1	+	+	NUM
ejpam-340	275	2	dx	dx	PROPN
ejpam-340	275	3	y	y	PROPN
ejpam-340	275	4	−	−	PROPN
ejpam-340	276	1	[	[	X
ejpam-340	276	2	x	x	X
ejpam-340	276	3	,	,	PUNCT
ejpam-340	276	4	y	y	PROPN
ejpam-340	276	5	]	]	PUNCT
ejpam-340	277	1	+	+	CCONJ
ejpam-340	277	2	[	[	X
ejpam-340	277	3	y	y	INTJ
ejpam-340	277	4	,	,	PUNCT
ejpam-340	277	5	x	x	X
ejpam-340	277	6	]	]	X
ejpam-340	277	7	=	=	SYM
ejpam-340	277	8	2	2	NUM
ejpam-340	277	9	(	(	PUNCT
ejpam-340	277	10	[	[	PUNCT
ejpam-340	277	11	x	x	X
ejpam-340	277	12	,	,	PUNCT
ejpam-340	277	13	y	y	PROPN
ejpam-340	277	14	]	]	PUNCT
ejpam-340	278	1	+	+	CCONJ
ejpam-340	278	2	b2[x	b2[x	NOUN
ejpam-340	278	3	,	,	PUNCT
ejpam-340	278	4	y	y	PROPN
ejpam-340	278	5	]	]	PUNCT
ejpam-340	279	1	+	+	CCONJ
ejpam-340	279	2	c	c	X
ejpam-340	279	3	ui([x	ui([x	PROPN
ejpam-340	279	4	,	,	PUNCT
ejpam-340	279	5	y	y	PROPN
ejpam-340	279	6	]	]	PUNCT
ejpam-340	279	7	)	)	PUNCT
ejpam-340	279	8	ui	ui	NOUN
ejpam-340	280	1	−	−	PROPN
ejpam-340	281	1	[	[	X
ejpam-340	281	2	x	x	X
ejpam-340	281	3	,	,	PUNCT
ejpam-340	281	4	y	y	PROPN
ejpam-340	281	5	]	]	PUNCT
ejpam-340	281	6	−	−	X
ejpam-340	282	1	[	[	X
ejpam-340	282	2	x	x	X
ejpam-340	282	3	,	,	PUNCT
ejpam-340	282	4	y	y	PROPN
ejpam-340	282	5	]	]	PUNCT
ejpam-340	282	6	)	)	PUNCT
ejpam-340	282	7	which	which	PRON
ejpam-340	282	8	on	on	ADP
ejpam-340	282	9	use	use	NOUN
ejpam-340	282	10	of	of	ADP
ejpam-340	282	11	(	(	PUNCT
ejpam-340	282	12	1	1	NUM
ejpam-340	282	13	)	)	PUNCT
ejpam-340	282	14	and	and	CCONJ
ejpam-340	282	15	(	(	PUNCT
ejpam-340	282	16	14	14	NUM
ejpam-340	282	17	)	)	PUNCT
ejpam-340	282	18	yields	yield	NOUN
ejpam-340	282	19	(	(	PUNCT
ejpam-340	282	20	50	50	NUM
ejpam-340	282	21	)	)	PUNCT
ejpam-340	282	22	.	.	PUNCT
ejpam-340	283	1	corollary	corollary	ADJ
ejpam-340	283	2	3	3	X
ejpam-340	283	3	.	.	PUNCT
ejpam-340	284	1	in	in	ADP
ejpam-340	284	2	vn	vn	PROPN
ejpam-340	284	3	,	,	PUNCT
ejpam-340	284	4	we	we	PRON
ejpam-340	284	5	have	have	VERB
ejpam-340	284	6	◦	◦	NOUN
ejpam-340	284	7	n	n	PROPN
ejpam-340	284	8	(	(	PUNCT
ejpam-340	284	9	x	x	X
ejpam-340	284	10	,	,	PUNCT
ejpam-340	284	11	ui	ui	PROPN
ejpam-340	284	12	)	)	PUNCT
ejpam-340	284	13	=	=	SYM
ejpam-340	284	14	2	2	NUM
ejpam-340	284	15	pi	pi	NOUN
ejpam-340	284	16	j	j	PROPN
ejpam-340	284	17	(	(	PUNCT
ejpam-340	284	18	[	[	PUNCT
ejpam-340	284	19	x	x	X
ejpam-340	284	20	,	,	PUNCT
ejpam-340	284	21	u	u	NOUN
ejpam-340	284	22	j	j	X
ejpam-340	284	23	]	]	X
ejpam-340	284	24	−	−	X
ejpam-340	285	1	[	[	X
ejpam-340	285	2	x	x	X
ejpam-340	285	3	,	,	PUNCT
ejpam-340	285	4	u	u	PROPN
ejpam-340	285	5	j	j	NOUN
ejpam-340	285	6	]	]	X
ejpam-340	285	7	)	)	PUNCT
ejpam-340	286	1	+	+	CCONJ
ejpam-340	286	2	2([x	2([x	NUM
ejpam-340	286	3	,	,	PUNCT
ejpam-340	286	4	ui]−	ui]−	PROPN
ejpam-340	286	5	[	[	X
ejpam-340	286	6	x	x	X
ejpam-340	286	7	,	,	PUNCT
ejpam-340	286	8	ui	ui	NOUN
ejpam-340	286	9	]	]	X
ejpam-340	286	10	)	)	PUNCT
ejpam-340	286	11	(	(	PUNCT
ejpam-340	286	12	51	51	NUM
ejpam-340	286	13	)	)	PUNCT
ejpam-340	286	14	let	let	VERB
ejpam-340	286	15	us	we	PRON
ejpam-340	286	16	define	define	VERB
ejpam-340	286	17	◦	◦	NOUN
ejpam-340	286	18	µ	µ	NOUN
ejpam-340	286	19	,	,	PUNCT
ejpam-340	286	20	◦	◦	NOUN
ejpam-340	286	21	ν	ν	NOUN
ejpam-340	286	22	,	,	PUNCT
ejpam-340	286	23	◦	◦	NOUN
ejpam-340	286	24	σ	σ	NOUN
ejpam-340	286	25	analogues	analogue	NOUN
ejpam-340	286	26	to	to	ADP
ejpam-340	286	27	µ	µ	NUM
ejpam-340	286	28	,	,	PUNCT
ejpam-340	286	29	ν	ν	NOUN
ejpam-340	286	30	,	,	PUNCT
ejpam-340	286	31	σ	σ	PROPN
ejpam-340	286	32	for	for	ADP
ejpam-340	286	33	connexion	connexion	PROPN
ejpam-340	286	34	e.	e.	PROPN
ejpam-340	286	35	◦	◦	PROPN
ejpam-340	286	36	µ	µ	X
ejpam-340	286	37	(	(	PUNCT
ejpam-340	286	38	x	x	INTJ
ejpam-340	286	39	,	,	PUNCT
ejpam-340	286	40	y	y	PROPN
ejpam-340	286	41	)	)	PUNCT
ejpam-340	286	42	de	de	PROPN
ejpam-340	286	43	f	f	PROPN
ejpam-340	286	44	=	=	PUNCT
ejpam-340	286	45	(	(	PUNCT
ejpam-340	286	46	ey	ey	INTJ
ejpam-340	286	47	ui)(x	ui)(x	PROPN
ejpam-340	286	48	)	)	PUNCT
ejpam-340	286	49	−	−	PROPN
ejpam-340	287	1	(	(	PUNCT
ejpam-340	287	2	ex	ex	X
ejpam-340	287	3	ui)(y	ui)(y	PROPN
ejpam-340	287	4	)	)	PUNCT
ejpam-340	288	1	+	+	CCONJ
ejpam-340	288	2	(	(	PUNCT
ejpam-340	288	3	ey	ey	INTJ
ejpam-340	288	4	ui)(x	ui)(x	PROPN
ejpam-340	288	5	)	)	PUNCT
ejpam-340	288	6	−	−	PROPN
ejpam-340	289	1	(	(	PUNCT
ejpam-340	289	2	ex	ex	X
ejpam-340	289	3	ui)(y	ui)(y	PROPN
ejpam-340	289	4	)	)	PUNCT
ejpam-340	289	5	(	(	PUNCT
ejpam-340	289	6	52	52	X
ejpam-340	289	7	)	)	PUNCT
ejpam-340	289	8	◦	◦	NOUN
ejpam-340	289	9	ν	ν	X
ejpam-340	289	10	(	(	PUNCT
ejpam-340	289	11	x	x	SYM
ejpam-340	289	12	)	)	PUNCT
ejpam-340	289	13	de	de	PROPN
ejpam-340	289	14	f	f	PROPN
ejpam-340	289	15	=	=	PUNCT
ejpam-340	289	16	(	(	PUNCT
ejpam-340	289	17	eui	eui	PROPN
ejpam-340	289	18	f(x	f(x	PROPN
ejpam-340	289	19	)	)	PUNCT
ejpam-340	289	20	−	−	PROPN
ejpam-340	290	1	(	(	PUNCT
ejpam-340	290	2	ex	ex	X
ejpam-340	290	3	f)(ui)−	f)(ui)−	VERB
ejpam-340	290	4	ex	ex	X
ejpam-340	290	5	ui	ui	PROPN
ejpam-340	290	6	(	(	PUNCT
ejpam-340	290	7	53	53	NUM
ejpam-340	290	8	)	)	PUNCT
ejpam-340	290	9	◦	◦	NOUN
ejpam-340	290	10	σ	σ	X
ejpam-340	290	11	(	(	PUNCT
ejpam-340	290	12	x	x	SYM
ejpam-340	290	13	)	)	PUNCT
ejpam-340	290	14	de	de	PROPN
ejpam-340	290	15	f	f	PROPN
ejpam-340	290	16	=	=	PUNCT
ejpam-340	290	17	(	(	PUNCT
ejpam-340	290	18	ex	ex	X
ejpam-340	290	19	u	u	NOUN
ejpam-340	290	20	j)(ui)−	j)(ui)−	PROPN
ejpam-340	290	21	(	(	PUNCT
ejpam-340	290	22	eui	eui	NOUN
ejpam-340	290	23	u	u	NOUN
ejpam-340	290	24	j)(x	j)(x	PROPN
ejpam-340	290	25	)	)	PUNCT
ejpam-340	290	26	(	(	PUNCT
ejpam-340	290	27	54	54	NUM
ejpam-340	290	28	)	)	PUNCT
ejpam-340	290	29	theorem	theorem	NOUN
ejpam-340	290	30	12	12	NUM
ejpam-340	290	31	.	.	PUNCT
ejpam-340	291	1	in	in	ADP
ejpam-340	291	2	vn	vn	PROPN
ejpam-340	291	3	,	,	PUNCT
ejpam-340	291	4	we	we	PRON
ejpam-340	291	5	have	have	VERB
ejpam-340	291	6	c	c	NOUN
ejpam-340	291	7	◦	◦	NOUN
ejpam-340	291	8	µ	µ	X
ejpam-340	291	9	(	(	PUNCT
ejpam-340	291	10	x	x	INTJ
ejpam-340	291	11	,	,	PUNCT
ejpam-340	291	12	y	y	PROPN
ejpam-340	291	13	)	)	PUNCT
ejpam-340	291	14	ui	ui	PROPN
ejpam-340	292	1	=	=	PROPN
ejpam-340	292	2	2c{ui([x	2c{ui([x	NUM
ejpam-340	292	3	,	,	PUNCT
ejpam-340	292	4	y	y	PROPN
ejpam-340	292	5	]	]	PUNCT
ejpam-340	292	6	)	)	PUNCT
ejpam-340	293	1	+	+	CCONJ
ejpam-340	294	1	ui([x	ui([x	ADJ
ejpam-340	294	2	,	,	PUNCT
ejpam-340	294	3	y	y	PROPN
ejpam-340	294	4	]	]	X
ejpam-340	294	5	)	)	PUNCT
ejpam-340	294	6	}	}	PUNCT
ejpam-340	294	7	(	(	PUNCT
ejpam-340	294	8	55a	55a	NOUN
ejpam-340	294	9	)	)	PUNCT
ejpam-340	294	10	◦	◦	NOUN
ejpam-340	294	11	ν	ν	X
ejpam-340	294	12	(	(	PUNCT
ejpam-340	294	13	x	x	X
ejpam-340	294	14	)	)	PUNCT
ejpam-340	294	15	=	=	PUNCT
ejpam-340	294	16	{	{	PUNCT
ejpam-340	294	17	[	[	X
ejpam-340	294	18	x	x	X
ejpam-340	294	19	,	,	PUNCT
ejpam-340	294	20	ui	ui	PROPN
ejpam-340	294	21	]	]	X
ejpam-340	295	1	+	+	CCONJ
ejpam-340	295	2	2[x	2[x	NUM
ejpam-340	295	3	,	,	PUNCT
ejpam-340	295	4	ui]−	ui]−	PROPN
ejpam-340	296	1	[	[	X
ejpam-340	296	2	x	x	X
ejpam-340	296	3	,	,	PUNCT
ejpam-340	296	4	ui	ui	NOUN
ejpam-340	296	5	]	]	PUNCT
ejpam-340	297	1	+	+	CCONJ
ejpam-340	297	2	eui	eui	NOUN
ejpam-340	297	3	x	x	X
ejpam-340	298	1	+	+	CCONJ
ejpam-340	298	2	dui	dui	PROPN
ejpam-340	298	3	x	x	SYM
ejpam-340	298	4	}	}	PUNCT
ejpam-340	298	5	(	(	PUNCT
ejpam-340	298	6	55b	55b	NUM
ejpam-340	298	7	)	)	PUNCT
ejpam-340	298	8	c	c	NOUN
ejpam-340	298	9	◦	◦	NOUN
ejpam-340	298	10	σ	σ	X
ejpam-340	298	11	(	(	PUNCT
ejpam-340	298	12	x	x	X
ejpam-340	298	13	)	)	PUNCT
ejpam-340	298	14	=	=	SYM
ejpam-340	299	1	2c{u	2c{u	NUM
ejpam-340	299	2	j([ui	j([ui	X
ejpam-340	299	3	,	,	PUNCT
ejpam-340	299	4	x	x	X
ejpam-340	299	5	]	]	X
ejpam-340	299	6	)	)	PUNCT
ejpam-340	299	7	}	}	PUNCT
ejpam-340	299	8	(	(	PUNCT
ejpam-340	299	9	55c	55c	NOUN
ejpam-340	299	10	)	)	PUNCT
ejpam-340	299	11	proof	proof	NOUN
ejpam-340	299	12	.	.	PUNCT
ejpam-340	300	1	on	on	ADP
ejpam-340	300	2	account	account	NOUN
ejpam-340	300	3	of	of	ADP
ejpam-340	300	4	(	(	PUNCT
ejpam-340	300	5	45	45	NUM
ejpam-340	300	6	)	)	PUNCT
ejpam-340	300	7	and	and	CCONJ
ejpam-340	300	8	(	(	PUNCT
ejpam-340	300	9	52	52	NUM
ejpam-340	300	10	)	)	PUNCT
ejpam-340	300	11	,	,	PUNCT
ejpam-340	300	12	we	we	PRON
ejpam-340	300	13	get(55a	get(55a	NOUN
ejpam-340	300	14	)	)	PUNCT
ejpam-340	300	15	.	.	PUNCT
ejpam-340	301	1	due	due	ADP
ejpam-340	301	2	to	to	ADP
ejpam-340	301	3	(	(	PUNCT
ejpam-340	301	4	42b	42b	NOUN
ejpam-340	301	5	)	)	PUNCT
ejpam-340	301	6	and	and	CCONJ
ejpam-340	301	7	(	(	PUNCT
ejpam-340	301	8	43b	43b	NUM
ejpam-340	301	9	)	)	PUNCT
ejpam-340	301	10	,	,	PUNCT
ejpam-340	301	11	we	we	PRON
ejpam-340	301	12	obtain	obtain	VERB
ejpam-340	301	13	(	(	PUNCT
ejpam-340	301	14	55b	55b	NUM
ejpam-340	301	15	)	)	PUNCT
ejpam-340	301	16	.	.	PUNCT
ejpam-340	302	1	finally	finally	ADV
ejpam-340	302	2	,	,	PUNCT
ejpam-340	302	3	(	(	PUNCT
ejpam-340	302	4	55c	55c	NOUN
ejpam-340	302	5	)	)	PUNCT
ejpam-340	302	6	is	be	AUX
ejpam-340	302	7	obtained	obtain	VERB
ejpam-340	302	8	by	by	ADP
ejpam-340	302	9	using	use	VERB
ejpam-340	302	10	(	(	PUNCT
ejpam-340	302	11	45	45	NUM
ejpam-340	302	12	)	)	PUNCT
ejpam-340	302	13	in	in	ADP
ejpam-340	302	14	(	(	PUNCT
ejpam-340	302	15	54	54	NUM
ejpam-340	302	16	)	)	PUNCT
ejpam-340	302	17	.	.	PUNCT
ejpam-340	303	1	corollary	corollary	ADJ
ejpam-340	303	2	4	4	NUM
ejpam-340	303	3	.	.	PUNCT
ejpam-340	304	1	◦	◦	NOUN
ejpam-340	304	2	µ	µ	X
ejpam-340	304	3	(	(	PUNCT
ejpam-340	304	4	x	x	INTJ
ejpam-340	304	5	,	,	PUNCT
ejpam-340	304	6	y	y	PROPN
ejpam-340	304	7	)	)	PUNCT
ejpam-340	304	8	is	be	AUX
ejpam-340	304	9	skew	skew	ADJ
ejpam-340	304	10	-	-	PUNCT
ejpam-340	304	11	symmetric	symmetric	ADJ
ejpam-340	304	12	in	in	ADP
ejpam-340	304	13	both	both	CCONJ
