The (α,β)(α,β)-metrics of scalar flag curvature

One of the most important problems in Finsler geometry is to classify Finsler metrics of scalar flag curvature. In this paper, we study and characterize the (α,β)(α,β)-metrics of scalar flag curvature. When the dimension of the manifold is greater than 2, we classify Randers metrics of weakly isotropic flag curvature (that is, Randers metrics of scalar flag curvature with isotropic S-curvature). Further, we characterize and classify (α,β)(α,β)-metrics of scalar flag curvature with isotropic S-curvature. Finally, we conclude that the non-trivial regular (α,β)(α,β)-metrics of scalar flag curvature with isotropic S-curvature on an n-dimensional manifold M  (n≥3)(n≥3) must be Randers metrics.