Clifford-Wolf translations of Homogeneous Randers spheres

2012/04/23 by Shaoqiang Deng, Ming Xu, Deng, Shaoqiang +1 · 1 citation
Physics and Astronomy · #22E46 #53C30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1204.5232

openalex publication_date 2012/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study Clifford-Wolf translations of homogeneous Randers metrics on spheres. It turns out that we can present a complete description of all the Clifford-Wolf translations of all the homogeneous Randers metrics on spheres. The most important point of this paper is that a new phenomena surfaces. Namely, we find that there are some CW-homogeneous Randers spaces which are essentially not symmetric. This is a great difference compared to Riemannian geometry, where any CW-homogeneous Riemannian manifold must be locally symmetric.

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• A counter example for the Homogeneity Conjecture

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