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 Γi;k associated to F and the Chern Finsler connection coefficients (Γ)a;c,Γa;r associated to F1,F2,respectively.As applications we prove that,if both (M1,F1) and (M2,F2) are strongly K(a)hler 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.
展开▼