Author:
Zhukova Nina,Dolgonosova Anna
Abstract
AbstractThe 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 foliations.
Reference16 articles.
1. Bel’ko I.V., Affine transformations of a transversal projectable connection of a manifold with a foliation, Math. USSRSb., 1983, 45, 191–204
2. Besse A.L., Einstein Manifolds, Classics Math., Springer, Berlin, 2008
3. Kamber F.W., Tondeur P., G-foliations and their characteristic classes, Bull. Amer. Math. Soc., 1978, 84(6), 1086–1124
4. Kobayashi S., Nomizu K., Foundations of Differential Geometry I, Interscience, New York-London, 1963
5. Kriegl A., Michor P.W., Aspects of the theory of infinite-dimensional manifolds, Differential Geom. Appl., 1991, 1(2), 159–176
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