Towards the classification of odd dimensional homogeneous reversible Finsler spaces with positive flag curvature

TL;DR

This paper classifies odd-dimensional homogeneous reversible Finsler spaces with positive flag curvature, extending known Riemannian results to the Finsler setting using a flag curvature formula.

Contribution

It generalizes the classification of positively curved homogeneous spaces from Riemannian to reversible Finsler geometry for odd dimensions.

Findings

Most features of Bérard-Bergery's Riemannian classification are extended to Finsler spaces.

The classification includes all odd-dimensional homogeneous reversible Finsler spaces with positive flag curvature.

Abstract

In this paper, we use the flag curvature formula for homogeneous Finsler spaces in our previous work to classify odd dimensional smooth coset spaces admitting positively curved reversible homogeneous Finsler metrics. We will show that the most features of L. B\'{e}rard-Bergery's classification results for odd dimensional positively curved Riemannian homogeneous spaces can be generalized to reversible Finsler spaces.