On product complex Finsler manifolds

Authors : Hongchuan XIA, Qian WEI

Pages : 422-438

View : 12 | Download : 7

Publication Date : 0000-00-00

Article Type : Research Paper

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