Normal homogeneous Finsler spaces

2014/11/12 by Ming Xu, Xu, Ming, Shaoqiang Deng +1 · 1 citation
Mathematics · #22E46 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:22E46 #msc:53C30

paper · pdf · doi:10.48550/arxiv.1411.3053

38 pages

arxiv created 2014/11/12 · arxiv updated 2014/11/13

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.

Cited by

• Very standard homogeneous Finsler manifolds with positive flag curvature

Related

• Even dimensional homogeneous Finsler spaces with positive flag curvature
• δ-homogeneity in Finsler geometry and the positive curvature problem
• Recent progress on homogeneous Finsler spaces with positive curvature
• Towards the classification of odd dimensional homogeneous reversible Finsler spaces with positive flag curvature
• Homogeneous Finsler spaces and the flag-wise positively curved condition