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=α2/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)(x)of h is discussed.The relationship between the scalar curvature r(x)of F and the scalar curvature(-r)(x)of h is obtained.In particular,when F is an Einstein-Kropina metric,it is proved that r(x)=(-r)(x).
关键词
Finsler度量/Kropina度量/数量曲率/S-曲率/导航数据
Key words
Finsler metric/Kropina metric/scalar curvature/S-curvature/navigation data
维普
万方数据