关于Kropina度量的数量曲率

【目的】主要研究和刻画Kropina度量的数量曲率。【方法】利用Kropina度量的导航术技巧及数量曲率的定义展开讨论。【结果】令F 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 bar{r}(x)的关系。【结论】给出了F 的数量曲率 和 h的数量曲率 的关系。特别地,当F 是一个Einstein-Kropina度量时,本文证明了r(x)=bar{r}(x) 。

On The Scalar Curvature of Kropina Metrics

[Purposes] The main purpose is to study and characterize the scalar curvature of Kropina metrics. [Methods]The discussions are carried out by using navigation technique of Kropina metrics and the definition of scalar curvature. [Findings] Let F 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 of is discussed. [Conclusions] The relationship between the scalar curvature of and the scalar curvature of h is obtained. In particular, when F is an Einstein-Kropina metric, it is proved that r(x)=bar{r}(x) .