Very standard homogeneous Finsler manifolds with positive flag curvature

Abstract

In this paper, we consider a homogeneous manifold $G/H$ in which $G$ is a compact connected simply connected simple Lie group and $H$ is a closed connected subgroup of $G$. We define standard and very standard homogeneous Finsler metrics on $G/H$, which generalize the standard homogeneous $({\alpha }_1,{\alpha }_2)$ metric in literature. We classify all these $G/H$ which admit positively curved very standard homogeneous Finsler metrics.