The equivalence on classical metrics  

作　　者：Wei-ping Yin An WANG 

机构地区：[1]School of Mathematical Sciences,Capital Normal University,Beijing 100037,China

出　　处：《Science China Mathematics》2007年第2期183-200,共18页中国科学：数学（英文版）

基　　金：partially supported by the National Natural Science Foundation of China(Grant No.10471097);the Scientific Research Common Program of Beijing Municipal Commission of Education(Grant No.KM200410028002);the Doctoral Programme Foundation of Ministry of Education of China(Grant No.20040028003)

摘　　要：In this paper we study the complete invariant metrics on Cartan-Hartogs domains which are the special types of Hua domains. Firstly, we introduce a class of new complete invariant metrics on these domains, and prove that these metrics are equivalent to the Bergman metric. Secondly, the Ricci curvatures under these new metrics are bounded from above and below by the negative constants. Thirdly, we estimate the holomorphic sectional curvatures of the new metrics, and prove that the holomorphic sectional curvatures are bounded from above and below by the negative constants. Finally, by using these new metrics and Yau’s Schwarz lemma we prove that the new metrics are equivalent to the Einstein-K?hler metric. That means that the Yau’s conjecture is true on Cartan-Hartogs domains.In this paper we study the complete invariant metrics on Cartan-Hartogs domains which are the special types of Hua domains. Firstly, we introduce a class of new complete invariant metrics on these domains, and prove that these metrics are equivalent to the Bergman metric. Secondly, the Ricci curvatures under these new metrics are bounded from above and below by the negative constants. Thirdly, we estimate the holomorphic sectional curvatures of the new metrics, and prove that the holomorphic sectional curvatures are bounded from above and below by the negative constants. Finally, by using these new metrics and Yau’s Schwarz lemma we prove that the new metrics are equivalent to the Einstein-Kahler metric. That means that the Yau’s conjecture is true on Cartan-Hartogs domains.

关 键 词：Bergman metric Einstein-Kahler metric Cartan-Hartogs domain equivalence on classical metrics 

分 类 号：O151.21[理学—数学]