Some results on product complex Finsler manifolds

Let (M,F) be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds (M1,F1) and (M2,F2). In this paper, we obtain the relationship between the Chern Finsler connection coefficients associated to F and the Chern Finsler connection coefficients associated to F1, F2, respectively. As applications we prove that, if both (M1,F1) and (M2,F2) are strongly Kähler Finsler (complex Berwald, or locally complex Minkowski, respectively) manifolds, so does (M,F). Furthermore, we prove that the holomorphic curvature KF = 0 if and only if KF1 = 0 and KF2 = 0.