On Negatively Curved Finsler Manifolds of Scalar Curvature

Xiaohuan Mo; Zhongmin Shen

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On Negatively Curved Finsler Manifolds of Scalar Curvature

Xiaohuan Mo·Zhongmin Shen

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Abstract

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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BibTeX RIS

Xiaohuan Mo, Zhongmin Shen. 2003-02-11. On Negatively Curved Finsler Manifolds of Scalar Curvature. https://arxiv.org/abs/math/0302124

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