Cartan-Hartogs域上Khler-Einstein度量与Bergman度量的等价(英文)  

Equivalence of the Khler-Einstein Metric and the Bergman Metric on Cartan-Hartogs Domain

作　　者：殷慰萍[1] 张利友[1] 

机构地区：[1]首都师范大学数学系,北京100037

出　　处：《数学进展》2008年第4期437-450,共14页Advances in Mathematics（China）

基　　金：NSFC(No.10771144);the Doctoral Programme Foundation of NEM of China.

摘　　要：本文研究的是华罗庚域的特殊类型第二类Cartan-Hartogs域的不变Bergman度量与K(?)hler-Einstein度量的等价问题.引入一种与Bergman度量等价的新的完备的K(?)hler度量ω_(gλ),其Ricci曲率和全纯截取率具有负的上下界.然后应用丘成桐对Schwarz引理的推广证明ω_(gλ)等价于K(?)hler-Einstein度量,从而得到了Bergman度量与K(?)hler-Einstein度量的等价,即丘成桐关于度量等价的猜想在第二类Cartan-Hartogs域上成立.We study the equivalence of the Kahler-Einstein metric and the Bergman metric on Cartan-Hartogs domain of the second type. By constructing a new complete Kahler metric ωgλ which is equivalent to the Bergman metric, we can get the R.icci curvature and the holomorphic sectional curvature with negative upper and lower bounds under this metric. Then applying Yau＇s Schwarz lemma we prove the Kahler-Einstein metric is also equivalent to the new metric ωgλ. As a result, we obtain that the Bergman metric is equivalent to the Kahler-Einstein metric.

关 键 词：BERGMAN度量 Kahler-Einstein度量 度量等价 

分 类 号：O174.55[理学—数学]