关于弱Einstein-Kropina度量的特征  

On the Characterizations of Weak Einstein-Kropina Metrics

作　　者：程新跃 谭聪 CHENG Xinyue;TAN Cong(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2020年第6期78-82,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11871126);重庆师范大学研究基金(No.17XLB022)。

摘　　要：[目的]着力刻画弱Einstein-Kropina度量的性质及结构。[方法]基于Kropina度量的Ricci曲率公式,利用偏微分方程及多元多项式理论展开讨论。[结果]得到了Kropina度量为弱Einstein度量的充分必要条件。特别地,在■为常数的条件下,证明了Kropina度量为弱Einstein度量的充分必要条件是α为Einstein度量且β是关于α的Killing1-形式。[结论]完全刻画了弱Einstein-Kropina度量的结构。[Purposes]To characterize the properties and structures of weak Einstein-Kropina metrics,which is one of the important topics in Finsler geometry.[Methods] Based on the Ricci curvature formula of Kropina metric,the discussion was carried out by using theories of partial differential equations and multivariate polynomial theory.[Findings] Sufficient and necessary conditions for Kropina metrics to be weak Einstein metrics are obtained.In particular,if ■ is a constant,it is proved that a Kropina metric is a weak Einstein metric if and only if α is an Einstein metric and β is a Killing 1-form.[Conclusions]The structure of weak Einstein-Kropina metrics is completely characterized.

关 键 词：芬斯勒度量 Kropina度量 RICCI曲率 弱Einstein度量 

分 类 号：O186.1[理学—数学]