Comparison and Wu’s theorems in Finsler geometry

In this paper, we first give several comparison theorems and their applications in Finsler geometry. Moreover, by means of the Hessian comparison theorems of a real Finsler manifold, Cartan connection, radial flag curvature and tangent curvature, we give Wu’s theorem on a strongly convex weakly Kähler Finsler manifold with a pole. Finally, by using the complex Rund connection and definition of radial flag curvature on a strongly pseudoconvex complex Finsler manifold, we further discuss Wu’s theorem on a strongly convex Kähler Finsler manifold.