关于射影Ricci曲率的比较定理与共形不变性  

On the Comparison Theorem and Conformal Invariance of a Projective Ricci Curvature

作　　者：程新跃 李婷婷 殷丽 CHENG Xin-yue;LI Ting-ting;YIN Li(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China;You Can Secondary School Department,Chongqing New Oriental Training School,Chongqing 400020,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]重庆新东方培训学校优能中学部,重庆400020

出　　处：《西南大学学报（自然科学版）》2019年第2期52-59,共8页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11871126);重庆师范大学科学研究基金项目(17XLB022)

摘　　要：主要研究了芬斯勒度量的射影Ricci曲率.首先,在一个完备的芬斯勒流形上,证明了关于芬斯勒度量的射影Ricci曲率的一个比较定理.其次,刻画了两个共形相关的芬斯勒度量的射影Ricci曲率的关系.在此基础上,证明了两个位似相关的芬斯勒度量的射影Ricci曲率是相等的.In this paper,we study the projective Ricci curvature in Finsler geometry.First,we obtain that a comparison theorem on the projective Ricci curvature on a complete Finsler manifold.Then,we characterize the relations between two projective Ricci curvatures for two conformally related Finsler metrics on a manifold.On this basis,we prove that if two Finsler metrics are homothetically related,then their projective Ricci curvatures are equal.

关 键 词：芬斯勒度量 射影Ricci曲率 RICCI曲率 S-曲率 共形相关 

分 类 号：O186[理学—数学]