Let ( M , F ) " role="presentation"> ( M , F ) ( M , F ) (M, F) be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds ( M 1 , F 1 ) " role="presentation"> ( M 1 , F 1 ) ( M 1 , F 1 ) (M_1, F_1) and ( M 2 , F 2 ) " role="presentation"> ( M 2 , F 2 ) ( M 2 , F 2 ) (M_2, F_2) with F = f ( K , H ) " role="presentation"> F = f ( K , H ) ‾ ‾ ‾ ‾ ‾ ‾ ‾ √ F = f ( K , H ) F=\sqrt{f(K, H)} and K = F 1 2 " role="presentation"> K = F 2 1 K = F 1 2 K=F_1^2 , H = F 2 2 " role="presentation"> H = F 2 2 H = F 2 2 H=F_2^2 . In this paper, we prove that ( M , F ) " role="presentation"> ( M , F ) ( M , F ) (M, F) is a weakly Kaahler-Finsler (resp. weakly complex Berwald) manifold if and only if ( M 1 , F 1 ) " role="presentation"> ( M 1 , F 1 ) ( M 1 , F 1 ) (M_1, F_1) and ( M 2 , F 2 ) " role="presentation"> ( M 2 , F 2 ) ( M 2 , F 2 ) (M_2, F_2) are both weakly Kahler-Finsler (resp. weakly complex Berwald) manifolds, which is independent of the choice of function f " role="presentation"> f f f . Meanwhile, we prove that ( M , F ) " role="presentation"> ( M , F ) ( M , F ) (M, F) is a complex Landsberg manifold if and only if either ( M 1 , F 1 ) " role="presentation"> ( M 1 , F 1 ) ( M 1 , F 1 ) (M_1, F_1) and ( M 2 , F 2 ) " role="presentation"> ( M 2 , F 2 ) ( M 2 , F 2 ) (M_2, F_2) are both complex Landsberg manifolds and f = c 1 K + c 2 H " role="presentation"> f = c 1 K + c 2 H f = c 1 K + c 2 H f=c_1K+c_2H with c 1 , c 2 " role="presentation"> c 1 , c 2 c 1 , c 2 c_1, c_2 positive constants, or ( M 1 , F 1 ) " role="presentation"> ( M 1 , F 1 ) ( M 1 , F 1 ) (M_1, F_1) and ( M 2 , F 2 ) " role="presentation"> ( M 2 , F 2 ) ( M 2 , F 2 ) (M_2, F_2) are both Kahler-Finsler manifolds.

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On product complex Finsler manifolds

A Remark on General Complex ( α, β ) Metrics

In this paper, we prove that a strongly convex complex Finsler metric F on a domain $$D\subset \mathbb {C}^n$$
 is projectively flat (resp. dually flat) if and only if F comes from a strongly convex complex Minkowski metric.

On strongly convex projectively flat and dually flat complex Finsler metrics

In this paper, we prove that a strongly convex complex Finsler metric $F$ on a domain $D\subset\mathbb{C}^n$ is projectively flat (resp. dually flat) if and only if $F$ comes from a strongly convex complex Minkowski metric.

Hongchuan Xia

Papers

On strongly convex projectively flat and dually flat complex Finsler metrics

On strongly convex projectively flat and dually flat complex Finsler metrics