局部对偶平坦的Randers度量

数学物理学报 ›› 2011, Vol. 31 ›› Issue (4): 1083-1090.

局部对偶平坦的Randers度量

周宇生

南京航空航天大学振动工程研究所南京 210016|贵阳学院数学系贵阳 550005

收稿日期:2008-10-10 修回日期:2010-04-06 出版日期:2011-08-25 发布日期:2011-08-25
基金资助:
贵阳学院院级项目(200809)资助

Locally Dual Flat Randers Metrics

ZHOU Yu-Sheng

Institute of Vibration Engineering Research, Nanjing University of Aeronautics and Astronautics, Nanjing 210016|Department of Mathematics, Guiyang University, Guiyang 550005

Received:2008-10-10 Revised:2010-04-06 Online:2011-08-25 Published:2011-08-25
Supported by:
贵阳学院院级项目(200809)资助

摘要/Abstract

摘要：

该文研究了形如F=α+β的Randers度量的性质, 得到了局部对偶平坦的Randers度量的充要条件. 同时刻画了当α具有常数曲率或β为闭的1 -形式时的Randers度量.

关键词: 局部对偶平坦, 局部射影平坦, Randers度量

Abstract:

In this paper, we find equations that charactrize locally dual flat Finsler metrics in the form F=α+β, where α=√a_i_jyⁱy^jis a Riemannian metric and β=b_iyⁱis a 1-form. Then we completely determine the local structure of those when α is of constant curvature or β is closed.

Key words: Locally dual flat, Locally projectively flat, Randers metrics

中图分类号:

53B40

周宇生. 局部对偶平坦的Randers度量[J]. 数学物理学报, 2011, 31(4): 1083-1090.

ZHOU Yu-Sheng. Locally Dual Flat Randers Metrics[J]. Acta mathematica scientia,Series A, 2011, 31(4): 1083-1090.