芬斯勒射影几何中的Ricci曲率(英文)  

THE RICCI CURVATURE IN FINSLER PROJECTIVE GEOMETRY

作　　者：杨文茂[1] 程新跃[2] 

机构地区：[1]仰恩大学数学系,福建泉州362014 [2]重庆工学院数理学院,重庆400050

出　　处：《数学杂志》2005年第5期473-479,共7页Journal of Mathematics

基　　金：SupportedbytheNationalNaturalScienceFundationofChina(10371138),theScienceFoundationofChongqingEducationCommittee

摘　　要：本文研究了保持Ricci曲率不变的Finsler射影变换。给定一个紧致无边的n维可微流形M,证明了:对于一个从M上的Berwald度量到Riemann度量的C射影变换,如果Berwald度量的Ricci曲率关于Riemann度量的迹不超过Riemann度量的标量曲率,则该射影变换是平凡的。In this paper we first study the Finsler projective change which preserves the Ricci curvature. Furthermore,given a compact and boundaryless n-dimensional differentiable manifold M, we show that any pointwise C-projective change from a Berwald space （M,F） to a Riemann space （M,F） is trivial if the trace of the Ricci curvature Ric of F with respect to F is less or equal to the scalar curvature of F.

关 键 词：FINSLER度量 测地线 射影变换 RICCI曲率 标量曲率 

分 类 号：O186.14[理学—数学]