Geometric Objects Associated with the Fundamental Connections in Finsler Geometry

The aim of the present paper is to provide an intrinsic investigation of the fundamental properties of the most important geometric objects associated with the fundamental linear connections on a Finsler manifold. We introduce and investigate intrinsically the most general properties concerning the torsion tensor fields and the curvature tensor fields associated with a certain regular connection on the pullback bundle. These properties play a key role in obtaining other results concerning the fundamental properties of the most important geometric objects associated with the fundamental connections on the pullback bundle of a Finsler manifold (M,L), namely, the Cartan connection, the Chern connection, the Hashiguchi connection and the Berwald 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.