The Einstein-Kahler metrics on Cartan-Hartogs domain of the first type  

作　　者：WANG An 

机构地区：[1]Department of Mathematics, Capital Normal University, Beijing 100037, China

出　　处：《Science China Mathematics》2004年第2期220-235,共16页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant Nos.10071051 and 10171068);Natural Science Foundation of Beijing(Grant Nos.1002004 and 1012004).

摘　　要：Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when K = mn+1/m+n, m ＞ 1, the explicit forms of the complete Einstein-Kahler metrics are obtained.Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when K =mn+1/m+n,m>1, the explicit forms of the complete Einstein-Kahler metrics are obtained.

关 键 词：Cartan-Hartogs domain  Einstein-Kahler metric  HOLOMORPHIC sectional curvature  GENERATING function. 

分 类 号：O1[理学—数学]