On Projectively Flat (α, β)-metrics

被引：57

作者：

Shen, Zhongmin ^{[1
]}

机构：

[1] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2009年 / 52卷 / 01期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

METRICS; CURVATURE;

D O I：

10.4153/CMB-2009-016-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The solutions to Hilbert's Fourth Problem in the regular case are projectively flat Finsler metrics. In this paper, we consider the so-called (alpha,beta)-metrics defined by a Riemannian metric alpha and a 1-form beta, and find a necessary and sufficient condition for such metrics to be projectively flat in dimension n >= 3.

引用

页码：132 / 144

页数：13

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