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On Negatively Curved Finsler Manifolds of Scalar Curvature

Published online by Cambridge University Press:  20 November 2018

Xiaohuan Mo
LMAM, School of Mathematical Sciences, Beijing University, Beijing 100871, P.R. China e-mail:
Zhongmin Shen
Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202-3216, U.S.A. e-mail:
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In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension $n\,\ge \,3$. 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.


Research Article
Copyright © Canadian Mathematical Society 2005


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