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Generalizations of Frobenius’ Theorem on Manifolds and Subcartesian Spaces
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Research Article
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- Copyright © Canadian Mathematical Society 2007
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