Towards the classification of odd dimensional homogeneous reversible Finsler spaces with positive flag curvature

2015/04/12 by Ming Xu, Xu, Ming, Shaoqiang Deng +1
Mathematics · Physics and Astronomy · #22E46 #53C30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:22E46 #msc:53C30

paper · pdf · doi:10.48550/arxiv.1504.03018

There are only some very minor changes in this newe version

openalex publication_date 2015/04/12 · arxiv created 2015/05/21 · arxiv updated 2015/05/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we use the flag curvature formula for homogeneous Finsler spaces in our previous work to classify odd dimensional smooth coset spaces admitting positively curved reversible homogeneous Finsler metrics. We will show that the most features of L. Bérard-Bergery's classification results for odd dimensional positively curved Riemannian homogeneous spaces can be generalized to reversible Finsler spaces.

Citations

• Homogeneous (α,β)-spaces with positive flag curvature and vanishing S-curvature
• Killing frames and S-curvature of homogeneous Finsler spaces

Related

• Even dimensional homogeneous Finsler spaces with positive flag curvature
• Reversible homogeneous Finsler metrics with positive flag curvature
• Normal homogeneous Finsler spaces
• Homogeneous Finsler spaces and the flag-wise positively curved condition
• Recent progress on homogeneous Finsler spaces with positive curvature