The Studies Of Some Problems On The Flag Curvature Of Finsler Metrics

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.