SOME RESULTS ON PRODUCT COMPLEX FINSLER MANIFOLDS  

作　　者：吴志成 钟春平 

机构地区：[1]School of Mathematical Sciences, Xiamen University

出　　处：《Acta Mathematica Scientia》2011年第4期1541-1552,共12页数学物理学报（B辑英文版）

基　　金：supported by Program for New Century Excellent Talents in Fujian Provincial University;the Natural Science Foundation of China (10971170; 10601040)

摘　　要：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 ）. In this paper, we obtain the relationship between the Chern Finsler connection coefficients Γ i ; k associated to F and the Chern Finsler connection coefficients Γ a ; c , Γα ; γ associated to F 1 , F 2 , respectively. As applications we prove that, if both （M 1 , F 1 ） and （M 2 , F 2 ） are strongly Ka¨hler Finsler （complex Berwald, or locally complex Minkowski, respectively） manifolds, so does （M, F ）. Furthermore, we prove that the holomorphic curvature K F = 0 if and only if K F1 = 0 and K F2 = 0.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 ）. In this paper, we obtain the relationship between the Chern Finsler connection coefficients Γ i ; k associated to F and the Chern Finsler connection coefficients Γ a ; c , Γα ; γ associated to F 1 , F 2 , respectively. As applications we prove that, if both （M 1 , F 1 ） and （M 2 , F 2 ） are strongly Ka¨hler Finsler （complex Berwald, or locally complex Minkowski, respectively） manifolds, so does （M, F ）. Furthermore, we prove that the holomorphic curvature K F = 0 if and only if K F1 = 0 and K F2 = 0.

关 键 词：complex Finsler manifold product manifold holomorphic curvature 

分 类 号：O174.6[理学—数学]