Geodesic
Cohomogeneity One Randers Metrics
Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 575-584

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DOI

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.
DOI : 10.4153/CMB-2015-009-5
Mots-clés : 53C30, 53C60, Cohomogeneity one actions, normal geodesics, invariant vector fields, Randers metrics 
Li, Jifu; Hu, Zhiguang; Deng, Shaoqiang. Cohomogeneity One Randers Metrics. Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 575-584. doi: 10.4153/CMB-2015-009-5
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     title = {Cohomogeneity {One} {Randers} {Metrics}},
     journal = {Canadian mathematical bulletin},
     pages = {575--584},
     year = {2016},
     volume = {59},
     number = {3},
     doi = {10.4153/CMB-2015-009-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-009-5/}
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