id	sid	tid	token	lemma	pos
sb397655p81	1	1	mean	mean	VERB
sb397655p81	1	2	curvature	curvature	NOUN
sb397655p81	1	3	flow	flow	NOUN
sb397655p81	1	4	describes	describe	VERB
sb397655p81	1	5	the	the	DET
sb397655p81	1	6	process	process	NOUN
sb397655p81	1	7	by	by	ADP
sb397655p81	1	8	which	which	PRON
sb397655p81	1	9	a	a	DET
sb397655p81	1	10	submanifold	submanifold	NOUN
sb397655p81	1	11	is	be	AUX
sb397655p81	1	12	deformed	deform	VERB
sb397655p81	1	13	in	in	ADP
sb397655p81	1	14	the	the	DET
sb397655p81	1	15	direction	direction	NOUN
sb397655p81	1	16	of	of	ADP
sb397655p81	1	17	its	its	PRON
sb397655p81	1	18	mean	mean	ADJ
sb397655p81	1	19	curvature	curvature	NOUN
sb397655p81	1	20	vector	vector	NOUN
sb397655p81	1	21	.	.	PUNCT
sb397655p81	2	1	a	a	DET
sb397655p81	2	2	polar	polar	ADJ
sb397655p81	2	3	action	action	NOUN
sb397655p81	2	4	is	be	AUX
sb397655p81	2	5	noteworthy	noteworthy	ADJ
sb397655p81	2	6	in	in	ADP
sb397655p81	2	7	this	this	DET
sb397655p81	2	8	context	context	NOUN
sb397655p81	2	9	because	because	SCONJ
sb397655p81	2	10	it	it	PRON
sb397655p81	2	11	admits	admit	VERB
sb397655p81	2	12	complete	complete	ADJ
sb397655p81	2	13	submanifolds	submanifold	NOUN
sb397655p81	2	14	called	call	VERB
sb397655p81	2	15	sections	section	NOUN
sb397655p81	2	16	that	that	PRON
sb397655p81	2	17	intersect	intersect	VERB
sb397655p81	2	18	each	each	DET
sb397655p81	2	19	orbit	orbit	NOUN
sb397655p81	2	20	orthogonally	orthogonally	ADV
sb397655p81	2	21	.	.	PUNCT
sb397655p81	3	1	the	the	DET
sb397655p81	3	2	mean	mean	ADJ
sb397655p81	3	3	curvature	curvature	NOUN
sb397655p81	3	4	vector	vector	NOUN
sb397655p81	3	5	of	of	ADP
sb397655p81	3	6	a	a	DET
sb397655p81	3	7	polar	polar	ADJ
sb397655p81	3	8	orbit	orbit	NOUN
sb397655p81	3	9	is	be	AUX
sb397655p81	3	10	tangent	tangent	NOUN
sb397655p81	3	11	to	to	ADP
sb397655p81	3	12	this	this	DET
sb397655p81	3	13	section	section	NOUN
sb397655p81	3	14	,	,	PUNCT
sb397655p81	3	15	so	so	CCONJ
sb397655p81	3	16	the	the	DET
sb397655p81	3	17	problem	problem	NOUN
sb397655p81	3	18	of	of	ADP
sb397655p81	3	19	solving	solve	VERB
sb397655p81	3	20	for	for	ADP
sb397655p81	3	21	the	the	DET
sb397655p81	3	22	flow	flow	NOUN
sb397655p81	3	23	of	of	ADP
sb397655p81	3	24	these	these	DET
sb397655p81	3	25	orbits	orbit	NOUN
sb397655p81	3	26	reduces	reduce	VERB
sb397655p81	3	27	to	to	ADP
sb397655p81	3	28	solving	solve	VERB
sb397655p81	3	29	a	a	DET
sb397655p81	3	30	system	system	NOUN
sb397655p81	3	31	of	of	ADP
sb397655p81	3	32	ordinary	ordinary	ADJ
sb397655p81	3	33	dierential	dierential	ADJ
sb397655p81	3	34	equations	equation	NOUN
sb397655p81	3	35	over	over	ADP
sb397655p81	3	36	a	a	DET
sb397655p81	3	37	section	section	NOUN
sb397655p81	3	38	.	.	PUNCT
sb397655p81	4	1	for	for	ADP
sb397655p81	4	2	this	this	DET
sb397655p81	4	3	reason	reason	NOUN
sb397655p81	4	4	the	the	DET
sb397655p81	4	5	symmetry	symmetry	NOUN
sb397655p81	4	6	properties	property	NOUN
sb397655p81	4	7	of	of	ADP
sb397655p81	4	8	a	a	DET
sb397655p81	4	9	section	section	NOUN
sb397655p81	4	10	may	may	AUX
sb397655p81	4	11	be	be	AUX
sb397655p81	4	12	used	use	VERB
sb397655p81	4	13	to	to	PART
sb397655p81	4	14	construct	construct	VERB
sb397655p81	4	15	the	the	DET
sb397655p81	4	16	possible	possible	ADJ
sb397655p81	4	17	flow	flow	NOUN
sb397655p81	4	18	lines	line	NOUN
sb397655p81	4	19	and	and	CCONJ
sb397655p81	4	20	predict	predict	VERB
sb397655p81	4	21	which	which	DET
sb397655p81	4	22	points	point	NOUN
sb397655p81	4	23	are	be	AUX
sb397655p81	4	24	invariant	invariant	ADJ
sb397655p81	4	25	under	under	ADP
sb397655p81	4	26	the	the	DET
sb397655p81	4	27	flow	flow	NOUN
sb397655p81	4	28	.	.	PUNCT
sb397655p81	5	1	the	the	DET
sb397655p81	5	2	corresponding	correspond	VERB
sb397655p81	5	3	orbits	orbit	NOUN
sb397655p81	5	4	are	be	AUX
sb397655p81	5	5	minimal	minimal	ADJ
sb397655p81	5	6	submanifolds	submanifold	NOUN
sb397655p81	5	7	.	.	PUNCT