The existence and uniqueness of Hashiguchi connection in KG-approach

Abstract

In this study, we treat intrinsic Finsler geometry using the Klein-Grifone approach (KG-approach). A uniqueness and existence theorem for the Hashiguchi connection on a Finsler manifold is investigated intrinsically (in coordinate-free fashion). Calculations are made for the Hashiguchi connection's torsion and curvature tensors. Some properties are examined, together with the Bianchi identities of the associated curvature and torsion tensors. An overview of the four fundamental linear connections in Finsler geometry in the KG-approach is provided globally for comparison's sake and completeness.