A class of metrics and foliations on tangent bundle of Finsler manifolds

Abstract

Let (M,F) be a Finsler manifold, and let TM₀ be the slit tangent bundle of M with a generalized Riemannian metric G, which is induced by F. In this paper, we extract many natural foliations of (TM₀,G) and study their geometric properties. Next, we use this approach to obtain new characterizations of Finsler manifolds with positive constant flag curvature. We also investigate the relations between Levi-Civita connection, Cartan connection, Vaisman connection, vertical foliation, and Reinhart spaces.

Keywords

Finsler manifold / foliation / constant flag curvature / Vaisman connection

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Higher Education Press and Springer-Verlag Berlin Heidelberg