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On Randers changes of $m$th root Finsler metrics $L=\sqrt [m]{A}$ without irreducibility of $A$

Volume 119 / 2017

Guangzu Chen, Lihong Liu Annales Polonici Mathematici 119 (2017), 239-253 MSC: Primary 53B40; Secondary 53C60. DOI: 10.4064/ap4092-8-2017 Published online: 28 September 2017

Abstract

We study Randers changes of $m$th root Finsler metrics, and provide necessary and sufficient conditions for the Finsler metric obtained by a Randers change of an $m$th root metric to be dually flat. We also prove that if the Finsler metric obtained by a Randers change of an $m$th root metric is projectively flat, then the $m$th root metric is locally Minkowskian or Riemannian.

Authors

  • Guangzu ChenSchool of Science East China JiaoTong University Nanchang 330013, P.R. China
    e-mail
  • Lihong LiuSchool of Science East China JiaoTong University Nanchang 330013, P.R. China
    e-mail

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