ejpam-340	304	14	the	the	DET
ejpam-340	304	15	slots	slot	NOUN
ejpam-340	304	16	x	x	PUNCT
ejpam-340	304	17	and	and	CCONJ
ejpam-340	304	18	y	y	PROPN
ejpam-340	304	19	,	,	PUNCT
ejpam-340	304	20	i.e.	i.e.	X
ejpam-340	304	21	◦	◦	NOUN
ejpam-340	304	22	µ	µ	X
ejpam-340	304	23	(	(	PUNCT
ejpam-340	304	24	x	x	INTJ
ejpam-340	304	25	,	,	PUNCT
ejpam-340	304	26	y	y	PROPN
ejpam-340	304	27	)	)	PUNCT
ejpam-340	305	1	+	+	PUNCT
ejpam-340	305	2	◦	◦	NOUN
ejpam-340	305	3	µ	µ	X
ejpam-340	305	4	(	(	PUNCT
ejpam-340	305	5	y	y	PROPN
ejpam-340	305	6	,	,	PUNCT
ejpam-340	305	7	x	x	X
ejpam-340	305	8	)	)	PUNCT
ejpam-340	306	1	=	=	SYM
ejpam-340	306	2	0	0	PUNCT
ejpam-340	306	3	(	(	PUNCT
ejpam-340	306	4	56	56	NUM
ejpam-340	306	5	)	)	PUNCT
ejpam-340	306	6	let	let	VERB
ejpam-340	306	7	us	we	PRON
ejpam-340	306	8	define	define	VERB
ejpam-340	306	9	a	a	DET
ejpam-340	306	10	vector	vector	NOUN
ejpam-340	306	11	valued	value	VERB
ejpam-340	306	12	,	,	PUNCT
ejpam-340	306	13	bilinear	bilinear	NOUN
ejpam-340	306	14	function	function	NOUN
ejpam-340	306	15	◦	◦	NOUN
ejpam-340	306	16	m	m	VERB
ejpam-340	306	17	by	by	ADP
ejpam-340	306	18	◦	◦	NOUN
ejpam-340	306	19	m	m	VERB
ejpam-340	306	20	(	(	PUNCT
ejpam-340	306	21	x	x	X
ejpam-340	306	22	,	,	PUNCT
ejpam-340	306	23	y	y	PROPN
ejpam-340	306	24	)	)	PUNCT
ejpam-340	306	25	de	de	PROPN
ejpam-340	306	26	f	f	X
ejpam-340	306	27	=	=	PUNCT
ejpam-340	306	28	ex	ex	ADJ
ejpam-340	306	29	y	y	PROPN
ejpam-340	306	30	+	+	CCONJ
ejpam-340	306	31	ex	ex	VERB
ejpam-340	306	32	y	y	NOUN
ejpam-340	306	33	−	−	X
ejpam-340	306	34	ex	ex	INTJ
ejpam-340	306	35	y	y	PROPN
ejpam-340	306	36	−	−	X
ejpam-340	306	37	ex	ex	X
ejpam-340	306	38	y	y	PROPN
ejpam-340	306	39	(	(	PUNCT
ejpam-340	306	40	57	57	NUM
ejpam-340	306	41	)	)	PUNCT
ejpam-340	306	42	r.	r.	PROPN
ejpam-340	306	43	singh	singh	PROPN
ejpam-340	306	44	and	and	CCONJ
ejpam-340	306	45	s.	s.	PROPN
ejpam-340	306	46	singh	singh	PROPN
ejpam-340	306	47	/	/	SYM
ejpam-340	306	48	eur	eur	PROPN
ejpam-340	306	49	.	.	PUNCT
ejpam-340	307	1	j.	j.	PROPN
ejpam-340	307	2	pure	pure	PROPN
ejpam-340	307	3	appl	appl	PROPN
ejpam-340	307	4	.	.	PROPN
ejpam-340	307	5	math	math	PROPN
ejpam-340	307	6	,	,	PUNCT
ejpam-340	307	7	3	3	NUM
ejpam-340	307	8	(	(	PUNCT
ejpam-340	307	9	2010	2010	NUM
ejpam-340	307	10	)	)	PUNCT
ejpam-340	307	11	,	,	PUNCT
ejpam-340	307	12	839	839	NUM
ejpam-340	307	13	-	-	SYM
ejpam-340	307	14	852	852	NUM
ejpam-340	307	15	848	848	NUM
ejpam-340	307	16	theorem	theorem	NOUN
ejpam-340	307	17	13	13	NUM
ejpam-340	307	18	.	.	PUNCT
ejpam-340	308	1	in	in	ADP
ejpam-340	308	2	vn	vn	PROPN
ejpam-340	308	3	,	,	PUNCT
ejpam-340	308	4	we	we	PRON
ejpam-340	308	5	have	have	VERB
ejpam-340	308	6	◦	◦	NOUN
ejpam-340	308	7	m	m	VERB
ejpam-340	308	8	(	(	PUNCT
ejpam-340	308	9	x	x	INTJ
ejpam-340	308	10	,	,	PUNCT
ejpam-340	308	11	y	y	PROPN
ejpam-340	308	12	)	)	PUNCT
ejpam-340	308	13	−	−	PROPN
ejpam-340	309	1	[	[	PUNCT
ejpam-340	309	2	x	x	X
ejpam-340	309	3	,	,	PUNCT
ejpam-340	309	4	y	y	PROPN
ejpam-340	309	5	]	]	PUNCT
ejpam-340	309	6	−	−	X
ejpam-340	310	1	[	[	X
ejpam-340	310	2	x	x	X
ejpam-340	310	3	,	,	PUNCT
ejpam-340	310	4	y	y	PROPN
ejpam-340	310	5	]	]	PUNCT
ejpam-340	311	1	+	+	CCONJ
ejpam-340	312	1	[	[	X
ejpam-340	312	2	x	x	X
ejpam-340	312	3	,	,	PUNCT
ejpam-340	312	4	y	y	PROPN
ejpam-340	312	5	]	]	PUNCT
ejpam-340	313	1	+	+	CCONJ
ejpam-340	314	1	[	[	X
ejpam-340	314	2	x	x	X
ejpam-340	314	3	,	,	PUNCT
ejpam-340	314	4	y	y	PROPN
ejpam-340	314	5	]	]	PUNCT
ejpam-340	315	1	=	=	SYM
ejpam-340	315	2	0	0	NUM
ejpam-340	315	3	(	(	PUNCT
ejpam-340	315	4	58a	58a	NOUN
ejpam-340	315	5	)	)	PUNCT
ejpam-340	315	6	◦	◦	NOUN
ejpam-340	315	7	m	m	VERB
ejpam-340	315	8	(	(	PUNCT
ejpam-340	315	9	x	x	X
ejpam-340	315	10	,	,	PUNCT
ejpam-340	315	11	y	y	PROPN
ejpam-340	315	12	)	)	PUNCT
ejpam-340	315	13	−n(x	−n(x	PROPN
ejpam-340	315	14	,	,	PUNCT
ejpam-340	315	15	y	y	PROPN
ejpam-340	315	16	)	)	PUNCT
ejpam-340	316	1	=	=	SYM
ejpam-340	316	2	0	0	NUM
ejpam-340	316	3	(	(	PUNCT
ejpam-340	316	4	58b	58b	NUM
ejpam-340	316	5	)	)	PUNCT
ejpam-340	316	6	proof	proof	NOUN
ejpam-340	316	7	.	.	PUNCT
ejpam-340	317	1	using	use	VERB
ejpam-340	317	2	(	(	PUNCT
ejpam-340	317	3	12	12	NUM
ejpam-340	317	4	)	)	PUNCT
ejpam-340	317	5	,	,	PUNCT
ejpam-340	317	6	(	(	PUNCT
ejpam-340	317	7	14	14	NUM
ejpam-340	317	8	)	)	PUNCT
ejpam-340	317	9	and	and	CCONJ
ejpam-340	317	10	(	(	PUNCT
ejpam-340	317	11	41	41	NUM
ejpam-340	317	12	)	)	PUNCT
ejpam-340	317	13	in	in	ADP
ejpam-340	317	14	(	(	PUNCT
ejpam-340	317	15	57	57	NUM
ejpam-340	317	16	)	)	PUNCT
ejpam-340	317	17	,	,	PUNCT
ejpam-340	317	18	we	we	PRON
ejpam-340	317	19	get	get	VERB
ejpam-340	317	20	(	(	PUNCT
ejpam-340	317	21	58a	58a	NOUN
ejpam-340	317	22	)	)	PUNCT
ejpam-340	317	23	and	and	CCONJ
ejpam-340	317	24	(	(	PUNCT
ejpam-340	317	25	58b	58b	NUM
ejpam-340	317	26	)	)	PUNCT
ejpam-340	317	27	.	.	PUNCT
ejpam-340	318	1	corollary	corollary	ADJ
ejpam-340	318	2	5	5	NUM
ejpam-340	318	3	.	.	PUNCT
ejpam-340	319	1	◦	◦	NOUN
ejpam-340	319	2	m	m	VERB
ejpam-340	319	3	(	(	PUNCT
ejpam-340	319	4	x	x	X
ejpam-340	319	5	,	,	PUNCT
ejpam-340	319	6	y	y	PROPN
ejpam-340	319	7	)	)	PUNCT
ejpam-340	319	8	is	be	AUX
ejpam-340	319	9	skew	skew	ADJ
ejpam-340	319	10	-	-	PUNCT
ejpam-340	319	11	symmetric	symmetric	ADJ
ejpam-340	319	12	in	in	ADP
ejpam-340	319	13	both	both	CCONJ
ejpam-340	319	14	the	the	DET
ejpam-340	319	15	slots	slot	NOUN
ejpam-340	319	16	x	x	PUNCT
ejpam-340	319	17	and	and	CCONJ
ejpam-340	319	18	y	y	PROPN
ejpam-340	319	19	,	,	PUNCT
ejpam-340	319	20	i.e.	i.e.	X
ejpam-340	319	21	◦	◦	NOUN
ejpam-340	319	22	m	m	VERB
ejpam-340	319	23	(	(	PUNCT
ejpam-340	319	24	x	x	INTJ
ejpam-340	319	25	,	,	PUNCT
ejpam-340	319	26	y	y	PROPN
ejpam-340	319	27	)	)	PUNCT
ejpam-340	320	1	+	+	PUNCT
ejpam-340	320	2	◦	◦	NOUN
ejpam-340	320	3	m	m	VERB
ejpam-340	320	4	(	(	PUNCT
ejpam-340	320	5	y	y	NOUN
ejpam-340	320	6	,	,	PUNCT
ejpam-340	320	7	x	x	X
ejpam-340	320	8	)	)	PUNCT
ejpam-340	321	1	=	=	SYM
ejpam-340	321	2	0	0	NUM
ejpam-340	321	3	(	(	PUNCT
ejpam-340	321	4	59	59	NUM
ejpam-340	321	5	)	)	PUNCT
ejpam-340	321	6	corollary	corollary	NOUN
ejpam-340	321	7	6	6	NUM
ejpam-340	321	8	.	.	PUNCT
ejpam-340	322	1	in	in	ADP
ejpam-340	322	2	,	,	PUNCT
ejpam-340	322	3	vn	vn	INTJ
ejpam-340	322	4	,	,	PUNCT
ejpam-340	322	5	we	we	PRON
ejpam-340	322	6	have	have	VERB
ejpam-340	322	7	◦	◦	NOUN
ejpam-340	322	8	m	m	VERB
ejpam-340	322	9	(	(	PUNCT
ejpam-340	322	10	x	x	NOUN
ejpam-340	322	11	,	,	PUNCT
ejpam-340	322	12	ui	ui	PROPN
ejpam-340	322	13	)	)	PUNCT
ejpam-340	322	14	=	=	PUNCT
ejpam-340	323	1	[	[	X
ejpam-340	323	2	x	x	X
ejpam-340	323	3	,	,	PUNCT
ejpam-340	323	4	ui]−	ui]−	PROPN
ejpam-340	323	5	[	[	X
ejpam-340	323	6	x	x	X
ejpam-340	323	7	,	,	PUNCT
ejpam-340	323	8	ui	ui	PROPN
ejpam-340	323	9	]	]	X
ejpam-340	323	10	+	+	CCONJ
ejpam-340	323	11	pi	pi	NOUN
ejpam-340	323	12	j{[x	j{[x	PROPN
ejpam-340	323	13	,	,	PUNCT
ejpam-340	323	14	u	u	NOUN
ejpam-340	323	15	j]−	j]−	NOUN
ejpam-340	324	1	[	[	X
ejpam-340	324	2	x	x	X
ejpam-340	324	3	,	,	PUNCT
ejpam-340	324	4	u	u	PROPN
ejpam-340	324	5	j	j	PROPN
ejpam-340	324	6	]	]	X
ejpam-340	324	7	}	}	PUNCT
ejpam-340	324	8	(	(	PUNCT
ejpam-340	324	9	60	60	NUM
ejpam-340	324	10	)	)	PUNCT
ejpam-340	324	11	it	it	PRON
ejpam-340	324	12	can	can	AUX
ejpam-340	324	13	be	be	AUX
ejpam-340	324	14	obtained	obtain	VERB
ejpam-340	324	15	that	that	SCONJ
ejpam-340	324	16	,	,	PUNCT
ejpam-340	324	17	k(x	k(x	PROPN
ejpam-340	324	18	,	,	PUNCT
ejpam-340	324	19	y	y	PROPN
ejpam-340	324	20	,	,	PUNCT
ejpam-340	324	21	ui	ui	PROPN
ejpam-340	324	22	)	)	PUNCT
ejpam-340	324	23	=	=	SYM
ejpam-340	324	24	0	0	NUM
ejpam-340	324	25	(	(	PUNCT
ejpam-340	324	26	61a	61a	NOUN
ejpam-340	324	27	)	)	PUNCT
ejpam-340	324	28	k(x	k(x	PROPN
ejpam-340	324	29	,	,	PUNCT
ejpam-340	324	30	y	y	PROPN
ejpam-340	324	31	,	,	PUNCT
ejpam-340	324	32	z	z	NOUN
ejpam-340	324	33	)	)	PUNCT
ejpam-340	324	34	=	=	SYM
ejpam-340	324	35	k(x	k(x	PROPN
ejpam-340	324	36	,	,	PUNCT
ejpam-340	324	37	y	y	PROPN
ejpam-340	324	38	,	,	PUNCT
ejpam-340	324	39	z	z	NOUN
ejpam-340	324	40	)	)	PUNCT
ejpam-340	324	41	(	(	PUNCT
ejpam-340	324	42	61b	61b	NOUN
ejpam-340	324	43	)	)	PUNCT
ejpam-340	324	44	where	where	SCONJ
ejpam-340	324	45	k	k	PROPN
ejpam-340	324	46	is	be	AUX
ejpam-340	324	47	the	the	DET
ejpam-340	324	48	curvature	curvature	NOUN
ejpam-340	324	49	tensor	tensor	NOUN
ejpam-340	324	50	of	of	ADP
ejpam-340	324	51	(	(	PUNCT
ejpam-340	324	52	f	f	X
ejpam-340	324	53	,	,	PUNCT
ejpam-340	324	54	ui	ui	PROPN
ejpam-340	324	55	,	,	PUNCT
ejpam-340	324	56	u	u	NOUN
ejpam-340	324	57	i)-connexion	i)-connexion	NOUN
ejpam-340	324	58	.	.	PUNCT
ejpam-340	325	1	let	let	VERB
ejpam-340	325	2	us	we	PRON
ejpam-340	325	3	define	define	VERB
ejpam-340	325	4	a	a	DET
ejpam-340	325	5	curvature	curvature	NOUN
ejpam-340	325	6	tensor	tensor	NOUN
ejpam-340	325	7	◦	◦	NOUN
ejpam-340	325	8	k	k	NOUN
ejpam-340	325	9	with	with	ADP
ejpam-340	325	10	respect	respect	NOUN
ejpam-340	325	11	to	to	ADP
ejpam-340	325	12	connexion	connexion	NOUN
ejpam-340	325	13	e	e	NOUN
ejpam-340	325	14	,	,	PUNCT
ejpam-340	325	15	by	by	ADP
ejpam-340	325	16	◦	◦	NOUN
ejpam-340	325	17	k	k	X
ejpam-340	325	18	(	(	PUNCT
ejpam-340	325	19	x	x	INTJ
ejpam-340	325	20	,	,	PUNCT
ejpam-340	325	21	y	y	PROPN
ejpam-340	325	22	,	,	PUNCT
ejpam-340	325	23	z	z	NOUN
ejpam-340	325	24	)	)	PUNCT
ejpam-340	325	25	de	de	PROPN
ejpam-340	325	26	f	f	X
ejpam-340	325	27	=	=	X
ejpam-340	325	28	ex	ex	X
ejpam-340	325	29	ey	ey	PROPN
ejpam-340	325	30	z	z	NOUN
ejpam-340	325	31	−	−	PROPN
ejpam-340	325	32	ey	ey	INTJ
ejpam-340	325	33	ex	ex	ADJ
ejpam-340	325	34	z	z	NOUN
ejpam-340	325	35	−	−	NOUN
ejpam-340	325	36	e[x	e[x	NOUN
ejpam-340	325	37	,	,	PUNCT
ejpam-340	325	38	y]z	y]z	NOUN
