Geometric objects associated with the fundamental connections in Finsler geometry

Abstract

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.

Abstract and Introduction changed, Changes and corrections throughout the paper

References in corpus (1)

• Cartan and Berwald connections in the pullback formalism

Cited by in corpus (9)

• On Concircularly Recurrent Finsler Manifolds
• Some Types of Recurrence in Finsler geometry
• Characterization of Finsler Spaces of Scalar Curvature
• Intrinsic Theory of Projective Changes in Finsler Geometry
• Coordinate-free study of Finsler spaces of $H_p$-scalar curvature
• A note on "Sur le noyau de l'opérateur de courbure d'une variété finslérienne" [C. R. Acad. Sci. Paris, t. 272 (1971), 807-810]
• New Special Finsler Spaces
• Conformal change of special Finsler spaces
• On Hyper-Generalized Recurrent Finsler Spaces