ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS

Let (M-1, F-1) and (M-2, F-2) be two strongly pseudoconvex complex Finsler manifolds. The doubly wraped product complex Finsler manifold ((f2) M-1 X (f1) M-2, F) of (M-1,F-1) and (M-2, F-2) is the product manifold M-1 x M-2 endowed with the warped product complex Finsler metric F-2 =f(2)(2)F(1)(2) + f(1)(2)F(2)(2), where f(1) and f(2) are positive smooth functions on M-1 and M-2, respectively. In this paper, the most often used complex Finsler connections, holomorphic curvature, Ricci scalar curvature, and real geodesics of the DWP-complex Finsler manifold are derived in terms of the corresponding objects of its components. Necessary and sufficient conditions for the DWP-complex Finsler manifold to be Kahler Finsler (resp., weakly Kahler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg) manifold are obtained, respectively. It is proved that if (M-1, F-1) and (M-2, F-2) are projectively flat, then the DWP-complex Finsler manifold is projectively flat if and only if f(1) and f(2) are positive constants.