The existence and uniqueness of Hashiguchi connection in KG-approach

TL;DR

This paper investigates the existence and uniqueness of the Hashiguchi connection within intrinsic Finsler geometry using the Klein-Grifone approach, providing a coordinate-free proof and analyzing its geometric properties.

Contribution

It establishes a coordinate-free existence and uniqueness theorem for the Hashiguchi connection in Finsler geometry via the KG-approach, including detailed tensor calculations.

Findings

Proved the existence and uniqueness of the Hashiguchi connection.

Analyzed torsion and curvature tensors of the connection.

Compared fundamental linear connections in Finsler geometry.

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.