ejpam-340	325	39	(	(	PUNCT
ejpam-340	325	40	62	62	NUM
ejpam-340	325	41	)	)	PUNCT
ejpam-340	325	42	theorem	theorem	VERB
ejpam-340	325	43	14	14	NUM
ejpam-340	325	44	.	.	PUNCT
ejpam-340	326	1	in	in	ADP
ejpam-340	326	2	,	,	PUNCT
ejpam-340	326	3	vn	vn	INTJ
ejpam-340	326	4	,	,	PUNCT
ejpam-340	326	5	we	we	PRON
ejpam-340	326	6	have	have	VERB
ejpam-340	326	7	◦	◦	NOUN
ejpam-340	327	1	k	k	X
ejpam-340	327	2	(	(	PUNCT
ejpam-340	327	3	x	x	INTJ
ejpam-340	327	4	,	,	PUNCT
ejpam-340	327	5	y	y	PROPN
ejpam-340	327	6	,	,	PUNCT
ejpam-340	327	7	z	z	NOUN
ejpam-340	327	8	)	)	PUNCT
ejpam-340	327	9	=	=	SYM
ejpam-340	327	10	k(x	k(x	PROPN
ejpam-340	327	11	,	,	PUNCT
ejpam-340	327	12	y	y	PROPN
ejpam-340	327	13	,	,	PUNCT
ejpam-340	327	14	z	z	NOUN
ejpam-340	327	15	)	)	PUNCT
ejpam-340	328	1	+	+	CCONJ
ejpam-340	328	2	2d[x	2d[x	NUM
ejpam-340	328	3	,	,	PUNCT
ejpam-340	328	4	y]z	y]z	NOUN
ejpam-340	328	5	−	−	PUNCT
ejpam-340	329	1	[	[	X
ejpam-340	329	2	x	x	X
ejpam-340	329	3	,	,	PUNCT
ejpam-340	329	4	dy	dy	NOUN
ejpam-340	329	5	z	z	X
ejpam-340	329	6	]	]	X
ejpam-340	330	1	+	+	CCONJ
ejpam-340	330	2	[	[	X
ejpam-340	330	3	y	y	PROPN
ejpam-340	330	4	,	,	PUNCT
ejpam-340	330	5	dx	dx	PROPN
ejpam-340	330	6	z]−	z]−	PROPN
ejpam-340	330	7	dx	dx	PROPN
ejpam-340	330	8	(	(	PUNCT
ejpam-340	330	9	[	[	X
ejpam-340	330	10	y	y	PROPN
ejpam-340	330	11	,	,	PUNCT
ejpam-340	330	12	z	z	NOUN
ejpam-340	330	13	]	]	X
ejpam-340	330	14	)	)	PUNCT
ejpam-340	331	1	+	+	CCONJ
ejpam-340	331	2	dy	dy	NOUN
ejpam-340	331	3	(	(	PUNCT
ejpam-340	331	4	[	[	X
ejpam-340	331	5	x	x	X
ejpam-340	331	6	,	,	PUNCT
ejpam-340	331	7	z	z	NOUN
ejpam-340	331	8	]	]	X
ejpam-340	331	9	)	)	PUNCT
ejpam-340	331	10	(	(	PUNCT
ejpam-340	331	11	63	63	NUM
ejpam-340	331	12	)	)	PUNCT
ejpam-340	331	13	proof	proof	NOUN
ejpam-340	331	14	.	.	PUNCT
ejpam-340	332	1	from	from	ADP
ejpam-340	332	2	(	(	PUNCT
ejpam-340	332	3	41	41	NUM
ejpam-340	332	4	)	)	PUNCT
ejpam-340	332	5	,	,	PUNCT
ejpam-340	332	6	we	we	PRON
ejpam-340	332	7	have	have	VERB
ejpam-340	332	8	ex	ex	PRON
ejpam-340	332	9	ey	ey	PRON
ejpam-340	332	10	z	z	NOUN
ejpam-340	332	11	=	=	SYM
ejpam-340	332	12	dx	dx	PROPN
ejpam-340	332	13	dy	dy	NOUN
ejpam-340	332	14	z	z	PROPN
ejpam-340	333	1	−	−	PROPN
ejpam-340	334	1	[	[	X
ejpam-340	334	2	x	x	X
ejpam-340	334	3	,	,	PUNCT
ejpam-340	334	4	dy	dy	NOUN
ejpam-340	334	5	z]−	z]−	PROPN
ejpam-340	334	6	dx	dx	PROPN
ejpam-340	335	1	(	(	PUNCT
ejpam-340	335	2	[	[	X
ejpam-340	335	3	y	y	NOUN
ejpam-340	335	4	,	,	PUNCT
ejpam-340	335	5	z])+	z])+	PUNCT
ejpam-340	335	6	[	[	X
ejpam-340	335	7	x	x	X
ejpam-340	335	8	,	,	PUNCT
ejpam-340	335	9	[	[	X
ejpam-340	335	10	y	y	X
ejpam-340	335	11	,	,	PUNCT
ejpam-340	335	12	z	z	X
ejpam-340	335	13	]	]	X
ejpam-340	335	14	]	]	X
ejpam-340	335	15	(	(	PUNCT
ejpam-340	335	16	64	64	NUM
ejpam-340	335	17	)	)	PUNCT
ejpam-340	335	18	−ey	−ey	PROPN
ejpam-340	336	1	ex	ex	PRON
ejpam-340	336	2	z	z	NOUN
ejpam-340	336	3	=	=	SYM
ejpam-340	336	4	−dy	−dy	PROPN
ejpam-340	336	5	dx	dx	PROPN
ejpam-340	336	6	z	z	PROPN
ejpam-340	337	1	+	+	PROPN
ejpam-340	338	1	[	[	X
ejpam-340	338	2	y	y	PROPN
ejpam-340	338	3	,	,	PUNCT
ejpam-340	338	4	dx	dx	PROPN
ejpam-340	338	5	z	z	X
ejpam-340	338	6	]	]	X
ejpam-340	338	7	+	+	X
ejpam-340	338	8	dy	dy	NOUN
ejpam-340	338	9	(	(	PUNCT
ejpam-340	338	10	[	[	X
ejpam-340	338	11	x	x	X
ejpam-340	338	12	,	,	PUNCT
ejpam-340	338	13	z])−	z])−	PROPN
ejpam-340	339	1	[	[	X
ejpam-340	339	2	y	y	X
ejpam-340	339	3	,	,	PUNCT
ejpam-340	339	4	[	[	X
ejpam-340	339	5	x	x	X
ejpam-340	339	6	,	,	PUNCT
ejpam-340	339	7	z	z	PROPN
ejpam-340	339	8	]	]	X
ejpam-340	339	9	]	]	X
ejpam-340	339	10	(	(	PUNCT
ejpam-340	339	11	65	65	NUM
ejpam-340	339	12	)	)	PUNCT
ejpam-340	339	13	−e[x	−e[x	NOUN
ejpam-340	339	14	,	,	PUNCT
ejpam-340	339	15	y]z	y]z	NOUN
ejpam-340	339	16	=	=	SYM
ejpam-340	339	17	−d[x	−d[x	X
ejpam-340	339	18	,	,	PUNCT
ejpam-340	339	19	y]z	y]z	NOUN
ejpam-340	339	20	−	−	NOUN
ejpam-340	340	1	[	[	X
ejpam-340	340	2	[	[	X
ejpam-340	340	3	x	x	X
ejpam-340	340	4	,	,	PUNCT
ejpam-340	340	5	y	y	PROPN
ejpam-340	340	6	]	]	X
ejpam-340	340	7	,	,	PUNCT
ejpam-340	340	8	z	z	X
ejpam-340	340	9	]	]	X
ejpam-340	340	10	(	(	PUNCT
ejpam-340	340	11	66	66	NUM
ejpam-340	340	12	)	)	PUNCT
ejpam-340	340	13	adding	add	VERB
ejpam-340	340	14	(	(	PUNCT
ejpam-340	340	15	64	64	NUM
ejpam-340	340	16	)	)	PUNCT
ejpam-340	340	17	,	,	PUNCT
ejpam-340	340	18	(	(	PUNCT
ejpam-340	340	19	65	65	NUM
ejpam-340	340	20	)	)	PUNCT
ejpam-340	340	21	and	and	CCONJ
ejpam-340	340	22	(	(	PUNCT
ejpam-340	340	23	66	66	NUM
ejpam-340	340	24	)	)	PUNCT
ejpam-340	340	25	and	and	CCONJ
ejpam-340	340	26	using	use	VERB
ejpam-340	340	27	(	(	PUNCT
ejpam-340	340	28	11	11	NUM
ejpam-340	340	29	)	)	PUNCT
ejpam-340	340	30	,	,	PUNCT
ejpam-340	340	31	jacobi	jacobi	PROPN
ejpam-340	340	32	identity	identity	NOUN
ejpam-340	340	33	(	(	PUNCT
ejpam-340	340	34	[	[	X
ejpam-340	340	35	x	x	X
ejpam-340	340	36	,	,	PUNCT
ejpam-340	340	37	[	[	X
ejpam-340	340	38	y	y	X
ejpam-340	340	39	,	,	PUNCT
ejpam-340	340	40	z	z	X
ejpam-340	340	41	]	]	X
ejpam-340	340	42	]	]	PUNCT
ejpam-340	341	1	+	+	CCONJ
ejpam-340	341	2	[	[	X
ejpam-340	341	3	y	y	X
ejpam-340	341	4	,	,	PUNCT
ejpam-340	341	5	[	[	X
ejpam-340	341	6	z	z	X
ejpam-340	341	7	,	,	PUNCT
ejpam-340	341	8	x	x	X
ejpam-340	341	9	]	]	X
ejpam-340	341	10	]	]	PUNCT
ejpam-340	342	1	+	+	CCONJ
ejpam-340	343	1	[	[	X
ejpam-340	343	2	z	z	X
ejpam-340	343	3	,	,	PUNCT
ejpam-340	343	4	[	[	X
ejpam-340	343	5	x	x	X
ejpam-340	343	6	,	,	PUNCT
ejpam-340	343	7	y	y	PROPN
ejpam-340	343	8	]	]	X
ejpam-340	343	9	]	]	X
ejpam-340	343	10	=	=	PUNCT
ejpam-340	343	11	0	0	NUM
ejpam-340	343	12	)	)	PUNCT
ejpam-340	343	13	and	and	CCONJ
ejpam-340	343	14	(	(	PUNCT
ejpam-340	343	15	62	62	NUM
ejpam-340	343	16	)	)	PUNCT
ejpam-340	343	17	,	,	PUNCT
ejpam-340	343	18	we	we	PRON
ejpam-340	343	19	get	get	VERB
ejpam-340	343	20	(	(	PUNCT
ejpam-340	343	21	63	63	NUM
ejpam-340	343	22	)	)	PUNCT
ejpam-340	343	23	.	.	PUNCT
ejpam-340	344	1	corollary	corollary	ADJ
ejpam-340	344	2	7	7	NUM
ejpam-340	344	3	.	.	PUNCT
ejpam-340	345	1	in	in	ADP
ejpam-340	345	2	,	,	PUNCT
ejpam-340	345	3	vn	vn	INTJ
ejpam-340	345	4	,	,	PUNCT
ejpam-340	345	5	we	we	PRON
ejpam-340	345	6	have	have	VERB
ejpam-340	345	7	◦	◦	NOUN
ejpam-340	345	8	k	k	X
ejpam-340	345	9	(	(	PUNCT
ejpam-340	345	10	x	x	INTJ
ejpam-340	345	11	,	,	PUNCT
ejpam-340	345	12	y	y	PROPN
ejpam-340	345	13	,	,	PUNCT
ejpam-340	345	14	ui	ui	NOUN
ejpam-340	345	15	)	)	PUNCT
ejpam-340	345	16	=	=	VERB
ejpam-340	346	1	dy	dy	NOUN
ejpam-340	346	2	(	(	PUNCT
ejpam-340	346	3	[	[	X
ejpam-340	346	4	x	x	X
ejpam-340	346	5	,	,	PUNCT
ejpam-340	346	6	ui])−	ui])−	VERB
ejpam-340	346	7	dx	dx	PROPN
ejpam-340	346	8	(	(	PUNCT
ejpam-340	346	9	[	[	X
ejpam-340	346	10	y	y	PROPN
ejpam-340	346	11	,	,	PUNCT
ejpam-340	346	12	ui	ui	NOUN
ejpam-340	346	13	]	]	X
ejpam-340	346	14	)	)	PUNCT
ejpam-340	346	15	(	(	PUNCT
ejpam-340	346	16	67a	67a	NUM
ejpam-340	346	17	)	)	PUNCT
ejpam-340	346	18	◦	◦	NOUN
ejpam-340	347	1	k	k	X
ejpam-340	347	2	(	(	PUNCT
ejpam-340	347	3	x	x	INTJ
ejpam-340	347	4	,	,	PUNCT
ejpam-340	347	5	ui	ui	PROPN
ejpam-340	347	6	,	,	PUNCT
ejpam-340	347	7	ui	ui	PROPN
ejpam-340	347	8	)	)	PUNCT
ejpam-340	347	9	=	=	SYM
ejpam-340	347	10	dui	dui	PROPN
ejpam-340	347	11	(	(	PUNCT
ejpam-340	347	12	[	[	X
ejpam-340	347	13	x	x	X
ejpam-340	347	14	,	,	PUNCT
ejpam-340	347	15	ui	ui	NOUN
ejpam-340	347	16	]	]	X
ejpam-340	347	17	)	)	PUNCT
ejpam-340	347	18	(	(	PUNCT
ejpam-340	347	19	67b	67b	NOUN
ejpam-340	347	20	)	)	PUNCT
ejpam-340	347	21	proof	proof	NOUN
ejpam-340	347	22	.	.	PUNCT
ejpam-340	348	1	replacing	replace	VERB
ejpam-340	348	2	ui	ui	NOUN
ejpam-340	348	3	for	for	ADP
ejpam-340	348	4	z	z	PROPN
ejpam-340	348	5	in	in	ADP
ejpam-340	348	6	(	(	PUNCT
ejpam-340	348	7	63	63	NUM
ejpam-340	348	8	)	)	PUNCT
ejpam-340	348	9	and	and	CCONJ
ejpam-340	348	10	using	use	VERB
ejpam-340	348	11	(	(	PUNCT
ejpam-340	348	12	12	12	NUM
ejpam-340	348	13	)	)	PUNCT
ejpam-340	348	14	and	and	CCONJ
ejpam-340	348	15	(	(	PUNCT
ejpam-340	348	16	61a	61a	NOUN
ejpam-340	348	17	)	)	PUNCT
ejpam-340	348	18	,	,	PUNCT
ejpam-340	348	19	we	we	PRON
ejpam-340	348	20	get	get	VERB
ejpam-340	348	21	(	(	PUNCT
ejpam-340	348	22	67a	67a	NUM
ejpam-340	348	23	)	)	PUNCT
ejpam-340	348	24	.	.	PUNCT
ejpam-340	349	1	(	(	PUNCT
ejpam-340	349	2	67b	67b	NOUN
ejpam-340	349	3	)	)	PUNCT
ejpam-340	349	4	is	be	AUX
ejpam-340	349	5	obtained	obtain	VERB
ejpam-340	349	6	by	by	ADP
ejpam-340	349	7	putting	put	VERB
ejpam-340	349	8	ui	ui	NOUN
ejpam-340	349	9	for	for	ADP
ejpam-340	349	10	y	y	PROPN
ejpam-340	349	11	in	in	ADP
ejpam-340	349	12	(	(	PUNCT
ejpam-340	349	13	67a	67a	NUM
ejpam-340	349	14	)	)	PUNCT
ejpam-340	349	15	.	.	PUNCT
ejpam-340	350	1	r.	r.	PROPN
ejpam-340	350	2	singh	singh	PROPN
ejpam-340	350	3	and	and	CCONJ
ejpam-340	350	4	s.	s.	PROPN
ejpam-340	350	5	singh	singh	PROPN
ejpam-340	350	6	/	/	SYM
ejpam-340	350	7	eur	eur	PROPN
ejpam-340	350	8	.	.	PUNCT
ejpam-340	351	1	j.	j.	PROPN
ejpam-340	351	2	pure	pure	PROPN
ejpam-340	351	3	appl	appl	PROPN
ejpam-340	351	4	.	.	PROPN
ejpam-340	351	5	math	math	PROPN
ejpam-340	351	6	,	,	PUNCT
ejpam-340	351	7	3	3	NUM
ejpam-340	351	8	(	(	PUNCT
ejpam-340	351	9	2010	2010	NUM
ejpam-340	351	10	)	)	PUNCT
ejpam-340	351	11	,	,	PUNCT
ejpam-340	351	12	839	839	NUM
ejpam-340	351	13	-	-	SYM
ejpam-340	351	14	852	852	NUM
ejpam-340	351	15	849	849	NUM
ejpam-340	351	16	4	4	NUM
ejpam-340	351	17	.	.	PUNCT
ejpam-340	352	1	an	an	DET
ejpam-340	352	2	affine	affine	NOUN
ejpam-340	352	3	connexion	connexion	NOUN
ejpam-340	352	4	iii	iii	NUM
ejpam-340	352	5	in	in	ADP
ejpam-340	352	6	this	this	DET
ejpam-340	352	7	section	section	NOUN
ejpam-340	352	8	an	an	DET
ejpam-340	352	9	affine	affine	NOUN
ejpam-340	352	10	connexion	connexion	NOUN
