Existence and uniqueness of Chern connection in the Klein-Grifone approach

TL;DR

This paper establishes the global existence and uniqueness of the Chern connection within the Klein-Grifone framework of Finsler geometry, analyzing its properties and comparing it with other classical connections.

Contribution

It provides the first global existence and uniqueness theorem for the Chern connection in the Klein-Grifone approach, including detailed properties and identities.

Findings

Derived torsion and curvature tensors of the Chern connection

Proved Bianchi identities for the Chern connection

Compared Chern, Berwald, and Cartan connections

Abstract

The Klein-Grifone approach to global Finsler geometry is adopted. A global existence and uniqueness theorem for Chern connection is formulated and proved. The torsion and curvature tensors of Chern connection are derived. Some properties and the Bianchi identities for this connection are investigated. A concise comparison between Berwald, Cartan and Chern connections is presented.