具有标量曲率的Randers流形  

On Randers manifold with scalar curvature

作　　者：王辉[1] 

机构地区：[1]南京邮电大学理学院,江苏南京210023

出　　处：《南京邮电大学学报（自然科学版）》2015年第3期120-122,126,共4页Journal of Nanjing University of Posts and Telecommunications：Natural Science Edition

基　　金：南京邮电大学校科研基金(NY214106)资助项目

摘　　要：文中主要研究了具有曲率的一类特殊的芬斯勒流形——Randers流形。首先回顾了芬斯勒流形的基本知识及芬斯勒流形的导航问题的有关事实。进一步通过对导航问题的研究转化为将Randers流形转化为黎曼流形的研究,利用Schur引理,证明了Randers流形具有标量旗曲率当且仅当该流形具有常曲率这一性质。The class of the special Finsler manifolds-Randers manifolds with the scalar curvature is stud- ied. Firstly, the basic acknowledge of the Finsler manifolds and the navigation problems are reviewed. Then, the problems of Randers manifolds are translated into the problems of Riemannian geometry, by studying the navigation problems on Finsler manifolds. Finally, the main result shows that any Randers manifold has scalar curvature if and only if it has constant flag curvature is proved, by the Schur Lemma.

关 键 词：RANDERS度量 标量曲率 常曲率 

分 类 号：O1[理学—数学]