Foliations admitting transverse systems of differential equations
Robert Wolak (1988)
Compositio Mathematica
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Robert Wolak (1988)
Compositio Mathematica
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Nina Zhukova, Anna Dolgonosova (2013)
Open Mathematics
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The category of foliations is considered. In this category morphisms are differentiable maps sending leaves of one foliation into leaves of the other foliation. We prove that the automorphism group of a foliation with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. This result extends the corresponding result of Macias-Virgós and Sanmartín Carbón for Riemannian foliations. In particular, our result is valid for Lorentzian and pseudo-Riemannian...
Molino, Pierre
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Włodzimierz M. Mikulski (1992)
Mathematica Bohemica
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A classification of natural liftings of foliations to the tangent bundle is given.
Robert A. Wolak (1989)
Publicacions Matemàtiques
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In this short note we find some conditions which ensure that a G foliation of finite type with all leaves compact is a Riemannian foliation of equivalently the space of leaves of such a foliation is a Satake manifold. A particular attention is paid to transversaly affine foliations. We present several conditions which ensure completeness of such foliations.