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