射影Ricci曲率及其射影不变性  

Projective Ricci Curvature and Its Projective Invariance

作　　者：程新跃[1] 马小玉[1] 沈玉玲[1] 

机构地区：[1]重庆理工大学数学与统计学院,重庆400054

出　　处：《西南大学学报（自然科学版）》2015年第8期92-96,共5页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11371386);欧盟FP7(SEVENTHFRAMEWORKPROGRAMME)资助项目(PIRSES-GA-2012-317721)

摘　　要：研究了芬斯勒几何中一类新的几何量,即射影Ricci曲率.刻划了两个射影等价的芬斯勒度量的射影Ricci曲率的关系.特别地,在一个给定体积形式的流形上,如果两个芬斯勒度量F和F是射影等价的,那么它们的射影Ricci曲率是相等的,即此时的射影Ricci曲率是射影不变量.In this paper, we study a new class of geometric quantities in Finsler geometry, that is, the projective Ricci curvature. We characterize the relations between two projective Ricci curvatures for two projective equivalent Finsler metrics. In particular, we show that, if the Finsler metrics F and F are projectively equivalent on a manifold with a fixed volume form, then their projective Ricci curvatures are equal. In other words, the projective Ricci curvature is a projective invariant in this case.

关 键 词：芬斯勒度量 RICCI曲率 S-曲率 射影Ricci曲率 射影不变量 

分 类 号：O186.13[理学—数学]