On Negatively Curved Finsler Manifolds of Scalar Curvature

Details On Negatively Curved Finsler Manifolds of Scalar Curvature On Negatively Curved Finsler Manifolds of Scalar Curvature

2003-02-11

arxiv.org/abs/math/0302124v1

Mathematics

Differential Geometry

10 pages

Scientific paper

In this paper, we prove a global rigidity theorem for negatively curved
Finsler metrics on a compact manifold of dimension n>2. 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.

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