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Turkish Journal of Mathematics

DOI

10.3906/mat-1809-3

Abstract

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

Keywords

Product manifold, weakly complex Berwald manifold, weakly Kähler-Finsler manifold, complex Landsberg manifold

First Page

422

Last Page

438

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