On negatively curved Finsler manifolds of scalar curvature

被引：22

作者：

Mo, XH ^{[1
]}

Shen, ZM

机构：

[1] Beijing Univ, Sch Math Sci, Beijing 100871, Peoples R China

[2] Indiana Univ Purdue Univ, Dept Math Sci, Indianapolis, IN 46202 USA

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2005年 / 48卷 / 01期

关键词：

D O I：

10.4153/CMB-2005-010-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension it greater than or equal to 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.

引用

页码：112 / 120

页数：9

共 26 条

[1]

Akbar-Zadeh H, 1988, Acad. R. Belg. Bull. Cl. Sci., V74, P281

[2]

Bacso S, 1997, PUBL MATH-DEBRECEN, V51, P385

[3] On Randers spaces of constant flag curvature [J].

Bao, D ;

Robles, C .

REPORTS ON MATHEMATICAL PHYSICS, 2003, 51 (01) :9-42

[4]

BAO D, IN PRESS J DIFF GEOM

[5]

Bao D, 2000, An introduction to Riemann-Finsler geometry

[6] On the n-dimensional geometry of constant curves in which the straight portions are short [J].

Berwald, L .

MATHEMATISCHE ZEITSCHRIFT, 1929, 30 :449-469

[7] Investigation of generalised metric curved areas with foundations prevailing in parallel [J].

Berwald, L .

MATHEMATISCHE ZEITSCHRIFT, 1926, 25 :40-73

[8]

BERWALD L, 1929, MONATSH MATH PHYS, V36, P315

[9]

Berwald L., 1928, Atti Congr. Intern. Mat. Bologna, V4, P263

[10]

Chen XY, 2003, OSAKA J MATH, V40, P87

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