SOME RESULTS ON PRODUCT COMPLEX FINSLER MANIFOLDS

作     者：吴志成 钟春平 

作者机构：School of Mathematical Sciences Xiamen University 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2011年第31卷第4期

页      面：1541-1552页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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

主　　题：complex Finsler manifold product manifold holomorphic curvature 

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.