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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Existence of smooth invariant measures for geodesic flows of foliations of Riemannian manifolds


Author: PawełG. Walczak
Journal: Proc. Amer. Math. Soc. 120 (1994), 903-906
MSC: Primary 58F18; Secondary 57R30, 58F17
DOI: https://doi.org/10.1090/S0002-9939-1994-1227531-6
MathSciNet review: 1227531
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Abstract: We construct a nontrivial smooth finite measure invariant under the geodesic flow of a foliation $ \mathcal{F}$ of a compact Riemannian manifold $ M$ assuming that the transverse mean curvature of $ \mathcal{F}$ is distributed "nicely" along some leaf geodesics.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1227531-6
Keywords: Foliation, Riemannian manifold, geodesic flow, invariant measure, entropy
Article copyright: © Copyright 1994 American Mathematical Society