Khler-Einstein度量和Bergman度量的等价问题  

Equivalentce Between Khler-Einstein and Bergman Metrics

作　　者：殷慰萍[1] 张利友[1] 

机构地区：[1]首都师范大学数学科学学院,北京100037

出　　处：《数学年刊（A辑）》2007年第4期545-556,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10471097);国家教育部博士点基金(No.20040028003)资助的项目。

摘　　要：华罗庚域的特殊类型Cartan-Hartogs域Y_Ⅱ(N,p;K)当K=p/2+1/(p+1)时,求解了该域上的复Monge-Ampère方程的边值问题,从而得到该域的完备K■hler-Einstein度量的显表达式,并且得到此度量下的全纯截曲率的负的上下确界,最后证明了此K■hler-Einstein度量与Bergman度量等价。The Cartan-Hartogs domain YH（N,p;K） is the special cases of Hua domains,when K=P/2＋1/p＋1,the solution of the Dirichlet problem of complex Monge-Ampere equation for domain YⅡ （N, p; K）,and the explicit formula of complete Kahler-Einstein metric of YⅡ （N, p; K） is obtained. Under this metric, the paper proves that the holomorphic sectional curvature has the negative upper and lower bounds, and in final it prove that the Kahler-Einstein metric is equivalent to the Bergman metric.

关 键 词：Kahler—Einstein度量 Caftan—Hartogs域 BERGMAN度量 

分 类 号：O174.5[理学—数学]