关键词: complex Finsler manifold, product manifold, holomorphic curvature

Abstract:

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,˜ Γ^α_;γ 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 K_F1 = 0 and K_F2 = 0.

Key words: complex Finsler manifold, product manifold, holomorphic curvature