Cohomogeneity One Randers Metrics

Canadian mathematical bulletin

Jifu Li¹  Shaoqiang Deng¹  Zhiguang Hu² 

[1] School of Mathematical Sciences and LPMC , Nankai University , Tianjin 300071 , People's Republic of China;College of Mathematics , Tianjin Normal University , Tianjin 300387, P.R. China

关键词: cohomogeneity one actions;    normal geodesics;    invariant vector fields;    Randers metrics;   

DOI  :  10.4153/CMB-2015-009-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

An action of a Lie group $G$ on a smooth manifold $M$ is called cohomogeneity one if the orbit space $M/G$ is of dimension $1$. A Finsler metric $F$ on $M$ is called invariant if $F$ is invariant under the action of $G$. In this paper, we study invariantRanders metrics on cohomogeneity one manifolds. We first give asufficient and necessary condition for the existence of invariantRanders metrics on cohomogeneity one manifolds. Then we obtainsome results on invariant Killing vector fields on the cohomogeneity one manifolds and use that to deduce some sufficient and necessary condition for a cohomogeneity one Randers metric to be Einstein.

【 授权许可】

Unknown