On product complex Finsler manifolds

Let (M, F) be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds (M-1, F-1) and (M-2, F-2) with F = root f (K, H) and K = F-1(2), H = F-2(2). In this paper, we prove that (M, F) is a weakly Kahler-Finsler (resp. weakly complex Berwald) manifold if and only if (M-1, F-1) and (M-2, F-2) are both weakly Kahler- Finsler (resp. weakly complex Berwald) manifolds, which is independent of the choice of function f . Meanwhile, we prove that (M, F) is a complex Landsberg manifold if and only if either (M-1, F-1) and (M-2, F-2) are both complex Landsberg manifolds and f = c(1)K + c(2)H with c(l), c(2) positive constants, or (M-1, F-1) and (M-2, F-2) are both Kahler- Finsler manifolds.