On globally Symmetric Finsler spaces

TL;DR

This paper investigates globally symmetric Finsler spaces, establishing conditions for their symmetry, representing them as coset spaces of Lie groups with invariant metrics, and proving they are necessarily Berwaldian.

Contribution

It provides new conditions characterizing globally symmetric Finsler spaces and demonstrates their structure as coset spaces with invariant metrics, also proving their Berwaldian property.

Findings

Globally symmetric Finsler spaces can be expressed as coset spaces of Lie groups.

Such spaces admit invariant Finsler metrics.

They are necessarily Berwaldian.

Abstract

The paper consider the symmetric of Finsler spaces. We give some conditions about globally symmetric Finsler spaces. Then we prove that these spaces can be written as a coset space of Lie group with an invariant Finsler metric. Finally, we prove that such a space must be Berwaldian