| WEIERSTRASS REPRESENTATION FORSURFACES WITH PRESCRIBED NORMALGAUSS MAP AND GAUSS CURVATURE IN H~3 |
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| 作者姓名： | SHI Shuguo |
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| 作者单位： | SHI SHUGUO Institute of Mathematics，Pudan University，Shanghai 200433，China. Academy of Mathematics，Shandong University，Jinan 250100，China. |
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| 基金项目： | Project supported by the 973 Project of the Ministry of Science and Technology of China and the Science Foundation of the Ministry of Education of China. |
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| 摘 要： | The author obtains a Weierstrass representation for surfaces with prescribed normal Gauss map and Gauss curvature in H3. A differential equation about the hyperbolic Gauss map is also obtained, which characterizes the relation among the hyperbolic Gauss map, the normal Gauss map and Gauss curvature. The author discusses the harmonicity of the normal Gauss map and the hyperbolic Gauss map from surface with constant Gauss curvature in H3 to S2 with certain altered conformal metric. Finally, the author considers the surface whose normal Gauss map is conformal and derives a completely nonlinear differential equation of second order which graph must satisfy.
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| 关 键 词： | 双曲空间 高斯映射 调和映射 Weierstrass表示 曲率 |
| 收稿时间： | 4/3/2004 12:00:00 AM |
| 修稿时间： | 2016/10/3 0:00:00 |
WEIERSTRASS REPRESENTATION FOR SURFACES WITH PRESCRIBED NORMAL GAUSS MAP AND GAUSS CURVATURE IN $H^{3}$ |
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| SHI Shuguo.WEIERSTRASS REPRESENTATION FORSURFACES WITH PRESCRIBED NORMALGAUSS MAP AND GAUSS CURVATURE IN H~3[J].Chinese Annals of Mathematics,Series B,2004,25(4):567-586. |
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| Authors: | SHI Shuguo |
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| Institution: | Institute of Mathematics, Fundan University, Shanghai 200433,China;Academy of Mathematics, Shandong University, Jinan 250100, China |
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| Abstract: | The author obtains a Weierstrass representation for surfaces with prescribed normal Gauss map and Gauss curvature in H3. A differential equation about the hyperbolic Gauss map is also obtained, which characterizes the relation among the hyperbolic Gauss map, the normal Gauss map and Gauss curvature. The author discusses the harmonicity of the normal Gauss map and the hyperbolic Gauss map from surface with constant Gauss curvature in H3 to S2 with certain altered conformal metric. Finally, the author considers the surface whose normal Gauss map is conformal and derives a completely nonlinear differential equation of second order which graph must satisfy. |
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| Keywords: | Hyperbolic space Hyperbolic Gauss map Normal Gauss map Weier-strass representation Harmonic map |
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