On the flag curvature of a class of Randers metric generated from the navigation problem

Let F ( x , y ) be a Randers metric of Douglas type on a manifold M and V be a conformal vector field on ( M , F ) . Let F ̃ ( x , y ) be a Randers metric generated from ( F , V ) by solving the navigation problem F ( x , y F ̃ ( x , y ) − V x ) = 1 . In this paper, we establish the relationship among the flag curvature of F , the flag curvature of F ̃ and the conformal vector field V (see Theorem 1.1).