| 3维双曲空间中曲面的双曲Gauss映照和法Gauss映照 |
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| 引用本文： | 史淑国.3维双曲空间中曲面的双曲Gauss映照和法Gauss映照[J].数学学报,2004,47(1):1-10. |
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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;山东大学数学院,济南,250100 |
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| 基金项目： | 国家自然科学基金973资助项目 |
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| 摘 要： | 本文导出了3维双曲空间中曲面的双曲Gauss映照和法Gauss映照的关系,发现了一般的曲面由双曲Gauss映照和平均曲率函数唯一确定,并证明了双曲Gauss映照所满足的二阶线性椭圆方程,给出了两种形式的关于双曲Gauss映照的三阶非线性偏微分方程(组)的一个解.
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| 关 键 词： | 双曲空间 双曲Gauss映照 法Gauss映照 |
| 文章编号： | 0583-1431(2004)01-0001-10 |
The Hyperbolic Gauss Map and Normal Gauss Map of Surfaces in 3-Dimensioual Hyperbolic Space |
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| Shu Guo SHI.The Hyperbolic Gauss Map and Normal Gauss Map of Surfaces in 3-Dimensioual Hyperbolic Space[J].Acta Mathematica Sinica,2004,47(1):1-10. |
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| Authors: | Shu Guo SHI |
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| Institution: | Shu Guo SHI
(Institute of Mathematics, Fudan University, Shanghai 200433, P. R. China) (Academy of Mathematics, Shandong University, Jinan 250100, P. R. China) |
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| Abstract: | In this paper, a relation between hyperbolic Gauss map and the normal Gauss map of surfaces in a 3-dimensional hyperbolic space has been obtained. It is proved that generic surfaces are determined uniquely by the hyperbolic Gauss map and the mean curvature function. A linear elliptic equation of second order for the hyperbolic Gauss map has been derived. The author also obtains a solution for two kinds of nonlinear partial differential equations (systems) of third order for the hyperbolic Gauss map. |
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| Keywords: | Hyperbolic space Hyperbolic Gauss map Normal Gauss map |
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