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# Cohomogeneity One Randers Metrics

Published:2016-04-18
Printed: Sep 2016
• Jifu Li,
School of Mathematical Sciences and LPMC , Nankai University , Tianjin 300071 , People's Republic of China
• Zhiguang Hu,
College of Mathematics , Tianjin Normal University , Tianjin 300387, P.R. China
• Shaoqiang Deng,
School of Mathematical Sciences and LPMC , Nankai University , Tianjin 300071 , People's Republic of China
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## Abstract

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 invariant Randers metrics on cohomogeneity one manifolds. We first give a sufficient and necessary condition for the existence of invariant Randers metrics on cohomogeneity one manifolds. Then we obtain some 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.
 Keywords: cohomogeneity one actions, normal geodesics, invariant vector fields, Randers metrics
 MSC Classifications: 53C30 - Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15] 53C60 - Finsler spaces and generalizations (areal metrics) [See also 58B20]

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