射影Ricci平坦的Kropina度量  

ON PROJECTIVE RICCI FLAT KROPINA METRICS

作　　者：程新跃[1] 马小玉[1] 沈玉玲[1] CHENG Xin-yue;MA Xiao-yu;SHEN Yu-ling(School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China)

机构地区：[1]重庆理工大学数学与统计学院,重庆400054

出　　处：《数学杂志》2017年第4期705-713,共9页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China(11371386);the European Union’s Seventh Framework Programme(FP7/2007-2013)under grant agreement(317721)

摘　　要：本文研究和刻画了射影Ricci平坦的Kropina度量.利用Kropina度量的S-曲率和Ricci曲率的公式,得到了Kropina度量的射影Ricci曲率公式.在此基础上得到了Kropina度量是射影Ricci平坦度量的充分必要条件.进一步,作为自然的应用,本文研究和刻画了由一个黎曼度量和一个具有常数长度的Killing 1-形式定义的射影Ricci平坦的Kropina度量,也刻画了具有迷向S-曲率的射影Ricci平坦的Kropina度量.在这种情形下,Kropina度量是Ricci平坦度量.In this paper,we study and characterize projective Ricci°at Kropina metrics.By using the formulas of S-curvature and Ricci curvature for Kropina metrics,we obtain the formula of the projective Ricci curvature for Kropina metrics.Based on this,we obtain the necessary and su±cient conditions for Kropina metrics to be projective Ricci°at metrics.Further,as a natural application,we study and characterize projective Ricci°at Kropina metrics deˉned by a Riemannian metric and a Killing1-form of constant length.We also characterize projective Ricci°at Kropina metrics with isotropic S-curvature.In this case,the Kropina metrics are Ricci°atmetrics.

关 键 词：芬斯勒度量 Kropina度量 RICCI曲率 S-曲率 射影Ricci曲率 

分 类 号：O186.1[理学—数学]