Journal of Mathematical Sciences

, Volume 219, Issue 1, pp 112–124 | Cite as

Typical Properties of Leaves of Cartan Foliations with Ehresmann Connection

  • N. I. ZhukovaEmail author

We consider a Cartan foliation (M,F) of an arbitrary codimension q admitting an Ehresmann connection such that all leaves of (M,F) are embedded submanifolds of M. We prove that for any foliation (M,F) there exists an open, not necessarily connected, saturated, and everywhere dense subset M0 of M and a manifold L0 such that the induced foliation (M0, FM0) is formed by the fibers of a locally trivial fibration with the standard fiber L0 over (possibly, non-Hausdorff) smooth q-dimensional manifold. In the case of codimension 1, the induced foliation on each connected component of the manifold M0 is formed by the fibers of a locally trivial fibration over a circle or over a line.


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsNizhny NovgorodRussia

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