Geodesic
Generalizations of Frobenius’ Theorem on Manifolds and Subcartesian Spaces
Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 447-459

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DOI

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.
DOI : 10.4153/CMB-2007-044-2
Mots-clés : 58A30, 58A40, differential spaces, generalized distributions, orbits, Frobenius’ theorem, Sussmann's theorem 
Śniatycki, Jędrzej. Generalizations of Frobenius’ Theorem on Manifolds and Subcartesian Spaces. Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 447-459. doi: 10.4153/CMB-2007-044-2
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     title = {Generalizations of {Frobenius{\textquoteright}} {Theorem} on {Manifolds} and {Subcartesian} {Spaces}},
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