(untitled) (Journal of Mathematical Study, 2022)
Let (M_1,F_1) and (M_2,F_2) be two strongly pseudoconvex complex Finsler manifolds. The doubly twisted product (abbreviated as DTP) complex Finsler manifold (M_1×_(λ_1,λ_2)M_2,F) is the product manifold M_1× M_2 endowed with the twisted product complex Finsler metric F^2=λ_1^2F_1^2+λ_2^2F_2^2, where λ_1 and λ_2 are positive smooth functions on M_1× M_2. In this paper, the relationships between the geometric objects (e.g. complex Finsler connections, holomorphic and Ricci scalar curvatures, and real geodesic) of a DTP-complex Finsler manifold and its components are derived. The necessary and sufficient conditions under which the DTP-complex Finsler manifold is a Kähler Finsler (respctively weakly Kähler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg) manifold are obtained. By means of these, we provide a possible way to construct a weakly complex Berwald manifold, and then give a characterization for a complex Landsberg metric that is not a Berwald metric.