Normal homogeneous Finsler spaces

Abstract

In this paper, we study normal homogeneous Finsler spaces. We first define the notion of a normal homogeneous Finsler space, using the method of isometric submersion of Finsler metrics. Then we study the geometric properties. In particular, we establish a technique to reduce the classification of normal homogeneous Finsler spaces of positive flag curvature to an algebraic problem. The main result of this paper is a classification of positively curved normal homogeneous Finsler spaces. It turns out that a coset space $G/H$ admits a positively curved normal homogeneous Finsler metric if and only if it admits a positively curved normal homogeneous Riemannian metric. We will also give a complete description of the coset spaces admitting non-Riemannian positively curved normal homogeneous Finsler spaces.

38 pages

References in corpus (1)

• Even dimensional homogeneous Finsler spaces with positive flag curvature

Cited by in corpus (5)

• Even dimensional homogeneous Finsler spaces with positive flag curvature
• 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