Even dimensional homogeneous Finsler spaces with positive flag curvature

Abstract

In this paper, we use the technique of Finslerian submersion to deduce a flag curvature formula for homogeneous Finsler spaces. Based on this formula, we give a complete classification of even-dimensional smooth coset spaces $G/H$ admitting $G$-invariant Finsler metrics with positive flag curvature. It turns out that the classification list coincides with that of the even dimensional homogeneous Riemannian manifolds with positive sectional curvature obtained by N.R. Wallach. We also find out all the coset spaces admitting invariant non-Riemannian Finsler metrics with positive flag curvature.

The title is changed from 'Homogeneous Finsler spaces with positive flag curvature' to 'Even dimensional homogeneous Finsler spaces with positive flag curvature'. Add a flag curvature formula for homogeneous Finsler spaces and correct some typos

References in corpus (2)

• Normal homogeneous Finsler spaces
• Sp(2)/U(1) and a Positive Curvature Problem

Cited by in corpus (5)

• Normal homogeneous Finsler spaces
• Sp(2)/U(1) and a Positive Curvature Problem
• Towards the classification of odd dimensional homogeneous reversible Finsler spaces with positive flag curvature
• $\delta$-homogeneity in Finsler geometry and the positive curvature problem
• Recent progress on homogeneous Finsler spaces with positive curvature