New Finsler Package

TL;DR

This paper introduces an improved Finsler geometry software package that fixes previous issues, extends capabilities to multiple connections and dimensions, and simplifies tensor calculations, enhancing computational tools in Finsler geometry.

Contribution

The authors develop a new Finsler package that addresses previous limitations, supports various connections and dimensions, and simplifies tensor expressions, advancing computational methods in Finsler geometry.

Findings

Corrected hv-curvature calculations in the package

Extended package to arbitrary dimensions and multiple connections

Simplified tensor expression computations

Abstract

The book "Handbook of Finsler geometry" has been included with a CD containing an elegant Maple package, FINSLER, for calculations in Finsler geometry. Using this package, an example concerning a Finsler generalization of Einstein's vacuum field equations was treated. In this example, the calculation of the components of the hv-curvature of Cartan connection leads to wrong expressions. On the other hand, the FINSLER package works only in dimension four. We introduce a new Finsler package in which we fix the two problems and solve them. Moreover, we extend this package to compute not only the geometric objects associated with Cartan connection but also those associated with Berwald, Chern and Hashiguchi connections in any dimension. These improvements have been illustrated by a concrete example. Furthermore, the problem of simplifying tensor expressions is treated. This paper is intended to make calculations in Finsler geometry more easier and simpler.