| 一类拟凸域的Bergman度量与Kobayashi度量的比较定理 |
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| 引用本文： | 殷慰萍. 一类拟凸域的Bergman度量与Kobayashi度量的比较定理[J]. 数学进展, 1997, 26(4): 323-334 |
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| 作者姓名： | 殷慰萍 |
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| 作者单位： | 首都师范大学数学所 |
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| 基金项目： | 国家自然科学基金委员会 |
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| 摘 要： | 本文对一类拟凸域Ｅ（ｍ，ｎ，Ｋ）给出其不变Ｋａｈｌｅｒ度量下的全纯截曲率的显表达式，并构造了Ｅ（ｍ，ｎ，Ｋ）的一个不变的完备的Ｋａｈｌｅｒ度量，使得它大于或等于Ｂｅｒｇｍａｎ度量，而且其全纯截曲率的上界是一个负常数，从而得到Ｅ（ｍ，ｎ，Ｋ）的Ｂｅｒｇｍａｎ度量和Ｋｏｂａｙａｓｈｉ度量的比较定理。
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| 关 键 词： | 拟凸域 比较定理 Bergman度量 Kobayashi度量 |
The Comparison Theorem for the Bergman and Kobayashi Metrics on a Class of Pseudoconvex Domains |
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| Yin Weiping. The Comparison Theorem for the Bergman and Kobayashi Metrics on a Class of Pseudoconvex Domains[J]. Advances in Mathematics(China), 1997, 26(4): 323-334 |
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| Authors: | Yin Weiping |
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| Abstract: | The holomorphic sectional curvatures under invariant Khler metrics on a class of pseudoconvex domains E(m,n,K) are given in the explicit forms. In the meantime, we construct an invariant Khler metric, which is complete and not less than Bergman metric, such that its holomorphic sectional curvature is bounded above by a negative constant. Hence we obtain the comparison theorem for the Bergman and Kobayashi metrics on E(m,n,K). |
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| Keywords: | pseudoconvex domain holomorphic sectional curvature invariant metric comparison theorem |
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