| 3维双曲空间中给定平均曲率曲面的Weierstrass表示 |
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| 引用本文： | 史淑国.3维双曲空间中给定平均曲率曲面的Weierstrass表示[J].数学年刊A辑(中文版),2001(6). |
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| 作者姓名： | 史淑国 |
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| 作者单位： | 复旦大学数学研究所 上海200433 |
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| 摘 要： | 首先叙述双曲空间中曲面的Ｇａｕｓｓ映照的定义；导出Ｇａｕｓｓ映照所满足的Ｂｅｌｔｒａｍｉ方程；给出了给定平均曲率曲面的Ｗｅｉｅｒｓｔｒａｓｓ表示公式；并讨论了这种表示的完全可积条件．
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| 关 键 词： | 双曲空间 平均曲率 Weierstrass表示 |
WEIERSTRASS REPRESENTATION FOR SURFACES OF PRESCRIBED MEAN CURVATURE IN THE HYPERBOLIC 3-DIMENSIONAL SPACE |
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| SHI Shuguo Institute of Mathematics,Fudan University,Shanghai ,China..WEIERSTRASS REPRESENTATION FOR SURFACES OF PRESCRIBED MEAN CURVATURE IN THE HYPERBOLIC 3-DIMENSIONAL SPACE[J].Chinese Annals of Mathematics,2001(6). |
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| Authors: | SHI Shuguo Institute of Mathematics Fudan University Shanghai China |
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| Institution: | SHI Shuguo Institute of Mathematics,Fudan University,Shanghai 200433,China. |
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| Abstract: | At the first, the author defines the Gauss map for surfaces in the hyperbolic space and prove that the Gauss map must satisfy a Beltrami equation. Next a representation formula for surfaces of prescribed mean curvature is obtained. The author also obtains a partial differential equations of two order for Gauss map and prove that this equation is the complete integrability condition of the above obtained representation. |
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| Keywords: | Hyperbolic space Mean curvature Weierstrass representation |
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