ejpam-340	352	11	is	be	AUX
ejpam-340	352	12	considered	consider	VERB
ejpam-340	352	13	which	which	PRON
ejpam-340	352	14	is	be	AUX
ejpam-340	352	15	different	different	ADJ
ejpam-340	352	16	one	one	NUM
ejpam-340	352	17	from	from	ADP
ejpam-340	352	18	section	section	NOUN
ejpam-340	352	19	2	2	NUM
ejpam-340	352	20	and	and	CCONJ
ejpam-340	352	21	section	section	NOUN
ejpam-340	352	22	3	3	NUM
ejpam-340	352	23	.	.	PUNCT
ejpam-340	353	1	its	its	PRON
ejpam-340	353	2	properties	property	NOUN
ejpam-340	353	3	are	be	AUX
ejpam-340	353	4	also	also	ADV
ejpam-340	353	5	have	have	AUX
ejpam-340	353	6	been	be	AUX
ejpam-340	353	7	studied	study	VERB
ejpam-340	353	8	.	.	PUNCT
ejpam-340	354	1	let	let	VERB
ejpam-340	354	2	us	we	PRON
ejpam-340	354	3	consider	consider	VERB
ejpam-340	354	4	an	an	DET
ejpam-340	354	5	affine	affine	NOUN
ejpam-340	354	6	connexion	connexion	NOUN
ejpam-340	354	7	d	d	PROPN
ejpam-340	354	8	in	in	ADP
ejpam-340	354	9	a	a	DET
ejpam-340	354	10	generalised	generalise	VERB
ejpam-340	354	11	structure	structure	NOUN
ejpam-340	354	12	manifold	manifold	ADJ
ejpam-340	354	13	vn	vn	NOUN
ejpam-340	354	14	with	with	ADP
ejpam-340	354	15	torsion	torsion	NOUN
ejpam-340	354	16	tensor	tensor	NOUN
ejpam-340	354	17	s	s	PRON
ejpam-340	354	18	such	such	ADJ
ejpam-340	354	19	that	that	PRON
ejpam-340	354	20	(	(	PUNCT
ejpam-340	354	21	dx	dx	PROPN
ejpam-340	354	22	ui)(y	ui)(y	PROPN
ejpam-340	354	23	)	)	PUNCT
ejpam-340	355	1	+	+	CCONJ
ejpam-340	355	2	(	(	PUNCT
ejpam-340	355	3	dy	dy	NOUN
ejpam-340	355	4	ui)(x	ui)(x	PROPN
ejpam-340	355	5	)	)	PUNCT
ejpam-340	356	1	=	=	SYM
ejpam-340	356	2	0	0	NUM
ejpam-340	356	3	(	(	PUNCT
ejpam-340	356	4	68a	68a	NOUN
ejpam-340	356	5	)	)	PUNCT
ejpam-340	356	6	(	(	PUNCT
ejpam-340	356	7	dx	dx	PROPN
ejpam-340	356	8	f)(y	f)(y	NUM
ejpam-340	356	9	)	)	PUNCT
ejpam-340	357	1	+	+	CCONJ
ejpam-340	357	2	(	(	PUNCT
ejpam-340	357	3	dy	dy	NOUN
ejpam-340	357	4	f)(x	f)(x	PROPN
ejpam-340	357	5	)	)	PUNCT
ejpam-340	357	6	=	=	SYM
ejpam-340	357	7	0	0	NUM
ejpam-340	357	8	(	(	PUNCT
ejpam-340	357	9	68b	68b	NOUN
ejpam-340	357	10	)	)	PUNCT
ejpam-340	357	11	(	(	PUNCT
ejpam-340	357	12	dx	dx	PROPN
ejpam-340	357	13	ui	ui	PROPN
ejpam-340	357	14	)	)	PUNCT
ejpam-340	357	15	=	=	SYM
ejpam-340	357	16	0	0	NUM
ejpam-340	357	17	(	(	PUNCT
ejpam-340	357	18	68c	68c	NOUN
ejpam-340	357	19	)	)	PUNCT
ejpam-340	357	20	theorem	theorem	NOUN
ejpam-340	357	21	15	15	NUM
ejpam-340	357	22	.	.	PUNCT
ejpam-340	358	1	in	in	ADP
ejpam-340	358	2	,	,	PUNCT
ejpam-340	358	3	vn	vn	INTJ
ejpam-340	358	4	,	,	PUNCT
ejpam-340	358	5	we	we	PRON
ejpam-340	358	6	have	have	VERB
ejpam-340	358	7	dui	dui	PROPN
ejpam-340	358	8	y	y	PROPN
ejpam-340	358	9	=	=	PROPN
ejpam-340	358	10	dui	dui	PROPN
ejpam-340	358	11	y	y	PROPN
ejpam-340	358	12	(	(	PUNCT
ejpam-340	358	13	69a	69a	X
ejpam-340	358	14	)	)	PUNCT
ejpam-340	358	15	dy	dy	NOUN
ejpam-340	358	16	x	x	PUNCT
ejpam-340	359	1	+	+	CCONJ
ejpam-340	359	2	b2dx	b2dx	SYM
ejpam-340	359	3	y	y	PROPN
ejpam-340	359	4	−	−	PROPN
ejpam-340	359	5	(	(	PUNCT
ejpam-340	359	6	dx	dx	PROPN
ejpam-340	359	7	y	y	PROPN
ejpam-340	359	8	+	+	CCONJ
ejpam-340	359	9	dy	dy	X
ejpam-340	359	10	x	x	NOUN
ejpam-340	359	11	)	)	PUNCT
ejpam-340	360	1	=	=	PUNCT
ejpam-340	360	2	−c	−c	NOUN
ejpam-340	360	3	x	x	SYM
ejpam-340	360	4	(	(	PUNCT
ejpam-340	360	5	ui(y	ui(y	NUM
ejpam-340	360	6	)	)	PUNCT
ejpam-340	360	7	)	)	PUNCT
ejpam-340	361	1	ui	ui	PROPN
ejpam-340	361	2	(	(	PUNCT
ejpam-340	361	3	69b	69b	NOUN
ejpam-340	361	4	)	)	PUNCT
ejpam-340	361	5	dx	dx	PROPN
ejpam-340	362	1	y	y	PROPN
ejpam-340	363	1	+	+	CCONJ
ejpam-340	363	2	dy	dy	X
ejpam-340	363	3	x	x	X
ejpam-340	363	4	−	−	PROPN
ejpam-340	363	5	b2(dx	b2(dx	NUM
ejpam-340	363	6	y	y	PROPN
ejpam-340	363	7	+	+	CCONJ
ejpam-340	363	8	dy	dy	X
ejpam-340	363	9	x	x	PROPN
ejpam-340	363	10	)	)	PUNCT
ejpam-340	364	1	=	=	PUNCT
ejpam-340	365	1	c	c	NOUN
ejpam-340	365	2	ui(dx	ui(dx	NOUN
ejpam-340	365	3	y	y	PROPN
ejpam-340	365	4	+	+	CCONJ
ejpam-340	365	5	dy	dy	X
ejpam-340	365	6	x	x	PROPN
ejpam-340	365	7	)	)	PUNCT
ejpam-340	365	8	ui	ui	PROPN
ejpam-340	365	9	(	(	PUNCT
ejpam-340	365	10	69c	69c	NUM
ejpam-340	365	11	)	)	PUNCT
ejpam-340	365	12	b2(dx	b2(dx	ADP
ejpam-340	365	13	y	y	PROPN
ejpam-340	365	14	+	+	CCONJ
ejpam-340	365	15	dy	dy	X
ejpam-340	365	16	x	x	PROPN
ejpam-340	365	17	)	)	PUNCT
ejpam-340	365	18	−	−	PROPN
ejpam-340	365	19	(	(	PUNCT
ejpam-340	365	20	dx	dx	PROPN
ejpam-340	365	21	y	y	PROPN
ejpam-340	365	22	+	+	CCONJ
ejpam-340	365	23	dy	dy	X
ejpam-340	365	24	x	x	SYM
ejpam-340	365	25	)	)	PUNCT
ejpam-340	366	1	=	=	SYM
ejpam-340	366	2	−c	−c	NOUN
ejpam-340	366	3	{	{	PUNCT
ejpam-340	366	4	x	x	X
ejpam-340	366	5	(	(	PUNCT
ejpam-340	366	6	ui(y	ui(y	NUM
ejpam-340	366	7	)	)	PUNCT
ejpam-340	366	8	)	)	PUNCT
ejpam-340	367	1	+	+	CCONJ
ejpam-340	367	2	y	y	PROPN
ejpam-340	367	3	(	(	PUNCT
ejpam-340	367	4	ui(x	ui(x	INTJ
ejpam-340	367	5	)	)	PUNCT
ejpam-340	367	6	)	)	PUNCT
ejpam-340	367	7	}	}	PUNCT
ejpam-340	367	8	(	(	PUNCT
ejpam-340	367	9	69d	69d	X
ejpam-340	367	10	)	)	PUNCT
ejpam-340	367	11	dx	dx	PROPN
ejpam-340	368	1	y	y	PROPN
ejpam-340	369	1	+	+	CCONJ
ejpam-340	369	2	dy	dy	X
ejpam-340	369	3	x	x	PUNCT
ejpam-340	369	4	−	−	PROPN
ejpam-340	369	5	dx	dx	PROPN
ejpam-340	369	6	y	y	PROPN
ejpam-340	369	7	−	−	PROPN
ejpam-340	369	8	dy	dy	X
ejpam-340	369	9	x	x	X
ejpam-340	369	10	=	=	SYM
ejpam-340	369	11	0	0	NUM
ejpam-340	369	12	(	(	PUNCT
ejpam-340	369	13	69e	69e	NOUN
ejpam-340	369	14	)	)	PUNCT
ejpam-340	369	15	proof	proof	NOUN
ejpam-340	369	16	.	.	PUNCT
ejpam-340	370	1	taking	take	VERB
ejpam-340	370	2	covariant	covariant	ADJ
ejpam-340	370	3	derivative	derivative	NOUN
ejpam-340	370	4	of	of	ADP
ejpam-340	370	5	f(y	f(y	PROPN
ejpam-340	370	6	)	)	PUNCT
ejpam-340	371	1	=	=	SYM
ejpam-340	371	2	y	y	PROPN
ejpam-340	371	3	with	with	ADP
ejpam-340	371	4	respect	respect	NOUN
ejpam-340	371	5	to	to	ADP
ejpam-340	371	6	ui	ui	NOUN
ejpam-340	371	7	and	and	CCONJ
ejpam-340	371	8	using	use	VERB
ejpam-340	371	9	(	(	PUNCT
ejpam-340	371	10	68c	68c	NOUN
ejpam-340	371	11	)	)	PUNCT
ejpam-340	371	12	,	,	PUNCT
ejpam-340	371	13	we	we	PRON
ejpam-340	371	14	get	get	VERB
ejpam-340	371	15	(	(	PUNCT
ejpam-340	371	16	69a	69a	ADJ
ejpam-340	371	17	)	)	PUNCT
ejpam-340	371	18	.	.	PUNCT
ejpam-340	372	1	now	now	ADV
ejpam-340	372	2	,	,	PUNCT
ejpam-340	372	3	(	(	PUNCT
ejpam-340	372	4	68b	68b	NOUN
ejpam-340	372	5	)	)	PUNCT
ejpam-340	372	6	is	be	AUX
ejpam-340	372	7	equivalent	equivalent	ADJ
ejpam-340	372	8	to	to	ADP
ejpam-340	372	9	dx	dx	PROPN
ejpam-340	372	10	y	y	PROPN
ejpam-340	372	11	+	+	CCONJ
ejpam-340	372	12	dy	dy	X
ejpam-340	372	13	x	x	PROPN
ejpam-340	373	1	=	=	X
ejpam-340	373	2	dx	dx	PROPN
ejpam-340	373	3	y	y	PROPN
ejpam-340	374	1	+	+	CCONJ
ejpam-340	374	2	dy	dy	X
ejpam-340	374	3	x	x	SYM
ejpam-340	374	4	(	(	PUNCT
ejpam-340	374	5	70	70	NUM
ejpam-340	374	6	)	)	PUNCT
ejpam-340	374	7	replacing	replace	VERB
ejpam-340	374	8	y	y	PRON
ejpam-340	374	9	by	by	ADP
ejpam-340	374	10	y	y	PROPN
ejpam-340	374	11	in	in	ADP
ejpam-340	374	12	(	(	PUNCT
ejpam-340	374	13	70	70	NUM
ejpam-340	374	14	)	)	PUNCT
ejpam-340	374	15	and	and	CCONJ
ejpam-340	374	16	using	use	VERB
ejpam-340	374	17	(	(	PUNCT
ejpam-340	374	18	1	1	NUM
ejpam-340	374	19	)	)	PUNCT
ejpam-340	374	20	,	,	PUNCT
ejpam-340	374	21	we	we	PRON
ejpam-340	374	22	get	get	VERB
ejpam-340	374	23	(	(	PUNCT
ejpam-340	374	24	69b	69b	NOUN
ejpam-340	374	25	)	)	PUNCT
ejpam-340	374	26	.	.	PUNCT
ejpam-340	375	1	by	by	ADP
ejpam-340	375	2	operating	operate	VERB
ejpam-340	375	3	f	f	PROPN
ejpam-340	375	4	on	on	ADP
ejpam-340	375	5	both	both	DET
ejpam-340	375	6	sides	side	NOUN
ejpam-340	375	7	of	of	ADP
ejpam-340	375	8	(	(	PUNCT
ejpam-340	375	9	70	70	NUM
ejpam-340	375	10	)	)	PUNCT
ejpam-340	375	11	and	and	CCONJ
ejpam-340	375	12	using	use	VERB
ejpam-340	375	13	(	(	PUNCT
ejpam-340	375	14	1	1	NUM
ejpam-340	375	15	)	)	PUNCT
ejpam-340	375	16	,	,	PUNCT
ejpam-340	375	17	(	(	PUNCT
ejpam-340	375	18	69c	69c	NOUN
ejpam-340	375	19	)	)	PUNCT
ejpam-340	375	20	can	can	AUX
ejpam-340	375	21	be	be	AUX
ejpam-340	375	22	obtained	obtain	VERB
ejpam-340	375	23	.	.	PUNCT
ejpam-340	376	1	replacing	replace	VERB
ejpam-340	376	2	x	x	PUNCT
ejpam-340	376	3	by	by	ADP
ejpam-340	376	4	x	x	SYM
ejpam-340	376	5	in	in	ADP
ejpam-340	376	6	(	(	PUNCT
ejpam-340	376	7	69b	69b	NOUN
ejpam-340	376	8	)	)	PUNCT
ejpam-340	376	9	,	,	PUNCT
ejpam-340	376	10	we	we	PRON
ejpam-340	376	11	get	get	VERB
ejpam-340	376	12	(	(	PUNCT
ejpam-340	376	13	69d	69d	NOUN
ejpam-340	376	14	)	)	PUNCT
ejpam-340	376	15	.	.	PUNCT
ejpam-340	377	1	replacing	replace	VERB
ejpam-340	377	2	x	x	PUNCT
ejpam-340	377	3	by	by	ADP
ejpam-340	377	4	x	x	PUNCT
ejpam-340	377	5	and	and	CCONJ
ejpam-340	377	6	y	y	PROPN
ejpam-340	377	7	by	by	ADP
ejpam-340	377	8	y	y	PROPN
ejpam-340	377	9	in	in	ADP
ejpam-340	377	10	(	(	PUNCT
ejpam-340	377	11	70	70	NUM
ejpam-340	377	12	)	)	PUNCT
ejpam-340	377	13	separately	separately	ADV
ejpam-340	377	14	and	and	CCONJ
ejpam-340	377	15	adding	add	VERB
ejpam-340	377	16	the	the	DET
ejpam-340	377	17	resulting	result	VERB
ejpam-340	377	18	equations	equation	NOUN
ejpam-340	377	19	,	,	PUNCT
ejpam-340	377	20	we	we	PRON
ejpam-340	377	21	get	get	VERB
ejpam-340	377	22	dx	dx	PROPN
ejpam-340	377	23	y	y	PROPN
ejpam-340	378	1	+	+	PROPN
ejpam-340	378	2	dy	dy	X
ejpam-340	378	3	x	x	PUNCT
ejpam-340	378	4	−	−	PROPN
ejpam-340	378	5	dx	dx	PROPN
ejpam-340	378	6	y	y	PROPN
ejpam-340	378	7	−	−	PROPN
ejpam-340	378	8	dy	dy	X
ejpam-340	378	9	x	x	X
ejpam-340	378	10	=	=	PUNCT
ejpam-340	378	11	dy	dy	NOUN
ejpam-340	378	12	x	x	PUNCT
ejpam-340	379	1	+	+	NUM
ejpam-340	379	2	dx	dx	PROPN
ejpam-340	379	3	y	y	PROPN
ejpam-340	379	4	−	−	PROPN
ejpam-340	379	5	dx	dx	PROPN
ejpam-340	379	6	y	y	PROPN
ejpam-340	379	7	−	−	PROPN
