一类Hartogs域的完备Einstein-Khler度量和比较定理(英文)  

Einstein-Khler Metric and Comparison Theorem on a Class of Hartogs Domain

作　　者：郝毅红[1] 唐俊丽[1] 王安[1] 

机构地区：[1]首都师范大学数学科学学院,北京100048

出　　处：《数学进展》2013年第6期823-836,共14页Advances in Mathematics（China）

基　　金：supported by NSFC(No.11071171);the Beijing Natural Science Foundation(No.1122010);the Science and Technology Project of Beijing Municipal Commission of Education(No.KM201210028007)

摘　　要：本文研究的是一类赋予完备Einstein-K(a|¨)hler度量的非齐性Hartogs域Ω_(μ,v).首先得到了该度量的K(a|¨)hler势函数隐函数形式的表达式;其次当参数满足一定条件时,将隐函数转化为了显函数;最后还得到了该类域上Einstein-K(a|¨)hler度量和Kobayashi度量的比较定理.In this paper, we consider a class of non-homogeneous Hartogs domains Ωμ,ν endowed with a complete Einstein-Kahler metric. First, we get the Kahler potential function which is an implicit function. Second, we get the explicit function from the implicit function when the parameters satisfy certain conditions. Finally, we obtain the comparison theorem between Einstein-Kahler metric and Kobayashi metric on those domains.

关 键 词：Einstein-Ka..hler度量 MONGE-AMPERE方程 全纯截曲率 比较定理 

分 类 号：O174.56[理学—数学]