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Israel Journal of Mathematics

, 162:197 | Cite as

On symmetric Finsler spaces

  • Shaoqiang DengEmail author
  • Zixin Hou
Article

Abstract

In this paper, we study symmetric Finsler spaces. We first study some geometric properties of globally symmetric Finsler spaces and prove that any such space can be written as a coset space of a Lie group with an invariant Finsler metric. Then we prove that a globally symmetric Finsler space is a Berwald space. As an application, we use the notion of Minkowski symmetric Lie algebras to give an algebraic description of symmetric Finsler spaces and obtain the formulas for flag curvature and Ricci scalar. Finally, some rigidity results of locally symmetric Finsler spaces related to the flag curvature are also given.

Keywords

Ricci Scalar Holonomy Group Finsler Space Finsler Manifold Finsler Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Hebrew University of Jerusalem 2007

Authors and Affiliations

  1. 1.School of Mathematical SciencesNankai UniversityTianjinP. R. China

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