The Einstein-Khler Metric on the Third Cartan-Hartogs Domain  

作　　者：Wen Juan ZHANG Wei Ping YIN 

机构地区：[1]Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China [2]Department of Mathematics, Capital Normal University, Beijing 100037, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第10期1703-1712,共10页数学学报（英文版）

基　　金：the NSF of China (Grant NO.10471097)

摘　　要：In this paper we discuss the Einstein-Kahler metric on the third Cartan-Hartogs domain Y111（n, q; K）. Firstly we get the complete Einstein Kahler metric with explicit form on Y111（n, q; K） in the case of K=q/2 ＋ 1/q-1. Secondly we obtain the holomorphic sectional curvature under this metric and get the sharp estimate for this holomorphic curvature. Finally we prove that the complete Einstein-Kahler metric is equivalent to the Bergman metric on Y111（n, q; K） in case of K=q/2＋1/q-1.In this paper we discuss the Einstein-Kahler metric on the third Cartan-Hartogs domain Y111（n, q; K）. Firstly we get the complete Einstein Kahler metric with explicit form on Y111（n, q; K） in the case of K=q/2 ＋ 1/q-1. Secondly we obtain the holomorphic sectional curvature under this metric and get the sharp estimate for this holomorphic curvature. Finally we prove that the complete Einstein-Kahler metric is equivalent to the Bergman metric on Y111（n, q; K） in case of K=q/2＋1/q-1.

关 键 词：Einstein Kahler metric holomorphic sectional curvature holomorphic automorphism group 

分 类 号：O21[理学—概率论与数理统计]