ejpam-340	380	1	dy	dy	X
ejpam-340	380	2	x	x	SYM
ejpam-340	380	3	(	(	PUNCT
ejpam-340	380	4	71	71	NUM
ejpam-340	380	5	)	)	PUNCT
ejpam-340	380	6	using	use	VERB
ejpam-340	380	7	(	(	PUNCT
ejpam-340	380	8	1	1	NUM
ejpam-340	380	9	)	)	PUNCT
ejpam-340	380	10	,	,	PUNCT
ejpam-340	380	11	(	(	PUNCT
ejpam-340	380	12	68a	68a	NOUN
ejpam-340	380	13	)	)	PUNCT
ejpam-340	380	14	and	and	CCONJ
ejpam-340	380	15	(	(	PUNCT
ejpam-340	380	16	69c	69c	NOUN
ejpam-340	380	17	)	)	PUNCT
ejpam-340	380	18	in	in	ADP
ejpam-340	380	19	(	(	PUNCT
ejpam-340	380	20	71	71	NUM
ejpam-340	380	21	)	)	PUNCT
ejpam-340	380	22	,	,	PUNCT
ejpam-340	380	23	we	we	PRON
ejpam-340	380	24	get	get	VERB
ejpam-340	380	25	(	(	PUNCT
ejpam-340	380	26	69e	69e	NOUN
ejpam-340	380	27	)	)	PUNCT
ejpam-340	380	28	.	.	PUNCT
ejpam-340	381	1	let	let	VERB
ejpam-340	381	2	us	we	PRON
ejpam-340	381	3	define	define	VERB
ejpam-340	381	4	a	a	DET
ejpam-340	381	5	tensor	tensor	NOUN
ejpam-340	381	6	h	h	NOUN
ejpam-340	381	7	of	of	ADP
ejpam-340	381	8	the	the	DET
ejpam-340	381	9	type	type	NOUN
ejpam-340	381	10	(	(	PUNCT
ejpam-340	381	11	1,2	1,2	NUM
ejpam-340	381	12	)	)	PUNCT
ejpam-340	381	13	by	by	ADP
ejpam-340	381	14	h(x	h(x	PROPN
ejpam-340	381	15	,	,	PUNCT
ejpam-340	381	16	y	y	PROPN
ejpam-340	381	17	)	)	PUNCT
ejpam-340	381	18	de	de	PROPN
ejpam-340	381	19	f	f	PROPN
ejpam-340	381	20	=	=	SYM
ejpam-340	381	21	dx	dx	PROPN
ejpam-340	382	1	y	y	PROPN
ejpam-340	382	2	−	−	PROPN
ejpam-340	382	3	dx	dx	PROPN
ejpam-340	382	4	y	y	PROPN
ejpam-340	382	5	(	(	PUNCT
ejpam-340	382	6	72	72	NUM
ejpam-340	382	7	)	)	PUNCT
ejpam-340	382	8	theorem	theorem	VERB
ejpam-340	382	9	16	16	NUM
ejpam-340	382	10	.	.	PUNCT
ejpam-340	383	1	in	in	ADP
ejpam-340	383	2	,	,	PUNCT
ejpam-340	383	3	vn	vn	INTJ
ejpam-340	383	4	,	,	PUNCT
ejpam-340	383	5	we	we	PRON
ejpam-340	383	6	have	have	VERB
ejpam-340	383	7	the	the	DET
ejpam-340	383	8	following	follow	VERB
ejpam-340	383	9	relations	relation	NOUN
ejpam-340	383	10	:	:	PUNCT
ejpam-340	383	11	h(x	h(x	PROPN
ejpam-340	383	12	,	,	PUNCT
ejpam-340	383	13	y	y	PROPN
ejpam-340	383	14	)	)	PUNCT
ejpam-340	384	1	+	+	SCONJ
ejpam-340	384	2	h(y	h(y	ADV
ejpam-340	384	3	,	,	PUNCT
ejpam-340	384	4	x	x	PUNCT
ejpam-340	384	5	)	)	PUNCT
ejpam-340	384	6	=	=	SYM
ejpam-340	384	7	0	0	NUM
ejpam-340	384	8	(	(	PUNCT
ejpam-340	384	9	73a	73a	NUM
ejpam-340	384	10	)	)	PUNCT
ejpam-340	384	11	h(x	h(x	PROPN
ejpam-340	384	12	,	,	PUNCT
ejpam-340	384	13	y	y	PROPN
ejpam-340	384	14	)	)	PUNCT
ejpam-340	385	1	+	+	SCONJ
ejpam-340	385	2	h(y	h(y	ADV
ejpam-340	385	3	,	,	PUNCT
ejpam-340	385	4	x	x	PUNCT
ejpam-340	385	5	)	)	PUNCT
ejpam-340	385	6	=	=	SYM
ejpam-340	385	7	0	0	NUM
ejpam-340	385	8	(	(	PUNCT
ejpam-340	385	9	73b	73b	NOUN
ejpam-340	385	10	)	)	PUNCT
ejpam-340	385	11	h(x	h(x	PROPN
ejpam-340	385	12	,	,	PUNCT
ejpam-340	385	13	y	y	PROPN
ejpam-340	385	14	)	)	PUNCT
ejpam-340	385	15	−	−	PROPN
ejpam-340	386	1	b2h(x	b2h(x	PROPN
ejpam-340	386	2	,	,	PUNCT
ejpam-340	386	3	y	y	PROPN
ejpam-340	386	4	)	)	PUNCT
ejpam-340	387	1	=	=	PUNCT
ejpam-340	388	1	−c[{p	−c[{p	NOUN
ejpam-340	388	2	j	j	PROPN
ejpam-340	389	1	i	i	PRON
ejpam-340	389	2	y	y	PROPN
ejpam-340	389	3	(	(	PUNCT
ejpam-340	389	4	u	u	PROPN
ejpam-340	389	5	j(x	j(x	PROPN
ejpam-340	389	6	)	)	PUNCT
ejpam-340	389	7	)	)	PUNCT
ejpam-340	390	1	ui}+	ui}+	PROPN
ejpam-340	390	2	y	y	PROPN
ejpam-340	390	3	(	(	PUNCT
ejpam-340	390	4	ui(x	ui(x	INTJ
ejpam-340	390	5	)	)	PUNCT
ejpam-340	390	6	)	)	PUNCT
ejpam-340	390	7	ui	ui	ADP
ejpam-340	390	8	]	]	X
ejpam-340	390	9	(	(	PUNCT
ejpam-340	390	10	73c	73c	NOUN
ejpam-340	390	11	)	)	PUNCT
ejpam-340	390	12	r.	r.	PROPN
ejpam-340	390	13	singh	singh	PROPN
ejpam-340	390	14	and	and	CCONJ
ejpam-340	390	15	s.	s.	PROPN
ejpam-340	390	16	singh	singh	PROPN
ejpam-340	390	17	/	/	SYM
ejpam-340	390	18	eur	eur	PROPN
ejpam-340	390	19	.	.	PUNCT
ejpam-340	391	1	j.	j.	PROPN
ejpam-340	391	2	pure	pure	PROPN
ejpam-340	391	3	appl	appl	PROPN
ejpam-340	391	4	.	.	PROPN
ejpam-340	391	5	math	math	PROPN
ejpam-340	391	6	,	,	PUNCT
ejpam-340	391	7	3	3	NUM
ejpam-340	391	8	(	(	PUNCT
ejpam-340	391	9	2010	2010	NUM
ejpam-340	391	10	)	)	PUNCT
ejpam-340	391	11	,	,	PUNCT
ejpam-340	391	12	839	839	NUM
ejpam-340	391	13	-	-	SYM
ejpam-340	391	14	852	852	NUM
ejpam-340	391	15	850	850	NUM
ejpam-340	391	16	proof	proof	NOUN
ejpam-340	391	17	.	.	PUNCT
ejpam-340	392	1	(	(	PUNCT
ejpam-340	392	2	73a	73a	NUM
ejpam-340	392	3	)	)	PUNCT
ejpam-340	392	4	follows	follow	VERB
ejpam-340	392	5	from	from	ADP
ejpam-340	392	6	(	(	PUNCT
ejpam-340	392	7	69e	69e	NOUN
ejpam-340	392	8	)	)	PUNCT
ejpam-340	392	9	and	and	CCONJ
ejpam-340	392	10	(	(	PUNCT
ejpam-340	392	11	72	72	NUM
ejpam-340	392	12	)	)	PUNCT
ejpam-340	392	13	.	.	PUNCT
ejpam-340	393	1	now	now	ADV
ejpam-340	393	2	replacing	replace	VERB
ejpam-340	393	3	y	y	PRON
ejpam-340	393	4	by	by	ADP
ejpam-340	393	5	y	y	PROPN
ejpam-340	393	6	in	in	ADP
ejpam-340	393	7	(	(	PUNCT
ejpam-340	393	8	72	72	NUM
ejpam-340	393	9	)	)	PUNCT
ejpam-340	393	10	and	and	CCONJ
ejpam-340	393	11	using	use	VERB
ejpam-340	393	12	(	(	PUNCT
ejpam-340	393	13	1	1	NUM
ejpam-340	393	14	)	)	PUNCT
ejpam-340	393	15	,	,	PUNCT
ejpam-340	393	16	we	we	PRON
ejpam-340	393	17	get	get	VERB
ejpam-340	393	18	h(x	h(x	PROPN
ejpam-340	393	19	,	,	PUNCT
ejpam-340	393	20	y	y	PROPN
ejpam-340	393	21	)	)	PUNCT
ejpam-340	394	1	=	=	PUNCT
ejpam-340	394	2	b2dx	b2dx	PUNCT
ejpam-340	395	1	y	y	PROPN
ejpam-340	396	1	+	+	CCONJ
ejpam-340	396	2	c	c	NOUN
ejpam-340	396	3	x	x	SYM
ejpam-340	396	4	(	(	PUNCT
ejpam-340	396	5	ui(y	ui(y	NUM
ejpam-340	396	6	)	)	PUNCT
ejpam-340	396	7	)	)	PUNCT
ejpam-340	396	8	ui	ui	PROPN
ejpam-340	397	1	−	−	PROPN
ejpam-340	397	2	dx	dx	PROPN
ejpam-340	397	3	y	y	PROPN
ejpam-340	397	4	(	(	PUNCT
ejpam-340	397	5	74	74	NUM
ejpam-340	397	6	)	)	PUNCT
ejpam-340	397	7	interchanging	interchange	VERB
ejpam-340	397	8	x	x	X
ejpam-340	397	9	and	and	CCONJ
ejpam-340	397	10	y	y	PROPN
ejpam-340	397	11	in	in	ADP
ejpam-340	397	12	(	(	PUNCT
ejpam-340	397	13	74	74	NUM
ejpam-340	397	14	)	)	PUNCT
ejpam-340	397	15	and	and	CCONJ
ejpam-340	397	16	adding	add	VERB
ejpam-340	397	17	the	the	DET
ejpam-340	397	18	resulting	result	VERB
ejpam-340	397	19	equation	equation	NOUN
ejpam-340	397	20	with	with	ADP
ejpam-340	397	21	(	(	PUNCT
ejpam-340	397	22	74	74	NUM
ejpam-340	397	23	)	)	PUNCT
ejpam-340	397	24	,	,	PUNCT
ejpam-340	397	25	we	we	PRON
ejpam-340	397	26	get	get	VERB
ejpam-340	397	27	(	(	PUNCT
ejpam-340	397	28	73b	73b	NOUN
ejpam-340	397	29	)	)	PUNCT
ejpam-340	397	30	,	,	PUNCT
ejpam-340	397	31	by	by	ADP
ejpam-340	397	32	making	make	VERB
ejpam-340	397	33	use	use	NOUN
ejpam-340	397	34	of	of	ADP
ejpam-340	397	35	(	(	PUNCT
ejpam-340	397	36	69d	69d	NOUN
ejpam-340	397	37	)	)	PUNCT
ejpam-340	397	38	.	.	PUNCT
ejpam-340	398	1	replacing	replace	VERB
ejpam-340	398	2	x	x	PUNCT
ejpam-340	398	3	by	by	ADP
ejpam-340	398	4	x	x	SYM
ejpam-340	398	5	in	in	ADP
ejpam-340	398	6	(	(	PUNCT
ejpam-340	398	7	73b	73b	NOUN
ejpam-340	398	8	)	)	PUNCT
ejpam-340	398	9	and	and	CCONJ
ejpam-340	398	10	using	use	VERB
ejpam-340	398	11	(	(	PUNCT
ejpam-340	398	12	1	1	NUM
ejpam-340	398	13	)	)	PUNCT
ejpam-340	398	14	and	and	CCONJ
ejpam-340	398	15	(	(	PUNCT
ejpam-340	398	16	5	5	NUM
ejpam-340	398	17	)	)	PUNCT
ejpam-340	398	18	,	,	PUNCT
ejpam-340	398	19	we	we	PRON
ejpam-340	398	20	obtain	obtain	VERB
ejpam-340	398	21	(	(	PUNCT
ejpam-340	398	22	73c	73c	NOUN
ejpam-340	398	23	)	)	PUNCT
ejpam-340	398	24	.	.	PUNCT
ejpam-340	399	1	theorem	theorem	NOUN
ejpam-340	399	2	17	17	NUM
ejpam-340	399	3	.	.	PUNCT
ejpam-340	400	1	in	in	ADP
ejpam-340	400	2	,	,	PUNCT
ejpam-340	400	3	vn	vn	INTJ
ejpam-340	400	4	,	,	PUNCT
ejpam-340	400	5	we	we	PRON
ejpam-340	400	6	have	have	VERB
ejpam-340	400	7	m(x	m(x	PROPN
ejpam-340	400	8	,	,	PUNCT
ejpam-340	400	9	y	y	PROPN
ejpam-340	400	10	)	)	PUNCT
ejpam-340	401	1	=	=	SYM
ejpam-340	401	2	2h(x	2h(x	NUM
ejpam-340	401	3	,	,	PUNCT
ejpam-340	401	4	y	y	PROPN
ejpam-340	401	5	)	)	PUNCT
ejpam-340	401	6	−	−	PROPN
ejpam-340	402	1	b(x	b(x	NOUN
ejpam-340	402	2	,	,	PUNCT
ejpam-340	402	3	y	y	PROPN
ejpam-340	402	4	)	)	PUNCT
ejpam-340	402	5	ui	ui	PROPN
ejpam-340	402	6	(	(	PUNCT
ejpam-340	402	7	75	75	NUM
ejpam-340	402	8	)	)	PUNCT
ejpam-340	403	1	where	where	SCONJ
ejpam-340	403	2	,	,	PUNCT
ejpam-340	403	3	b(x	b(x	NOUN
ejpam-340	403	4	,	,	PUNCT
ejpam-340	403	5	y	y	PROPN
ejpam-340	403	6	)	)	PUNCT
ejpam-340	403	7	=	=	PUNCT
ejpam-340	403	8	(	(	PUNCT
ejpam-340	403	9	dx	dx	PROPN
ejpam-340	403	10	ui)(y	ui)(y	PROPN
ejpam-340	403	11	)	)	PUNCT
ejpam-340	403	12	proof	proof	NOUN
ejpam-340	403	13	.	.	PUNCT
ejpam-340	404	1	adding	add	VERB
ejpam-340	404	2	(	(	PUNCT
ejpam-340	404	3	69b	69b	NOUN
ejpam-340	404	4	)	)	PUNCT
ejpam-340	404	5	and	and	CCONJ
ejpam-340	404	6	(	(	PUNCT
ejpam-340	404	7	69e	69e	NOUN
ejpam-340	404	8	)	)	PUNCT
ejpam-340	404	9	,	,	PUNCT
ejpam-340	404	10	we	we	PRON
ejpam-340	404	11	have	have	VERB
ejpam-340	404	12	dx	dx	PROPN
ejpam-340	404	13	y	y	PROPN
ejpam-340	404	14	−	−	PROPN
ejpam-340	404	15	dx	dx	PROPN
ejpam-340	405	1	y	y	PROPN
ejpam-340	405	2	−	−	PROPN
ejpam-340	405	3	dx	dx	PROPN
ejpam-340	405	4	y	y	PROPN
ejpam-340	405	5	+	+	CCONJ
ejpam-340	405	6	b2dx	b2dx	PUNCT
ejpam-340	405	7	y	y	PROPN
ejpam-340	406	1	+	+	NOUN
ejpam-340	406	2	c	c	NOUN
ejpam-340	406	3	x	x	SYM
ejpam-340	406	4	(	(	PUNCT
ejpam-340	406	5	ui(y	ui(y	NUM
ejpam-340	406	6	)	)	PUNCT
ejpam-340	406	7	)	)	PUNCT
ejpam-340	406	8	ui	ui	NOUN
ejpam-340	407	1	=	=	NOUN
ejpam-340	407	2	0	0	PUNCT
ejpam-340	407	3	(	(	PUNCT
ejpam-340	407	4	76	76	NUM
ejpam-340	407	5	)	)	PUNCT
ejpam-340	407	6	using	use	VERB
ejpam-340	407	7	(	(	PUNCT
ejpam-340	407	8	1	1	NUM
ejpam-340	407	9	)	)	PUNCT
ejpam-340	407	10	in	in	ADP
ejpam-340	407	11	(	(	PUNCT
ejpam-340	407	12	20	20	NUM
