关于共形平坦(α,β)-度量的两个刚性结果  

Two Rigidity Theorems on Conformally Flat (α, β)-Metrics

作　　者：程新跃 黄勤荣 吴莎莎 CHENG Xin-yue;HUANG Qin-rong;WU Sha-sha(School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China;College of Science, Chongqing University of Technology, Chongqing 400054, China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]重庆理工大学理学院,重庆400054

出　　处：《西南大学学报（自然科学版）》2019年第4期18-26,共9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：研究了共形平坦(α,β)-度量的刚性性质.首先,在β是关于α的共形1-形式且为闭的条件下,证明了共形平坦(α,β)-度量一定是局部Minkowski度量.其次,根据射影Ricci平坦Randers度量的特性,证明了共形平坦且射影Ricci平坦的Randers度量一定是局部Minkowski度量.In this paper, we study the rigidity properties of conformally flat (α,β)-metrics. Firstly, under the conditions that β is a closed and conformal 1-form with respect to α, we prove that conformally flat (α,β)-metrics must be Minkowskian. Further, by the properties of the conformally flat (α,β)-metrics and the characterization of projective Ricci flat Randers metrics, we prove that conformally flat and projective Ricci flat Randers metrics must be Minkowskian.

关 键 词：RANDERS度量 (Α Β)-度量 局部Minkowski度量 共形平坦度量 射影Ricci平坦度量 

分 类 号：O186.13[理学—数学]