| 在S2或T2上HCMU的曲率的光滑性 |
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| 引用本文： | 吴英毅.在S2或T2上HCMU的曲率的光滑性[J].中国科学院研究生院学报,2008,25(5):585-591. |
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| 作者姓名： | 吴英毅 |
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| 作者单位： | 中国科学院研究生院数学学院,北京,100049 |
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| 摘 要： | HCMU是一种在Riemann面上带奇点的extremal度量．在面积和Calabi能量有界的情况下， HCMU的Gauss曲率是Riemann面上的连续函数．本文得到一个在球面上没有Gauss曲率鞍点的HCMU的明显表达式，并进一步证明了在球面或环面上HCMU的Gauss曲率光滑的充要条件是度量的所有奇点的角度都是整数．
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| 关 键 词： | extremal度量 HCMU 锥奇点 奇角度 |
Smoothness of the curvature of an HCMU on S2 or T2 |
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| WU Ying-Yi.Smoothness of the curvature of an HCMU on S2 or T2[J].Journal of the Graduate School of the Chinese Academy of Sciences,2008,25(5):585-591. |
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| Authors: | WU Ying-Yi |
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| Institution: | School of Mathematical Sciences, Graduate University of the Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | An HCMU is a kind of extremal metric with singularities on a Riemann surface. If the area and Calabi energy are both bounded, the Gauss curvature of an HCMU is a continuous function on the Riemann surface. In this paper we get an explicit construction of an HCMU on S2 which has no saddle point of the Gauss curvature of the metric. Further more we prove that on S2 or T2 the Gauss curvature of an HCMU is smooth if and only all of the singular angles are integers. |
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| Keywords: | HCMU extremal metric HCMU conical singularity singular angle |
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