关于Kropina度量的数量曲率  

On the Scalar Curvature of Kropina Metrics

作　　者：程新跃 张雨 CHENG Xinyue;ZHANG Yu(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）》2024年第3期73-78,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.11871126,No.12141101)。

摘　　要：为了研究和刻画Kropina度量的数量曲率,利用Kropina度量的导航术技巧及数量曲率的定义展开讨论。令F=α^(2)/β是一个由导航数据(h, V)确定的Kropina度量。在F关于Busemann-Hausdorff体积形式的S-曲率是迷向的条件下,讨论了F的数量曲率r(x)和h的数量曲率■(x)的关系。特别地,当F是一个Einstein-Kropina度量时,证明了r(x)=■(x)。The main purpose is to study and characterize the scalar curvature of Kropina metrics.The discussions are carried out by using navigation technique of Kropina metrics and the definition of scalar curvature.Let F=α^(2)/β be a Kropina metric expressed by navigation data(h,V).If F is of isotropic S-curvature with respect to the Busemann-Hausdorff volume form,the relationship between the scalar curvature r(x)of F and the scalar curvature■(r)of h is discussed.The relationship between the scalar curvature r(x)of F and the scalar curvature■(r)of h is obtained.In particular,when F is an Einstein-Kropina metric,it is proved that r(x)=■(x).

关 键 词：FINSLER度量 Kropina度量 数量曲率 S-曲率 导航数据 

分 类 号：O186.1[理学—数学]