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Cohomogeneity One Randers Metrics

Published online by Cambridge University Press:  20 November 2018

Jifu Li ,
Zhiguang Hu  and
Shaoqiang Deng
Jifu Li
Affiliation:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People's Republic of China and School of Science, Tianjin University of Technology, Tianjin 30084, People's Republic of China e-mail: lijifu@mail.nankai.edu.cn
Zhiguang Hu
Affiliation:
College of Mathematics, Tianjin Normal University, Tianjin 300387, P.R. China e-mail: nankaitaiji@mail.nankai.edu.cn
Shaoqiang Deng
Affiliation:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People's Republic of China e-mail: dengsq@nankai.edu.cn
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Abstract

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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 them to deduce some sufficient and necessary conditions for a cohomogeneity one Randers metric to be Einstein.

Keywords

53C3053C60Cohomogeneity one actionsnormal geodesicsinvariant vector fieldsRanders metrics
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 3 , 01 September 2016 , pp. 575 - 584
Copyright
Copyright © Canadian Mathematical Society 2016

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