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.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
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)
