A class of Finsler metrics admitting first integrals

TL;DR

This paper characterizes a specific class of Finsler metrics that admit first integrals using two non-Riemannian curvature tensors, expanding understanding of their geometric properties.

Contribution

It introduces a novel characterization of Finsler metrics with first integrals through the use of $ ext{chi}$-curvature and mean Berwald curvature tensors.

Findings

Identification of a new class of Finsler metrics with first integrals

Use of $ ext{chi}$-curvature and mean Berwald curvature for characterization

Advancement in understanding Finsler geometric structures

Abstract

We use two non-Riemannian curvature tensors, the $\chi$-curvature and the mean Berwald curvature to characterise a class of Finsler metrics admitting first integrals.