 |
|
On Negatively Curved Finsler Manifolds of Scalar Curvature |
Canad. Math. Bull. 48(2005), 112-120
Published:2005-03-01
Printed: Mar 2005
Printed: Mar 2005
- Xiaohuan Mo
- Zhongmin Shen
Abstract
In this paper, we prove a global rigidity theorem for negatively
curved Finsler metrics on a compact manifold of dimension $n \geq 3$.
We show that for such a Finsler manifold, if the flag curvature is a
scalar function on the tangent bundle, then the Finsler metric is of
Randers type. We also study the case when the Finsler metric is
locally projectively flat
| MSC Classifications: | 53C60 - Finsler spaces and generalizations (areal metrics) [See also 58B20] |