Some rigid results on doubly twisted product complex Finsler manifolds  

作　　者：Hongchuan Xia Wei Xiao Chunping Zhong 

机构地区：[1]School of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000,China [2]School of Mathematical Sciences,Xiamen University,Xiamen 361005,China

出　　处：《Science China Mathematics》2025年第2期421-432,共12页中国科学(数学英文版)

基　　金：supported by National Natural Science Foundation of China(Grant Nos.12071386 and 11701494);the Nanhu Scholars Program for Young Scholars of Xinyang Normal University。

摘　　要：Let(M1×(λ_(1),λ_(2))M_(2),F)be a doubly twisted product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds(M_(1),F_(1))and(M_(2),F_(2)).Denote by M the product manifold of M1and M_(2).In this paper,we first give the characterization for(M,F)to be of constant holomorphic curvature,and prove that(M,F)is of constant holomorphic curvature if and only if(M,F),(M_(1),F_(1)),and(M_(2),F_(2))all have vanishing holomorphic curvature under the condition that lnλ_(1)and lnλ_(2)are both pluriharmonic functions.Secondly,we obtain the classification for(M,F)to be a complex Landsberg manifold.Finally,we prove that a strongly convex doubly twisted product complex Finsler manifold(M,F)is projectively flat(resp.dually flat)if and only ifλ_(1)F1andλ_(2)F_(2)are both complex Minkowski metrics.

关 键 词：doubly twisted product complex Finsler manifold holomorphic curvature complex Landsberg manifold 

分 类 号：O18[理学—数学]