CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

On Flag Curvature of Homogeneous Randers Spaces

  Published:2012-03-25
 Printed: Feb 2013
  • Shaoqiang Deng,
    School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People's Republic of China
  • Zhiguang Hu,
    College of Mathematics, Tianjin Normal University, Tianjin 300387, People's Republic of China
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   LaTeX   MathJax   PDF  

Abstract

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: homogeneous Randers manifolds, flag curvature, Douglas spaces, two-step nilpotent Lie groups homogeneous Randers manifolds, flag curvature, Douglas spaces, two-step nilpotent Lie groups
MSC Classifications: 22E46, 53C30 show english descriptions Semisimple Lie groups and their representations
Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
22E46 - Semisimple Lie groups and their representations
53C30 - Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/