ejpam-340	407	13	)	)	PUNCT
ejpam-340	407	14	,	,	PUNCT
ejpam-340	407	15	we	we	PRON
ejpam-340	407	16	get	get	VERB
ejpam-340	407	17	m(x	m(x	PROPN
ejpam-340	407	18	,	,	PUNCT
ejpam-340	407	19	y	y	PROPN
ejpam-340	407	20	)	)	PUNCT
ejpam-340	408	1	=	=	PUNCT
ejpam-340	408	2	dx	dx	PROPN
ejpam-340	408	3	y	y	PROPN
ejpam-340	409	1	+	+	CCONJ
ejpam-340	409	2	b2dx	b2dx	PUNCT
ejpam-340	409	3	y	y	PROPN
ejpam-340	409	4	+	+	NOUN
ejpam-340	409	5	c	c	NOUN
ejpam-340	409	6	ui(dx	ui(dx	ADP
ejpam-340	409	7	y	y	PROPN
ejpam-340	409	8	)	)	PUNCT
ejpam-340	409	9	ui	ui	PROPN
ejpam-340	410	1	−	−	PROPN
ejpam-340	410	2	dx	dx	PROPN
ejpam-340	410	3	y	y	PROPN
ejpam-340	410	4	−	−	PROPN
ejpam-340	411	1	dx	dx	PROPN
ejpam-340	411	2	y	y	PROPN
ejpam-340	411	3	(	(	PUNCT
ejpam-340	411	4	77	77	NUM
ejpam-340	411	5	)	)	PUNCT
ejpam-340	411	6	due	due	ADP
ejpam-340	411	7	to	to	ADP
ejpam-340	411	8	(	(	PUNCT
ejpam-340	411	9	76	76	NUM
ejpam-340	411	10	)	)	PUNCT
ejpam-340	411	11	and	and	CCONJ
ejpam-340	411	12	(	(	PUNCT
ejpam-340	411	13	77	77	X
ejpam-340	411	14	)	)	PUNCT
ejpam-340	411	15	yields	yield	NOUN
ejpam-340	411	16	(	(	PUNCT
ejpam-340	411	17	75	75	NUM
ejpam-340	411	18	)	)	PUNCT
ejpam-340	411	19	.	.	PUNCT
ejpam-340	412	1	theorem	theorem	VERB
ejpam-340	412	2	18	18	NUM
ejpam-340	412	3	.	.	PUNCT
ejpam-340	413	1	the	the	DET
ejpam-340	413	2	connexion	connexion	PROPN
ejpam-340	413	3	d	d	X
ejpam-340	413	4	is	be	AUX
ejpam-340	413	5	an	an	DET
ejpam-340	413	6	f	f	NOUN
ejpam-340	413	7	-	-	PUNCT
ejpam-340	413	8	connexion	connexion	NOUN
ejpam-340	413	9	if	if	SCONJ
ejpam-340	413	10	and	and	CCONJ
ejpam-340	413	11	only	only	ADV
ejpam-340	413	12	if	if	SCONJ
ejpam-340	413	13	h(x	h(x	PROPN
ejpam-340	413	14	,	,	PUNCT
ejpam-340	413	15	y	y	PROPN
ejpam-340	413	16	)	)	PUNCT
ejpam-340	413	17	=	=	SYM
ejpam-340	413	18	0	0	PUNCT
ejpam-340	413	19	(	(	PUNCT
ejpam-340	413	20	78	78	NUM
ejpam-340	413	21	)	)	PUNCT
ejpam-340	413	22	proof	proof	NOUN
ejpam-340	413	23	.	.	PUNCT
ejpam-340	414	1	let	let	VERB
ejpam-340	414	2	d	d	PRON
ejpam-340	414	3	be	be	AUX
ejpam-340	414	4	an	an	DET
ejpam-340	414	5	f	f	PROPN
ejpam-340	414	6	-connexion	-connexion	NOUN
ejpam-340	414	7	,	,	PUNCT
ejpam-340	414	8	then	then	ADV
ejpam-340	414	9	(	(	PUNCT
ejpam-340	414	10	13	13	NUM
ejpam-340	414	11	)	)	PUNCT
ejpam-340	414	12	&	&	CCONJ
ejpam-340	414	13	(	(	PUNCT
ejpam-340	414	14	72	72	NUM
ejpam-340	414	15	)	)	PUNCT
ejpam-340	414	16	,	,	PUNCT
ejpam-340	414	17	gives	give	VERB
ejpam-340	414	18	h(x	h(x	PROPN
ejpam-340	414	19	,	,	PUNCT
ejpam-340	414	20	y	y	PROPN
ejpam-340	414	21	)	)	PUNCT
ejpam-340	415	1	=	=	PUNCT
ejpam-340	415	2	0	0	X
ejpam-340	415	3	.	.	PUNCT
ejpam-340	416	1	conversely	conversely	ADV
ejpam-340	416	2	,	,	PUNCT
ejpam-340	416	3	if	if	SCONJ
ejpam-340	416	4	(	(	PUNCT
ejpam-340	416	5	78	78	NUM
ejpam-340	416	6	)	)	PUNCT
ejpam-340	416	7	is	be	AUX
ejpam-340	416	8	true	true	ADJ
ejpam-340	416	9	,	,	PUNCT
ejpam-340	416	10	then	then	ADV
ejpam-340	416	11	dx	dx	PROPN
ejpam-340	416	12	y	y	PROPN
ejpam-340	416	13	=	=	PROPN
ejpam-340	416	14	dx	dx	PROPN
ejpam-340	416	15	y	y	PROPN
ejpam-340	416	16	.	.	PUNCT
ejpam-340	417	1	replacing	replace	VERB
ejpam-340	417	2	x	x	PUNCT
ejpam-340	417	3	by	by	ADP
ejpam-340	417	4	x	x	PUNCT
ejpam-340	417	5	in	in	ADP
ejpam-340	417	6	this	this	DET
ejpam-340	417	7	relation	relation	NOUN
ejpam-340	417	8	,	,	PUNCT
ejpam-340	417	9	we	we	PRON
ejpam-340	417	10	get	get	VERB
ejpam-340	417	11	b2dx	b2dx	PUNCT
ejpam-340	418	1	y	y	PROPN
ejpam-340	418	2	+	+	PROPN
ejpam-340	418	3	c	c	PROPN
ejpam-340	418	4	ui(x	ui(x	PUNCT
ejpam-340	418	5	)	)	PUNCT
ejpam-340	419	1	dui	dui	PROPN
ejpam-340	419	2	y	y	PROPN
ejpam-340	419	3	=	=	PROPN
ejpam-340	419	4	b2	b2	PROPN
ejpam-340	419	5	dx	dx	PROPN
ejpam-340	419	6	y	y	PROPN
ejpam-340	419	7	+	+	PROPN
ejpam-340	419	8	c	c	PROPN
ejpam-340	419	9	ui(x	ui(x	PUNCT
ejpam-340	419	10	)	)	PUNCT
ejpam-340	419	11	dui	dui	PROPN
ejpam-340	419	12	y	y	PROPN
ejpam-340	419	13	(	(	PUNCT
ejpam-340	419	14	79	79	NUM
ejpam-340	419	15	)	)	PUNCT
ejpam-340	419	16	due	due	ADP
ejpam-340	419	17	to	to	ADP
ejpam-340	419	18	(	(	PUNCT
ejpam-340	419	19	69a	69a	ADJ
ejpam-340	419	20	)	)	PUNCT
ejpam-340	419	21	,	,	PUNCT
ejpam-340	419	22	(	(	PUNCT
ejpam-340	419	23	79	79	X
ejpam-340	419	24	)	)	PUNCT
ejpam-340	419	25	yields	yield	NOUN
ejpam-340	419	26	(	(	PUNCT
ejpam-340	419	27	dx	dx	PROPN
ejpam-340	419	28	f)(y	f)(y	NUM
ejpam-340	419	29	)	)	PUNCT
ejpam-340	420	1	=	=	PUNCT
ejpam-340	420	2	0	0	NUM
ejpam-340	420	3	,	,	PUNCT
ejpam-340	420	4	which	which	PRON
ejpam-340	420	5	implies	imply	VERB
ejpam-340	420	6	that	that	SCONJ
ejpam-340	420	7	d	d	NOUN
ejpam-340	420	8	is	be	AUX
ejpam-340	420	9	an	an	DET
ejpam-340	420	10	f	f	PROPN
ejpam-340	420	11	-connexion	-connexion	NOUN
ejpam-340	420	12	.	.	PUNCT
ejpam-340	421	1	theorem	theorem	NOUN
ejpam-340	421	2	19	19	NUM
ejpam-340	421	3	.	.	PUNCT
ejpam-340	422	1	when	when	SCONJ
ejpam-340	422	2	d	d	NOUN
ejpam-340	422	3	is	be	AUX
ejpam-340	422	4	an	an	DET
ejpam-340	422	5	f	f	NOUN
ejpam-340	422	6	-	-	PUNCT
ejpam-340	422	7	connexion	connexion	NOUN
ejpam-340	422	8	,	,	PUNCT
ejpam-340	422	9	any	any	DET
ejpam-340	422	10	one	one	NUM
ejpam-340	422	11	of	of	ADP
ejpam-340	422	12	the	the	DET
ejpam-340	422	13	following	following	NOUN
ejpam-340	422	14	holds	hold	VERB
ejpam-340	422	15	if	if	SCONJ
ejpam-340	422	16	remaining	remain	VERB
ejpam-340	422	17	two	two	NUM
ejpam-340	422	18	hold	hold	NOUN
ejpam-340	422	19	:	:	PUNCT
ejpam-340	422	20	(	(	PUNCT
ejpam-340	422	21	a	a	X
ejpam-340	422	22	)	)	PUNCT
ejpam-340	422	23	h(x	h(x	PROPN
ejpam-340	422	24	,	,	PUNCT
ejpam-340	422	25	y	y	PROPN
ejpam-340	422	26	)	)	PUNCT
ejpam-340	422	27	=	=	SYM
ejpam-340	422	28	0	0	PUNCT
ejpam-340	422	29	(	(	PUNCT
ejpam-340	422	30	b	b	NOUN
ejpam-340	422	31	)	)	PUNCT
ejpam-340	422	32	b(x	b(x	NOUN
ejpam-340	422	33	,	,	PUNCT
ejpam-340	422	34	y	y	PROPN
ejpam-340	422	35	)	)	PUNCT
ejpam-340	423	1	=	=	SYM
ejpam-340	423	2	0	0	PUNCT
ejpam-340	423	3	(	(	PUNCT
ejpam-340	423	4	c	c	NOUN
ejpam-340	423	5	)	)	PUNCT
ejpam-340	423	6	m(x	m(x	PROPN
ejpam-340	423	7	,	,	PUNCT
ejpam-340	423	8	y	y	PROPN
ejpam-340	423	9	)	)	PUNCT
ejpam-340	423	10	=	=	SYM
ejpam-340	423	11	0	0	NUM
ejpam-340	423	12	remark	remark	NOUN
ejpam-340	423	13	3	3	NUM
ejpam-340	423	14	.	.	PUNCT
ejpam-340	424	1	all	all	DET
ejpam-340	424	2	the	the	DET
ejpam-340	424	3	results	result	NOUN
ejpam-340	424	4	discussed	discuss	VERB
ejpam-340	424	5	in	in	ADP
ejpam-340	424	6	section	section	NOUN
ejpam-340	424	7	2	2	NUM
ejpam-340	424	8	,	,	PUNCT
ejpam-340	424	9	section	section	NOUN
ejpam-340	424	10	3	3	NUM
ejpam-340	424	11	and	and	CCONJ
ejpam-340	424	12	section	section	NOUN
ejpam-340	424	13	4	4	NUM
ejpam-340	424	14	are	be	AUX
ejpam-340	424	15	true	true	ADJ
ejpam-340	424	16	in	in	ADP
ejpam-340	424	17	an	an	DET
ejpam-340	424	18	almost	almost	ADV
ejpam-340	424	19	tangent	tangent	ADJ
ejpam-340	424	20	metric	metric	ADJ
ejpam-340	424	21	manifold	manifold	NOUN
ejpam-340	424	22	,	,	PUNCT
ejpam-340	424	23	an	an	DET
ejpam-340	424	24	almost	almost	ADV
ejpam-340	424	25	hermite	hermite	ADJ
ejpam-340	424	26	manifold	manifold	ADJ
ejpam-340	424	27	,	,	PUNCT
ejpam-340	424	28	metric	metric	ADJ
ejpam-340	424	29	π	π	NOUN
ejpam-340	424	30	-	-	ADJ
ejpam-340	424	31	structure	structure	ADJ
ejpam-340	424	32	manifold	manifold	NOUN
ejpam-340	424	33	,	,	PUNCT
ejpam-340	424	34	hsu	hsu	NOUN
ejpam-340	424	35	-	-	PUNCT
ejpam-340	424	36	structure	structure	NOUN
ejpam-340	424	37	manifold	manifold	NOUN
ejpam-340	424	38	,	,	PUNCT
ejpam-340	424	39	f	f	NOUN
ejpam-340	424	40	-	-	PUNCT
ejpam-340	424	41	structure	structure	NOUN
ejpam-340	424	42	manifold	manifold	NOUN
ejpam-340	424	43	,	,	PUNCT
ejpam-340	424	44	an	an	DET
ejpam-340	424	45	almost	almost	ADV
ejpam-340	424	46	product	product	NOUN
ejpam-340	424	47	riemannian	riemannian	NOUN
ejpam-340	424	48	manifold	manifold	NOUN
ejpam-340	424	49	,	,	PUNCT
ejpam-340	424	50	an	an	DET
ejpam-340	424	51	almost	almost	ADV
ejpam-340	424	52	grayan	grayan	ADJ
ejpam-340	424	53	manifold	manifold	NOUN
ejpam-340	424	54	and	and	CCONJ
ejpam-340	424	55	{	{	PUNCT
ejpam-340	424	56	f	f	X
ejpam-340	424	57	,	,	PUNCT
ejpam-340	424	58	g	g	PROPN
ejpam-340	424	59	,	,	PUNCT
ejpam-340	424	60	u1,u2	u1,u2	PROPN
ejpam-340	424	61	,	,	PUNCT
ejpam-340	424	62	u1	u1	NOUN
ejpam-340	424	63	,	,	PUNCT
ejpam-340	424	64	u2	u2	NOUN
ejpam-340	424	65	}	}	PUNCT
ejpam-340	424	66	structure	structure	NOUN
ejpam-340	424	67	manifold	manifold	ADJ
ejpam-340	424	68	if	if	SCONJ
ejpam-340	424	69	(	(	PUNCT
ejpam-340	424	70	b2	b2	NOUN
ejpam-340	424	71	=	=	SYM
ejpam-340	424	72	0	0	NUM
ejpam-340	424	73	,	,	PUNCT
ejpam-340	424	74	c	c	NOUN
ejpam-340	424	75	=	=	SYM
ejpam-340	424	76	0	0	NUM
ejpam-340	424	77	)	)	PUNCT
ejpam-340	424	78	;	;	PUNCT
ejpam-340	424	79	(	(	PUNCT
ejpam-340	424	80	b2	b2	NOUN
ejpam-340	424	81	=	=	SYM
ejpam-340	424	82	−1	−1	NOUN
ejpam-340	424	83	,	,	PUNCT
ejpam-340	424	84	c	c	NOUN
ejpam-340	424	85	=	=	SYM
ejpam-340	424	86	0	0	NUM
ejpam-340	424	87	)	)	PUNCT
ejpam-340	424	88	;	;	PUNCT
ejpam-340	424	89	(	(	PUNCT
ejpam-340	424	90	c	c	X
ejpam-340	424	91	=	=	SYM
ejpam-340	424	92	0	0	NUM
ejpam-340	424	93	)	)	PUNCT
ejpam-340	424	94	;	;	PUNCT
ejpam-340	424	95	(	(	PUNCT
ejpam-340	424	96	b2	b2	NOUN
ejpam-340	424	97	=	=	SYM
ejpam-340	424	98	λr	λr	NOUN
ejpam-340	424	99	,	,	PUNCT
ejpam-340	424	100	c	c	NOUN
ejpam-340	424	101	=	=	SYM
ejpam-340	424	102	0	0	NUM
ejpam-340	424	103	)	)	PUNCT
ejpam-340	424	104	;	;	PUNCT
ejpam-340	424	105	(	(	PUNCT
ejpam-340	424	106	b2	b2	NOUN
ejpam-340	424	107	=	=	SYM
ejpam-340	424	108	−1	−1	NOUN
ejpam-340	424	109	,	,	PUNCT
ejpam-340	424	110	p	p	NOUN
ejpam-340	424	111	j	j	PROPN
ejpam-340	424	112	i	i	NOUN
