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Sib. J. Pure and Appl. Math., 2017, Volume 17, Issue 1, Pages 73–77 (Mi vngu431)  

A lemma on Lie bracket under insufficient smoothness

K. V. Storozhukab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: Let two vector fields on a $C^2$-variety $M$ be tangent to a $C^1$-submanifold $F\subset M$. We show if that these fields are differentiable at a point $p\in F$, then their Lie bracket is also tangent to $F$. This statement is a weakening of the “easy part” assumptions of the Frobenius theorem.

Keywords: Lie bracket.

DOI: https://doi.org/10.17377/PAM.2017.17.106

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UDC: 514.763.22
Received: 10.08.2016

Citation: K. V. Storozhuk, “A lemma on Lie bracket under insufficient smoothness”, Sib. J. Pure and Appl. Math., 17:1 (2017), 73–77

Citation in format AMSBIB
\Bibitem{Sto17}
\by K.~V.~Storozhuk
\paper A lemma on Lie bracket under insufficient smoothness
\jour Sib. J. Pure and Appl. Math.
\yr 2017
\vol 17
\issue 1
\pages 73--77
\mathnet{http://mi.mathnet.ru/vngu431}
\crossref{https://doi.org/10.17377/PAM.2017.17.106}


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