| Einstein-K(a)hler metric on Cartan-Hartogs domain of the second type |
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| 作者姓名： | ZHAO Xiaoxi ZHANG Liyou YIN Weiping |
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| 作者单位： | Department of Computer Science, Beijing Language and Culture University,Department of Mathematics, Capital Normal University, Beijing 100037, China,Department of Mathematics, Capital Normal University, Beijing 100037, China |
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| 基金项目： | 国家自然科学基金，北京市自然科学基金 |
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| 摘 要： | The Einstein-Kahler metric for the Cartan-Hartogs domain of the second type is described. Firstly, the Monge-Ampère equation for the metric to an ordinary differential equation in the auxiliary function X=X(z,w) is reduced, by which an implicit function in X is obtained. Secondly, for some cases, the explicit forms of the complete Einstein-Kahler metrics on Cartan-Hartogs domains which are the non-homogeneous domains are obtained. Thirdly, the estimate of holomorphic sectional curvature under the Einstein-Kahler metric is given, and in some cases the comparison theorem for Kobayashi metric and Einstein-Kahler metric on Cartan-Hartogs domain of the second type is established.
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| 关 键 词： | Cartan-Hartogs domain Einstein-Kahler metric non-homogeneous domain comparison theorem |
Einstein-K(a)hler metric on Cartan-Hartogs domain of the second type |
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| ZHAO Xiaoxi,ZHANG Liyou,YIN Weiping.Einstein-K(a)hler metric on Cartan-Hartogs domain of the second type[J].Progress in Natural Science,2004,14(3):201-212. |
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| Authors: | Zhao Xiaoxia ZHANG Liyou YIN Weiping |
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| Institution: | 1. Department of Computer Science, Beijing Language and Culture University
2. Department of Mathematics, Capital Normal University, Beijing 100037, China |
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| Abstract: | The Einstein-Kahler metric for the Cartan-Hartogs domain of the second type is described. Firstly, the Monge-Ampère equation for the metric to an ordinary differential equation in the auxiliary function X=X(z,w) is reduced, by which an implicit function in X is obtained. Secondly, for some cases, the explicit forms of the complete Einstein-Kahler metrics on Cartan-Hartogs domains which are the non-homogeneous domains are obtained. Thirdly, the estimate of holomorphic sectional curvature under the Einstein-Kahler metric is given, and in some cases the comparison theorem for Kobayashi metric and Einstein-Kahler metric on Cartan-Hartogs domain of the second type is established. |
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| Keywords: | Cartan-Hartogs domain Einstein-Kahler metric non-homogeneous domain comparison theorem |
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