Geometric objects associated with the fundamental connections in Finsler geometry

Details Geometric objects associated with the fundamental connections in Finsler geometry Geometric objects associated with the fundamental connections in Finsler geometry

2008-05-16

arxiv.org/abs/0805.2489v2

J. Egypt. Math. Soc., 18(1) (2010), 67-90

Mathematics

Differential Geometry

Abstract and Introduction changed, Changes and corrections throughout the paper

Scientific paper

The aim of the present paper is to provide an \emph{intrinsic} investigation of the properties of the most important geometric objects associated with the fundamental linear connections in Finsler geometry. We investigate intrinsically the most general relations concerning the torsion tensor fields and the curvature tensor fields associated with a given regular connection on the pullback bundle of a Finsler manifold. These relations, in turn, play a key role in obtaining other interesting results concerning the properties of the most important geometric objects associated with the fundamental canonical linear connections on the pullback bundle of a Finsler manifold, namely, the Cartan connection, the Berwald connection, the Chern (Rund) connection and the Hashiguchi connection. For the sake of completeness and for comparison reasons, we provide an appendix presenting a global survey of canonical linear connections in Finsler geometry and the fundamental geometric objects associated with them.

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