标量曲率Finsler空间与Finsler度量的射影变换(英文)  

FINSLER SPACES OF SCALAR CURVATURE AND PROJECTIVE CHANGES OF FINSLER METRICS

作　　者：程新跃[1] 

机构地区：[1]重庆工学院数学系,重庆400050

出　　处：《数学杂志》2003年第4期455-462,共8页Journal of Mathematics

基　　金：SupportedbyNationalNaturalScienceFoundationofChina(10171117)andScienceFoundationofChongqingEducatonCommittee.

摘　　要：本文研究了与一个Ricci平坦Finsler空间或一个常曲率Finsler空间射影相关的标量曲率Finsler空间.我们给出了这种标量曲率Finsler空间成为常曲率空间的充分必要条件.特别地,我们给出了射影平坦Finsler空间具有常曲率的条件.In this paper,we study the Finsler spaces of scalar curvature which are pointwise projective to a Finsler space of Ricci-flat(i.e.the Ricci curvature Ric=0)or a Finsler space of constant curvature respectively.We obtain some sufficient and necessary conditions under which such Finsler spaces of scalar curvature become the Finsler spaces of constant curvature.Particularly,we give some conditions that a projectively flat Finsler space is of constant curvature.

关 键 词：FINSLER空间 RICCI曲率 射影变换 常曲率Finsler空间 

分 类 号：O186.14[理学—数学]