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

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 most important features of L. Bérard-Bergery’s classification results for odd-dimensional positively curved Riemannian homogeneous spaces can be generalized to reversible Finsler spaces.