ejpam-340	424	113	=	=	NOUN
ejpam-340	424	114	0	0	NUM
ejpam-340	424	115	)	)	PUNCT
ejpam-340	424	116	;	;	PUNCT
ejpam-340	424	117	(	(	PUNCT
ejpam-340	424	118	b2	b2	NOUN
ejpam-340	424	119	=	=	SYM
ejpam-340	424	120	1	1	NUM
ejpam-340	424	121	,	,	PUNCT
ejpam-340	424	122	c	c	NOUN
ejpam-340	424	123	=	=	SYM
ejpam-340	424	124	0	0	NUM
ejpam-340	424	125	)	)	PUNCT
ejpam-340	424	126	;	;	PUNCT
ejpam-340	424	127	(	(	PUNCT
ejpam-340	424	128	b2	b2	NOUN
ejpam-340	424	129	=	=	SYM
ejpam-340	424	130	−1	−1	NOUN
ejpam-340	424	131	,	,	PUNCT
ejpam-340	424	132	c	c	NOUN
ejpam-340	424	133	=	=	SYM
ejpam-340	424	134	1	1	NUM
ejpam-340	424	135	,	,	PUNCT
ejpam-340	424	136	p1	p1	NOUN
ejpam-340	424	137	1	1	NUM
ejpam-340	424	138	=	=	SYM
ejpam-340	424	139	0	0	NUM
ejpam-340	424	140	:	:	PUNCT
ejpam-340	424	141	i	i	PRON
ejpam-340	424	142	,	,	PUNCT
ejpam-340	424	143	j	j	PROPN
ejpam-340	424	144	=	=	NOUN
ejpam-340	424	145	1	1	NUM
ejpam-340	424	146	)	)	PUNCT
ejpam-340	424	147	;	;	PUNCT
ejpam-340	424	148	and	and	CCONJ
ejpam-340	424	149	(	(	PUNCT
ejpam-340	424	150	b2	b2	NOUN
ejpam-340	424	151	=	=	SYM
ejpam-340	424	152	−1	−1	NOUN
ejpam-340	424	153	,	,	PUNCT
ejpam-340	424	154	c	c	NOUN
ejpam-340	424	155	=	=	SYM
ejpam-340	424	156	1	1	NUM
ejpam-340	424	157	,	,	PUNCT
ejpam-340	424	158	p	p	NOUN
ejpam-340	424	159	j	j	PROPN
ejpam-340	425	1	i	i	PRON
ejpam-340	425	2	+	+	CCONJ
ejpam-340	425	3	pi	pi	NOUN
ejpam-340	425	4	j	j	PROPN
ejpam-340	425	5	=	=	NOUN
ejpam-340	425	6	0	0	NUM
ejpam-340	425	7	:	:	PUNCT
ejpam-340	425	8	i	i	PRON
ejpam-340	425	9	,	,	PUNCT
ejpam-340	425	10	j	j	PROPN
ejpam-340	425	11	=	=	SYM
ejpam-340	425	12	1,2	1,2	NUM
ejpam-340	425	13	)	)	PUNCT
ejpam-340	425	14	respectively	respectively	ADV
ejpam-340	425	15	.	.	PUNCT
ejpam-340	426	1	references	reference	NOUN
ejpam-340	426	2	851	851	NUM
ejpam-340	426	3	acknowledgements	acknowledgement	NOUN
ejpam-340	426	4	the	the	DET
ejpam-340	426	5	first	first	ADJ
ejpam-340	426	6	author	author	NOUN
ejpam-340	426	7	is	be	AUX
ejpam-340	426	8	very	very	ADV
ejpam-340	426	9	thankful	thankful	ADJ
ejpam-340	426	10	to	to	ADP
ejpam-340	426	11	university	university	NOUN
ejpam-340	426	12	grants	grant	NOUN
ejpam-340	426	13	commission	commission	PROPN
ejpam-340	426	14	for	for	ADP
ejpam-340	426	15	partial	partial	ADJ
ejpam-340	426	16	financial	financial	ADJ
ejpam-340	426	17	assistance	assistance	NOUN
ejpam-340	426	18	without	without	ADP
ejpam-340	426	19	which	which	PRON
ejpam-340	426	20	the	the	DET
ejpam-340	426	21	present	present	ADJ
ejpam-340	426	22	work	work	NOUN
ejpam-340	426	23	was	be	AUX
ejpam-340	426	24	not	not	PART
ejpam-340	426	25	possible	possible	ADJ
ejpam-340	426	26	.	.	PUNCT
ejpam-340	427	1	references	reference	NOUN
ejpam-340	427	2	[	[	X
ejpam-340	427	3	1	1	NUM
ejpam-340	427	4	]	]	PUNCT
ejpam-340	427	5	boothby	boothby	NOUN
ejpam-340	427	6	,	,	PUNCT
ejpam-340	427	7	w.	w.	PROPN
ejpam-340	427	8	m.	m.	PROPN
ejpam-340	427	9	an	an	DET
ejpam-340	427	10	introduction	introduction	NOUN
ejpam-340	427	11	to	to	PART
ejpam-340	427	12	differentiable	differentiable	VERB
ejpam-340	427	13	manifolds	manifold	NOUN
ejpam-340	427	14	and	and	CCONJ
ejpam-340	427	15	riemannian	riemannian	ADJ
ejpam-340	427	16	geometry	geometry	NOUN
ejpam-340	427	17	.	.	PUNCT
ejpam-340	428	1	academic	academic	ADJ
ejpam-340	428	2	press	press	NOUN
ejpam-340	428	3	,	,	PUNCT
ejpam-340	428	4	1975	1975	NUM
ejpam-340	428	5	.	.	PUNCT
ejpam-340	429	1	[	[	X
ejpam-340	429	2	2	2	NUM
ejpam-340	429	3	]	]	X
ejpam-340	429	4	goldberg	goldberg	PROPN
ejpam-340	429	5	,	,	PUNCT
ejpam-340	429	6	s.	s.	PROPN
ejpam-340	429	7	i.	i.	PROPN
ejpam-340	429	8	,	,	PUNCT
ejpam-340	429	9	and	and	CCONJ
ejpam-340	429	10	yano	yano	PROPN
ejpam-340	429	11	,	,	PUNCT
ejpam-340	429	12	k.	k.	PROPN
ejpam-340	429	13	on	on	ADP
ejpam-340	429	14	normal	normal	ADJ
ejpam-340	429	15	globally	globally	ADV
ejpam-340	429	16	farmed	farm	VERB
ejpam-340	429	17	f	f	X
ejpam-340	429	18	-	-	PUNCT
ejpam-340	429	19	manifolds	manifold	NOUN
ejpam-340	429	20	.	.	PUNCT
ejpam-340	430	1	tohoku	tohoku	PROPN
ejpam-340	430	2	math	math	PROPN
ejpam-340	430	3	.	.	PUNCT
ejpam-340	431	1	j.	j.	PROPN
ejpam-340	431	2	22	22	NUM
ejpam-340	431	3	(	(	PUNCT
ejpam-340	431	4	1970	1970	NUM
ejpam-340	431	5	)	)	PUNCT
ejpam-340	431	6	,	,	PUNCT
ejpam-340	431	7	362–370	362–370	NUM
ejpam-340	431	8	.	.	PUNCT
ejpam-340	432	1	[	[	X
ejpam-340	432	2	3	3	NUM
ejpam-340	432	3	]	]	X
ejpam-340	432	4	hit	hit	NOUN
ejpam-340	432	5	,	,	PUNCT
ejpam-340	432	6	r.	r.	VERB
ejpam-340	432	7	on	on	ADP
ejpam-340	432	8	almost	almost	ADV
ejpam-340	432	9	complex	complex	ADJ
ejpam-340	432	10	and	and	CCONJ
ejpam-340	432	11	almost	almost	ADV
ejpam-340	432	12	contact	contact	NOUN
ejpam-340	432	13	manifold	manifold	NOUN
ejpam-340	432	14	.	.	PUNCT
ejpam-340	433	1	revue	revue	PROPN
ejpam-340	433	2	de	de	PROPN
ejpam-340	433	3	faculte	faculte	PROPN
ejpam-340	433	4	des	des	PROPN
ejpam-340	433	5	sciences	sciences	PROPN
ejpam-340	433	6	de	de	X
ejpam-340	433	7	išuniversite	išuniversite	PROPN
ejpam-340	433	8	,	,	PUNCT
ejpam-340	433	9	dšistanbul	dšistanbul	PROPN
ejpam-340	433	10	39	39	NUM
ejpam-340	433	11	,	,	PUNCT
ejpam-340	433	12	a	a	DET
ejpam-340	433	13	(	(	PUNCT
ejpam-340	433	14	1974	1974	NUM
ejpam-340	433	15	)	)	PUNCT
ejpam-340	433	16	,	,	PUNCT
ejpam-340	433	17	1–5	1–5	X
ejpam-340	433	18	.	.	PUNCT
ejpam-340	434	1	[	[	X
ejpam-340	434	2	4	4	NUM
ejpam-340	434	3	]	]	X
ejpam-340	434	4	hsu	hsu	PROPN
ejpam-340	434	5	,	,	PUNCT
ejpam-340	434	6	c.	c.	PROPN
ejpam-340	434	7	j.	j.	PROPN
ejpam-340	434	8	on	on	ADP
ejpam-340	434	9	some	some	DET
ejpam-340	434	10	structures	structure	NOUN
ejpam-340	434	11	which	which	PRON
ejpam-340	434	12	are	be	AUX
ejpam-340	434	13	similar	similar	ADJ
ejpam-340	434	14	to	to	ADP
ejpam-340	434	15	quaternion	quaternion	NOUN
ejpam-340	434	16	structure	structure	NOUN
ejpam-340	434	17	.	.	PUNCT
ejpam-340	435	1	tohoku	tohoku	PROPN
ejpam-340	435	2	math	math	PROPN
ejpam-340	435	3	.	.	PUNCT
ejpam-340	436	1	j.	j.	PROPN
ejpam-340	436	2	12	12	NUM
ejpam-340	436	3	(	(	PUNCT
ejpam-340	436	4	1960	1960	NUM
ejpam-340	436	5	)	)	PUNCT
ejpam-340	436	6	,	,	PUNCT
ejpam-340	436	7	403–428	403–428	NUM
ejpam-340	436	8	.	.	PUNCT
ejpam-340	437	1	[	[	X
ejpam-340	437	2	5	5	NUM
ejpam-340	437	3	]	]	SYM
ejpam-340	437	4	hsuing	hsuing	NOUN
ejpam-340	437	5	,	,	PUNCT
ejpam-340	437	6	c.	c.	PROPN
ejpam-340	437	7	c.	c.	PROPN
ejpam-340	437	8	,	,	PUNCT
ejpam-340	437	9	and	and	CCONJ
ejpam-340	437	10	schanchin	schanchin	PROPN
ejpam-340	437	11	,	,	PUNCT
ejpam-340	437	12	j.	j.	PROPN
ejpam-340	437	13	k.	k.	PROPN
ejpam-340	437	14	affine	affine	PROPN
ejpam-340	437	15	differential	differential	PROPN
ejpam-340	437	16	geometry	geometry	NOUN
ejpam-340	437	17	of	of	ADP
ejpam-340	437	18	closed	closed	ADJ
ejpam-340	437	19	hypersurfaces	hypersurface	NOUN
ejpam-340	437	20	.	.	PUNCT
ejpam-340	438	1	proc	proc	NOUN
ejpam-340	438	2	.	.	PUNCT
ejpam-340	439	1	iond	iond	NOUN
ejpam-340	439	2	.	.	PUNCT
ejpam-340	440	1	math	math	NOUN
ejpam-340	440	2	.	.	PUNCT
ejpam-340	441	1	soc	soc	PROPN
ejpam-340	441	2	.	.	PUNCT
ejpam-340	442	1	17	17	NUM
ejpam-340	442	2	(	(	PUNCT
ejpam-340	442	3	1967	1967	NUM
ejpam-340	442	4	)	)	PUNCT
ejpam-340	442	5	,	,	PUNCT
ejpam-340	443	1	715–735	715–735	NUM
ejpam-340	443	2	.	.	PUNCT
ejpam-340	444	1	[	[	X
ejpam-340	444	2	6	6	NUM
ejpam-340	444	3	]	]	PUNCT
ejpam-340	444	4	kobayasi	kobayasi	PROPN
ejpam-340	444	5	,	,	PUNCT
ejpam-340	444	6	s.	s.	PROPN
ejpam-340	444	7	,	,	PUNCT
ejpam-340	444	8	and	and	CCONJ
ejpam-340	444	9	nomizu	nomizu	PROPN
ejpam-340	444	10	,	,	PUNCT
ejpam-340	444	11	k.	k.	PROPN
ejpam-340	444	12	foudation	foudation	NOUN
ejpam-340	444	13	of	of	ADP
ejpam-340	444	14	differential	differential	ADJ
ejpam-340	444	15	geometry	geometry	NOUN
ejpam-340	444	16	,	,	PUNCT
ejpam-340	444	17	vol	vol	NOUN
ejpam-340	444	18	.	.	PUNCT
ejpam-340	445	1	i	i	PRON
ejpam-340	445	2	,	,	PUNCT
ejpam-340	445	3	reprint	reprint	NOUN
ejpam-340	445	4	of	of	ADP
ejpam-340	445	5	the	the	DET
ejpam-340	445	6	1963	1963	NUM
ejpam-340	445	7	original	original	NOUN
ejpam-340	445	8	.	.	PUNCT
ejpam-340	446	1	willely	willely	ADV
ejpam-340	446	2	classical	classical	ADJ
ejpam-340	446	3	library	library	NOUN
ejpam-340	446	4	,	,	PUNCT
ejpam-340	446	5	john	john	PROPN
ejpam-340	446	6	wiley	wiley	PROPN
ejpam-340	446	7	and	and	CCONJ
ejpam-340	446	8	sons	son	NOUN
ejpam-340	446	9	,	,	PUNCT
ejpam-340	446	10	inc	inc	PROPN
ejpam-340	446	11	.	.	PROPN
ejpam-340	446	12	,	,	PUNCT
ejpam-340	446	13	new	new	PROPN
ejpam-340	446	14	york	york	PROPN
ejpam-340	446	15	,	,	PUNCT
ejpam-340	446	16	1996	1996	NUM
ejpam-340	446	17	.	.	PUNCT
ejpam-340	447	1	[	[	X
ejpam-340	447	2	7	7	NUM
ejpam-340	447	3	]	]	X
ejpam-340	447	4	legrand	legrand	PROPN
ejpam-340	447	5	,	,	PUNCT
ejpam-340	447	6	g.	g.	PROPN
ejpam-340	447	7	on	on	ADP
ejpam-340	447	8	almost	almost	ADV
ejpam-340	447	9	product	product	NOUN
ejpam-340	447	10	,	,	PUNCT
ejpam-340	447	11	almost	almost	ADV
ejpam-340	447	12	decomposable	decomposable	ADJ
ejpam-340	447	13	manifolds	manifold	NOUN
ejpam-340	447	14	.	.	PUNCT
ejpam-340	447	15	indian	indian	PROPN
ejpam-340	447	16	j.	j.	PROPN
ejpam-340	447	17	pure	pure	PROPN
ejpam-340	447	18	and	and	CCONJ
ejpam-340	447	19	app.math	app.math	NUM
ejpam-340	447	20	.	.	PROPN
ejpam-340	448	1	3	3	NUM
ejpam-340	448	2	,	,	PUNCT
ejpam-340	448	3	4	4	NUM
ejpam-340	448	4	(	(	PUNCT
ejpam-340	448	5	1972	1972	NUM
ejpam-340	448	6	)	)	PUNCT
ejpam-340	448	7	,	,	PUNCT
ejpam-340	448	8	632–636	632–636	NUM
ejpam-340	448	9	.	.	PUNCT
ejpam-340	449	1	[	[	X
ejpam-340	449	2	8	8	NUM
ejpam-340	449	3	]	]	X
ejpam-340	449	4	legrand	legrand	PROPN
ejpam-340	449	5	,	,	PUNCT
ejpam-340	449	6	g.	g.	PROPN
ejpam-340	449	7	a	a	DET
