Very standard homogeneous Finsler manifolds with positive flag curvature

TL;DR

This paper classifies homogeneous manifolds with positive flag curvature that admit very standard homogeneous Finsler metrics, extending previous work on standard metrics in differential geometry.

Contribution

It introduces and classifies a new class of homogeneous Finsler metrics called very standard, generalizing existing standard metrics, and identifies which manifolds support positive curvature.

Findings

Classification of manifolds with positive flag curvature

Introduction of very standard homogeneous Finsler metrics

Extension of curvature results to new metric classes

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.