Poincaré's Lemma on Heisenberg Groups

碩士 === 輔仁大學 === 數學系碩士班 === 105 === Let X1, Y1, X2, and Y2 be Heisenberg vector fields on 5-manifold. Given smooth functions a1, b1, a2, and b2 on 5-manifold, an intergrability condition is proved to be as a necessary and sufficient condition of the solvability to the sub-Riemannian system X1f = a1,...

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Main Authors:	LIN, YI-SHAN, 林億珊
Other Authors:	YANG, NAN-PING
Format:	Others
Language:	en_US
Published:	2017
Online Access:	http://ndltd.ncl.edu.tw/handle/4rwyt2

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spelling	ndltd-TW-105FJU004790012019-05-15T23:24:31Z http://ndltd.ncl.edu.tw/handle/4rwyt2 Poincaré's Lemma on Heisenberg Groups 海森堡群的龐加萊引理 LIN, YI-SHAN 林億珊碩士輔仁大學數學系碩士班 105 Let X1, Y1, X2, and Y2 be Heisenberg vector fields on 5-manifold. Given smooth functions a1, b1, a2, and b2 on 5-manifold, an intergrability condition is proved to be as a necessary and sufficient condition of the solvability to the sub-Riemannian system X1f = a1, Y1f = b1, X2f = a2, and Y2f = b2. In addition, the solution f of the system is given in an integral form and is just described as the work done by the force field a1X1 + b1Y1 + a2X2 + b2Y2 along any horizontal curve from the origin to the current point. YANG, NAN-PING 楊南屏 2017 學位論文 ; thesis 27 en_US
collection	NDLTD
language	en_US
format	Others
sources	NDLTD
description	碩士 === 輔仁大學 === 數學系碩士班 === 105 === Let X1, Y1, X2, and Y2 be Heisenberg vector fields on 5-manifold. Given smooth functions a1, b1, a2, and b2 on 5-manifold, an intergrability condition is proved to be as a necessary and sufficient condition of the solvability to the sub-Riemannian system X1f = a1, Y1f = b1, X2f = a2, and Y2f = b2. In addition, the solution f of the system is given in an integral form and is just described as the work done by the force field a1X1 + b1Y1 + a2X2 + b2Y2 along any horizontal curve from the origin to the current point.
author2	YANG, NAN-PING
author_facet	YANG, NAN-PING LIN, YI-SHAN 林億珊
author	LIN, YI-SHAN 林億珊
spellingShingle	LIN, YI-SHAN 林億珊 Poincaré's Lemma on Heisenberg Groups
author_sort	LIN, YI-SHAN
title	Poincaré's Lemma on Heisenberg Groups
title_short	Poincaré's Lemma on Heisenberg Groups
title_full	Poincaré's Lemma on Heisenberg Groups
title_fullStr	Poincaré's Lemma on Heisenberg Groups
title_full_unstemmed	Poincaré's Lemma on Heisenberg Groups
title_sort	poincaré's lemma on heisenberg groups
publishDate	2017
url	http://ndltd.ncl.edu.tw/handle/4rwyt2
work_keys_str_mv	AT linyishan poincareslemmaonheisenberggroups AT línyìshān poincareslemmaonheisenberggroups AT linyishan hǎisēnbǎoqúndepángjiāláiyǐnlǐ AT línyìshān hǎisēnbǎoqúndepángjiāláiyǐnlǐ
_version_	1719145650687311872

Poincaré's Lemma on Heisenberg Groups

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