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On Flag Curvature of Homogeneous Randers Spaces

Published online by Cambridge University Press:  20 November 2018

Shaoqiang Deng  and
Zhiguang Hu
Shaoqiang Deng
Affiliation:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People's Republic ofChina, e-mail: dengsq@nankai.edu.cn
Zhiguang Hu
Affiliation:
College of Mathematics, Tianjin Normal University, Tianjin 300387, People's Republic ofChina, e-mail: nankaitaiji@mail.nankai.edu.cn
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Abstract

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In this paper we give an explicit formula for the flag curvature of homogeneous Randers spaces of Douglas type and apply this formula to obtain some interesting results. We first deduce an explicit formula for the flag curvature of an arbitrary left invariant Randers metric on a two-step nilpotent Lie group. Then we obtain a classification of negatively curved homogeneous Randers spaces of Douglas type. This results, in particular, in many examples of homogeneous non-Riemannian Finsler spaces with negative flag curvature. Finally, we prove a rigidity result that a homogeneous Randers space of Berwald type whose flag curvature is everywhere nonzero must be Riemannian.

Keywords

22E4653C30homogeneous Randers manifoldsflag curvatureDouglas spacestwo-step nilpotent Lie groups
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 1 , 01 February 2013 , pp. 66 - 81
Copyright
Copyright © Canadian Mathematical Society 2013

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