ejpam-340	449	8	generalized	generalized	ADJ
ejpam-340	449	9	theory	theory	NOUN
ejpam-340	449	10	of	of	ADP
ejpam-340	449	11	differentiable	differentiable	ADJ
ejpam-340	449	12	structures	structure	NOUN
ejpam-340	449	13	.	.	PUNCT
ejpam-340	450	1	tensor	tensor	NOUN
ejpam-340	450	2	n.s	n.s	PROPN
ejpam-340	450	3	.	.	PROPN
ejpam-340	450	4	31	31	NUM
ejpam-340	450	5	(	(	PUNCT
ejpam-340	450	6	1977	1977	NUM
ejpam-340	450	7	)	)	PUNCT
ejpam-340	450	8	,	,	PUNCT
ejpam-340	450	9	155–164	155–164	NUM
ejpam-340	450	10	.	.	PUNCT
ejpam-340	451	1	[	[	X
ejpam-340	451	2	9	9	NUM
ejpam-340	451	3	]	]	SYM
ejpam-340	451	4	mishra	mishra	PROPN
ejpam-340	451	5	,	,	PUNCT
ejpam-340	451	6	r.	r.	PROPN
ejpam-340	451	7	s.	s.	PROPN
ejpam-340	451	8	almost	almost	ADV
ejpam-340	451	9	contact	contact	NOUN
ejpam-340	451	10	manifold	manifold	ADJ
ejpam-340	451	11	with	with	ADP
ejpam-340	451	12	a	a	DET
ejpam-340	451	13	specified	specify	VERB
ejpam-340	451	14	affine	affine	NOUN
ejpam-340	451	15	connexion	connexion	PROPN
ejpam-340	451	16	iii	iii	PROPN
ejpam-340	451	17	.	.	PROPN
ejpam-340	451	18	colloquim	colloquim	PROPN
ejpam-340	451	19	math	math	NOUN
ejpam-340	451	20	.	.	PUNCT
ejpam-340	452	1	26	26	NUM
ejpam-340	452	2	,	,	PUNCT
ejpam-340	452	3	3	3	NUM
ejpam-340	452	4	(	(	PUNCT
ejpam-340	452	5	1972	1972	NUM
ejpam-340	452	6	)	)	PUNCT
ejpam-340	452	7	,	,	PUNCT
ejpam-340	453	1	218–227	218–227	NUM
ejpam-340	453	2	.	.	PUNCT
ejpam-340	454	1	[	[	X
ejpam-340	454	2	10	10	NUM
ejpam-340	454	3	]	]	X
ejpam-340	454	4	mishra	mishra	PROPN
ejpam-340	454	5	,	,	PUNCT
ejpam-340	454	6	r.	r.	PROPN
ejpam-340	454	7	s.	s.	PROPN
ejpam-340	454	8	almost	almost	ADV
ejpam-340	454	9	contact	contact	NOUN
ejpam-340	454	10	manifold	manifold	ADJ
ejpam-340	454	11	with	with	ADP
ejpam-340	454	12	a	a	DET
ejpam-340	454	13	specified	specify	VERB
ejpam-340	454	14	affine	affine	NOUN
ejpam-340	454	15	connexion	connexion	PROPN
ejpam-340	454	16	ii	ii	PROPN
ejpam-340	454	17	.	.	PROPN
ejpam-340	454	18	journal	journal	PROPN
ejpam-340	454	19	of	of	ADP
ejpam-340	454	20	mathematical	mathematical	ADJ
ejpam-340	454	21	sciences	science	NOUN
ejpam-340	454	22	8	8	NUM
ejpam-340	454	23	(	(	PUNCT
ejpam-340	454	24	1973	1973	NUM
ejpam-340	454	25	)	)	PUNCT
ejpam-340	454	26	,	,	PUNCT
ejpam-340	454	27	63–70	63–70	NUM
ejpam-340	454	28	.	.	PUNCT
ejpam-340	455	1	[	[	X
ejpam-340	455	2	11	11	NUM
ejpam-340	455	3	]	]	X
ejpam-340	455	4	mishra	mishra	PROPN
ejpam-340	455	5	,	,	PUNCT
ejpam-340	455	6	r.	r.	PROPN
ejpam-340	455	7	s.	s.	PROPN
ejpam-340	455	8	on	on	ADP
ejpam-340	455	9	almost	almost	ADV
ejpam-340	455	10	contact	contact	NOUN
ejpam-340	455	11	manifold	manifold	NOUN
ejpam-340	455	12	.	.	PUNCT
ejpam-340	456	1	indian	indian	PROPN
ejpam-340	456	2	j.	j.	PROPN
ejpam-340	456	3	pure	pure	PROPN
ejpam-340	456	4	and	and	CCONJ
ejpam-340	456	5	app.math	app.math	NUM
ejpam-340	456	6	.	.	PROPN
ejpam-340	457	1	5	5	NUM
ejpam-340	457	2	,	,	PUNCT
ejpam-340	457	3	2	2	NUM
ejpam-340	457	4	(	(	PUNCT
ejpam-340	457	5	1974	1974	NUM
ejpam-340	457	6	)	)	PUNCT
ejpam-340	457	7	,	,	PUNCT
ejpam-340	458	1	156–164	156–164	NUM
ejpam-340	458	2	.	.	PUNCT
ejpam-340	459	1	[	[	X
ejpam-340	459	2	12	12	NUM
ejpam-340	459	3	]	]	X
ejpam-340	459	4	mishra	mishra	PROPN
ejpam-340	459	5	,	,	PUNCT
ejpam-340	459	6	r.	r.	PROPN
ejpam-340	459	7	s.	s.	PROPN
ejpam-340	459	8	structure	structure	PROPN
ejpam-340	459	9	on	on	ADP
ejpam-340	459	10	a	a	DET
ejpam-340	459	11	differentiable	differentiable	ADJ
ejpam-340	459	12	manifold	manifold	NOUN
ejpam-340	459	13	and	and	CCONJ
ejpam-340	459	14	their	their	PRON
ejpam-340	459	15	application	application	NOUN
ejpam-340	459	16	,	,	PUNCT
ejpam-340	459	17	.	.	PUNCT
ejpam-340	460	1	chandrma	chandrma	PROPN
ejpam-340	460	2	prakashan	prakashan	PROPN
ejpam-340	460	3	,	,	PUNCT
ejpam-340	460	4	allahabad	allahabad	PROPN
ejpam-340	460	5	,	,	PUNCT
ejpam-340	460	6	india	india	PROPN
ejpam-340	460	7	,	,	PUNCT
ejpam-340	460	8	1984	1984	NUM
ejpam-340	460	9	.	.	PUNCT
ejpam-340	461	1	[	[	X
ejpam-340	461	2	13	13	NUM
ejpam-340	461	3	]	]	SYM
ejpam-340	461	4	mishra	mishra	PROPN
ejpam-340	461	5	,	,	PUNCT
ejpam-340	461	6	r.	r.	PROPN
ejpam-340	461	7	s.	s.	PROPN
ejpam-340	461	8	,	,	PUNCT
ejpam-340	461	9	and	and	CCONJ
ejpam-340	461	10	singh	singh	PROPN
ejpam-340	461	11	,	,	PUNCT
ejpam-340	461	12	s.	s.	PROPN
ejpam-340	461	13	d.	d.	PROPN
ejpam-340	461	14	on	on	ADP
ejpam-340	461	15	gf	gf	NOUN
ejpam-340	461	16	-	-	NOUN
ejpam-340	461	17	structure	structure	NOUN
ejpam-340	461	18	.	.	PUNCT
ejpam-340	462	1	indian	indian	PROPN
ejpam-340	462	2	j.	j.	PROPN
ejpam-340	462	3	pure	pure	PROPN
ejpam-340	462	4	and	and	CCONJ
ejpam-340	462	5	app.math	app.math	PROPN
ejpam-340	462	6	.	.	PROPN
ejpam-340	463	1	6	6	NUM
ejpam-340	463	2	,	,	PUNCT
ejpam-340	463	3	1	1	NUM
ejpam-340	463	4	(	(	PUNCT
ejpam-340	463	5	1975	1975	NUM
ejpam-340	463	6	)	)	PUNCT
ejpam-340	463	7	,	,	PUNCT
ejpam-340	463	8	1317–1325	1317–1325	NUM
ejpam-340	463	9	.	.	PUNCT
ejpam-340	464	1	[	[	X
ejpam-340	464	2	14	14	NUM
ejpam-340	464	3	]	]	SYM
ejpam-340	464	4	nomizu	nomizu	PROPN
ejpam-340	464	5	,	,	PUNCT
ejpam-340	464	6	k.	k.	PROPN
ejpam-340	464	7	on	on	ADP
ejpam-340	464	8	hypersurfaces	hypersurface	NOUN
ejpam-340	464	9	satisfying	satisfy	VERB
ejpam-340	464	10	a	a	DET
ejpam-340	464	11	certain	certain	ADJ
ejpam-340	464	12	condition	condition	NOUN
ejpam-340	464	13	on	on	ADP
ejpam-340	464	14	the	the	DET
ejpam-340	464	15	curvature	curvature	NOUN
ejpam-340	464	16	tensor	tensor	NOUN
ejpam-340	464	17	.	.	PUNCT
ejpam-340	465	1	tohoku	tohoku	PROPN
ejpam-340	465	2	,	,	PUNCT
ejpam-340	465	3	math	math	NOUN
ejpam-340	465	4	.	.	PUNCT
ejpam-340	466	1	j.	j.	PROPN
ejpam-340	466	2	20	20	NUM
ejpam-340	466	3	(	(	PUNCT
ejpam-340	466	4	1968	1968	NUM
ejpam-340	466	5	)	)	PUNCT
ejpam-340	466	6	,	,	PUNCT
ejpam-340	466	7	46–59	46–59	PROPN
ejpam-340	466	8	.	.	PUNCT
ejpam-340	467	1	references	reference	NOUN
ejpam-340	467	2	852	852	NUM
ejpam-340	467	3	[	[	SYM
ejpam-340	467	4	15	15	NUM
ejpam-340	467	5	]	]	X
ejpam-340	467	6	obata	obata	NOUN
ejpam-340	467	7	,	,	PUNCT
ejpam-340	467	8	m.	m.	NOUN
ejpam-340	467	9	affine	affine	NOUN
ejpam-340	467	10	connexions	connexion	NOUN
ejpam-340	467	11	on	on	ADP
ejpam-340	467	12	manifolds	manifold	NOUN
ejpam-340	467	13	with	with	ADP
ejpam-340	467	14	almost	almost	ADV
ejpam-340	467	15	complex	complex	ADJ
ejpam-340	467	16	,	,	PUNCT
ejpam-340	467	17	quaternian	quaternian	NOUN
ejpam-340	467	18	or	or	CCONJ
ejpam-340	467	19	hermition	hermition	NOUN
ejpam-340	467	20	structure	structure	NOUN
ejpam-340	467	21	.	.	PUNCT
ejpam-340	468	1	japan	japan	PROPN
ejpam-340	468	2	j.	j.	PROPN
ejpam-340	468	3	math	math	PROPN
ejpam-340	468	4	.	.	PUNCT
ejpam-340	469	1	26	26	NUM
ejpam-340	469	2	(	(	PUNCT
ejpam-340	469	3	1956	1956	NUM
ejpam-340	469	4	)	)	PUNCT
ejpam-340	469	5	,	,	PUNCT
ejpam-340	469	6	43–77	43–77	NUM
ejpam-340	469	7	.	.	PUNCT
ejpam-340	470	1	[	[	X
ejpam-340	470	2	16	16	NUM
ejpam-340	470	3	]	]	X
ejpam-340	470	4	sasaki	sasaki	PROPN
ejpam-340	470	5	,	,	PUNCT
ejpam-340	470	6	s.	s.	PROPN
ejpam-340	470	7	on	on	ADP
ejpam-340	470	8	differentiable	differentiable	ADJ
ejpam-340	470	9	manifolds	manifold	NOUN
ejpam-340	470	10	with	with	ADP
ejpam-340	470	11	certain	certain	ADJ
ejpam-340	470	12	structure	structure	NOUN
ejpam-340	470	13	which	which	PRON
ejpam-340	470	14	is	be	AUX
ejpam-340	470	15	closely	closely	ADV
ejpam-340	470	16	related	related	ADJ
ejpam-340	470	17	to	to	ADP
ejpam-340	470	18	almost	almost	ADV
ejpam-340	470	19	contact	contact	VERB
ejpam-340	470	20	structures	structure	NOUN
ejpam-340	470	21	i.	i.	PROPN
ejpam-340	470	22	tohoku	tohoku	PROPN
ejpam-340	470	23	math	math	PROPN
ejpam-340	470	24	.	.	PUNCT
ejpam-340	471	1	j.	j.	PROPN
ejpam-340	471	2	12	12	NUM
ejpam-340	471	3	(	(	PUNCT
ejpam-340	471	4	1960	1960	NUM
ejpam-340	471	5	)	)	PUNCT
ejpam-340	471	6	,	,	PUNCT
ejpam-340	471	7	459–476	459–476	NUM
ejpam-340	471	8	.	.	PUNCT
ejpam-340	472	1	[	[	X
ejpam-340	472	2	17	17	NUM
ejpam-340	472	3	]	]	X
ejpam-340	472	4	sasaki	sasaki	PROPN
ejpam-340	472	5	,	,	PUNCT
ejpam-340	472	6	s.	s.	PROPN
ejpam-340	472	7	,	,	PUNCT
ejpam-340	472	8	and	and	CCONJ
ejpam-340	472	9	hatakeyama	hatakeyama	PROPN
ejpam-340	472	10	,	,	PUNCT
ejpam-340	472	11	y.	y.	NOUN
ejpam-340	472	12	on	on	ADP
ejpam-340	472	13	differentiable	differentiable	ADJ
ejpam-340	472	14	manifolds	manifold	NOUN
ejpam-340	472	15	with	with	ADP
ejpam-340	472	16	contact	contact	NOUN
ejpam-340	472	17	metric	metric	ADJ
ejpam-340	472	18	structures	structure	NOUN
ejpam-340	472	19	.	.	PUNCT
ejpam-340	473	1	j.	j.	PROPN
ejpam-340	473	2	math	math	PROPN
ejpam-340	473	3	.	.	PUNCT
ejpam-340	474	1	soc	soc	PROPN
ejpam-340	474	2	.	.	PUNCT
ejpam-340	475	1	japan	japan	PROPN
ejpam-340	475	2	14	14	NUM
ejpam-340	475	3	(	(	PUNCT
ejpam-340	475	4	1962	1962	NUM
ejpam-340	475	5	)	)	PUNCT
ejpam-340	475	6	,	,	PUNCT
ejpam-340	475	7	249–271	249–271	NUM
ejpam-340	475	8	.	.	PUNCT
ejpam-340	476	1	[	[	X
ejpam-340	476	2	18	18	NUM
ejpam-340	476	3	]	]	PUNCT
ejpam-340	476	4	on	on	ADP
ejpam-340	476	5	affine	affine	NOUN
ejpam-340	476	6	connexions	connexion	NOUN
ejpam-340	476	7	in	in	ADP
ejpam-340	476	8	almost	almost	ADV
ejpam-340	476	9	complex	complex	ADJ
ejpam-340	476	10	manifold	manifold	ADJ
ejpam-340	476	11	.	.	PUNCT
ejpam-340	477	1	indian	indian	PROPN
ejpam-340	477	2	j.	j.	PROPN
ejpam-340	477	3	pure	pure	PROPN
ejpam-340	477	4	and	and	CCONJ
ejpam-340	477	5	app.math	app.math	PROPN
ejpam-340	477	6	.	.	PROPN
ejpam-340	478	1	6	6	NUM
ejpam-340	478	2	,	,	PUNCT
ejpam-340	478	3	3	3	NUM
ejpam-340	478	4	(	(	PUNCT
ejpam-340	478	5	1975	1975	NUM
ejpam-340	478	6	)	)	PUNCT
ejpam-340	478	7	,	,	PUNCT
ejpam-340	478	8	247–252	247–252	NUM
ejpam-340	478	9	.	.	PUNCT