Invariant naturally reductive Randers metrics on homogeneous spaces

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• 作者：Dariush Latifi (1)
  Megerdich Toomanian (2)
  
• 关键词：Invariant randers metric ; Naturally reductive metric ; Homogeneous geodesic ; Geodesic vector ; 53C60 ; 53C30
• 刊名：Mathematical Sciences
• 出版年：2012
• 出版时间：December 2012
• 年：2012
• 卷：6
• 期：1
• 全文大小：141KB
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• 作者单位：Dariush Latifi (1)
  Megerdich Toomanian (2)
  
  1. Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, 5619911367, Iran
  2. Department of Mathematics, Islamic Azad University, Karaj branch, Karaj, 3148635731, Iran
  
• ISSN：2251-7456

文摘

Purpose The purpose of this paper is to study the geometric properties of naturally reductive homogeneous Randers spaces. Methods We use Lie theory methods in the study of Finsler geometry. Results We first prove that if a Randers metric is naturally reductive, then the underlying Riemannian metric is naturally reductive. Then, we show that, for Berwald type Randers metric, if the underlying Riemannian metric is naturally reductive, then the Randers metric is naturally reductive. Finally, we give a geometric criterion of homogeneous naturally reductive Randers spaces. Conclusions This paper provides a convenient method to construct naturally reductive Randers metrics on homogeneous Riemannian manifolds.