第三类超Cartan域上的比较定理  

The Comparison Theorem on Super-Cartan Domains of the Third Type

作　　者：殷慰萍[1] 赵晓霞[1] 

机构地区：[1]首都师范大学数学系,北京100037

出　　处：《数学学报（中文版）》2003年第2期223-236,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(19631010);北京市自然科学基金资助项目(1972002)

摘　　要：本文给出了第三类超Cartan域上不变Kalher度量下的全纯截曲率的表达式.利用其Bergman度量的完备性,构造了一个不比Bergman度量小的完备的不变Kalher度量,证明了在此Kalher度量下的全纯截曲率有一个负上界,从而证明了第三类超Cartan域的Bergman度量与Kobayashi度量的比较定理.In this note we get the explicit formula of holomorphic sectional curvature on super-Cartan domains of the third type under the invariant Kalher metric. By using the completeness of its Bergman metric, we construct an invariant Kalher metric which is not less than the Bergman metric and prove that the holomorphic sectional curvature with this invariant Kalher metric is bounded from above by a negative constant, hence we obtain the comparison theorm for the Bergman and Kobayashi metrics on super-Cartan domains of the third type.

关 键 词：第三类超Cartan域 比较定理 BERGMAN度量 KOBAYASHI度量 Kalher度量 多复分析 

分 类 号：O174.56[理学—数学]