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On Negatively Curved Finsler Manifolds of Scalar Curvature

Open Access article
 Printed: Mar 2005
  • Xiaohuan Mo
  • Zhongmin Shen
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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 show english descriptions Finsler spaces and generalizations (areal metrics) [See also 58B20] 53C60 - Finsler spaces and generalizations (areal metrics) [See also 58B20]

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