| In this paper,we mainly study some important problems on flag curvature in Finsler geometry.Firstly,we study the conformal vector fields on Kropina manifolds.We deeply study the conformal vector fields on a Kropina manifold of weakly isotropic flag curvature and obtain the explicit expressions of conformal vector fields on a Kropina manifold of weakly isotropic flag curvature.Secondly,we study Randers metrics of scalar flag curvature.Concretrly,we investigate the classification problems with Randers metric of scalar flag curvature.Under the condition that β is a Killing 1-form with respect to α,we obtain some necessary conditions for the Randers metric of scalar flag cruvature.Finally,as a joint work with other people,we study the Finsler metrics with some special flag curvature properties and obtain a identity equation for Finsler metrics of weakly isotropic flag curvature.Moreover,we prove that non-Riemann Finsler metrics with scalar flag curvature and constant mean Berwald curvature must have constant flag curvature in dimension greater than two. |
