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Generalizations of Frobenius’ Theorem on Manifolds and Subcartesian Spaces

Published online by Cambridge University Press:  20 November 2018

Jędrzej Śniatycki
Jędrzej Śniatycki*
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, AB, T2N 1N4
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Abstract

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Let $\mathcal{F}$ be a family of vector fields on a manifold or a subcartesian space spanning a distribution $D.$ We prove that an orbit $O$ of $\mathcal{F}$ is an integral manifold of $D$ if $D$ is involutive on $O$ and it has constant rank on $O$. This result implies Frobenius’ theorem, and its various generalizations, on manifolds as well as on subcartesian spaces.

Keywords

58A3058A40differential spacesgeneralized distributionsorbitsFrobenius’ theoremSussmann's theorem
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 3 , 01 September 2007 , pp. 447 - 459
Copyright
Copyright © Canadian Mathematical Society 2007

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