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On Flag Curvature of Homogeneous Randers Spaces |
Canad. J. Math. 65(2013), 66-81
Published:2012-03-25
Printed: Feb 2013
Printed: Feb 2013
- Shaoqiang Deng,
- Zhiguang Hu,
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 |
| MSC Classifications: |
22E46 - Semisimple Lie groups and their representations 53C30 - Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15] |