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 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.