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On Negatively Curved Finsler Manifolds of Scalar Curvature

Published online by Cambridge University Press:  20 November 2018

Xiaohuan Mo  and
Zhongmin Shen
Xiaohuan Mo
Affiliation:
LMAM, School of Mathematical Sciences, Beijing University, Beijing 100871, P.R. China e-mail: moxh@pku.edu.cn
Zhongmin Shen
Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202-3216, U.S.A. e-mail: zshen@math.iupui.edu
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Abstract

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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.

Keywords

53C60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 1 , 01 March 2005 , pp. 112 - 120
Copyright
Copyright © Canadian Mathematical Society 2005

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