Some Important Properities Of Finsler Metrics Of Scalar Flag Curvature

In this paper, we study some important properities of Finsler metrics of scalar flag curvature. Firstly, we characterize the flag curvature of Finsler metrics of scalar flag curvature under the condition that the mean Lansberg curvature satisfies a special condition. Secondly , we consider generalized Landsberg metrics of scalar flag curvature and prove that, if the Finsler metrics is generalized Landsberg metrics of non-zero scalar flag curvature, then the Finsler metrics must be Riemannian metrics and the flag curvature must be a constant. Finally, we study Generalized Douglas-Weyl metric and give the sufficient and necessary conditions that a Finsler is generalized Douglas-Weyl metric. Specially,we obstain a sufficient and necessary condition for a Finsler metric to be a generalized Douglas-Weyl metric of weakly isotropic flag curvature.