A classification of some Finsler connections and their applications

TL;DR

This paper classifies various Finsler connections based on their curvature properties, emphasizing the role of the Cartan tensor, and explores their applications in understanding different Finsler structures.

Contribution

It introduces a unified classification scheme for Finsler connections using curvature conditions and highlights their practical applications.

Findings

Vanishing hv-curvature characterizes Landsbergian, Berwaldian, and Riemannian structures.

Provides a comprehensive classification of Finsler connections.

Demonstrates applications in Finsler geometry analysis.

Abstract

Some general Finsler connections are defined. Emphasis is being made on the Cartan tensor and its derivatives. Vanishing of the hv-curvature tensors of these connections characterizes Landsbergian, Berwaldian as well as Riemannian structures. This view point makes it possible to give a smart representation of connection theory in Finsler geometry and yields to a classification of Finsler connections. Some practical applications of these connections are also considered.