一个关于Khler平坦的定理  

A flat theorem of Khler manifolds

作　　者：赵成兵[1] 俞能福[1] 

机构地区：[1]安徽建筑工业学院数理系,安徽合肥230022

出　　处：《合肥工业大学学报（自然科学版）》2008年第9期1528-1531,共4页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省教育厅重点资助项目(kj2008B237);安徽建筑工业学院博士启动基金(2007-6-3)

摘　　要：文章主要研究完备非紧的Khler流形,得到2个定理。首先在Khler流形有非负有界的全纯双截曲率和平均数量曲率满足一定的条件下得到关于数量曲率的一个积分估计和流形在不同时刻度量条件下体积保持极大增长的条件;其次在Khler流形有非负的全纯双截曲率,Ricci曲率有界和平均数量曲率满足一定条件下得到它双全纯等价于平坦的Khler流形的结果。In the paper, Kaehler manifolds are studied, and two results are gotten. First, as Kahler manifolds with nonnegative bisection curvature exist and some conditions of average scalar curvature are satisfied, an integral estimate of scalar curvature and the condition of manifolds which have maximal volume growth are obtained. Second, as Kahler manifolds with nonnegative bisection curvature exist, and Ricci curvature is bounded, and some conditions of average scalar curvature are satisfied, the studied Kahler manifolds are isometrically biholomorphic to fiat,complete Kahler manifolds.

关 键 词：Khler流形 RICCI流 平坦定理 

分 类 号：O186.1[理学—数学]