| 邱红兵.H~2×R中给定平均曲率曲面的Weierstrass表示[J].数学年刊A辑,2010,31(1):1~12 |
| H~2×R中给定平均曲率曲面的Weierstrass表示 |
| Weierstrass Representation for Surfaces of Prescribed Mean Curvature in H~2×R |
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| DOI： |
| 中文关键词: 法高斯映照 平均曲率 Weierstrass表示 |
| 英文关键词:Normal Gauss map Mean curvature Weierstrass representation2000 |
| 基金项目:国家自然科学基金(No.10571068)资助的项目 |
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| 中文摘要: |
| 定义了H~2×R中曲面的法高斯映照,给出了给定平均曲率曲面的Weierstrass表示,证明了法高斯映照满足一个二阶偏微分方程,并且该方程是所得到的Weierstrass表示的完全可积条件. |
| 英文摘要: |
| This paper defines the normal Gauss map of surfaces in H~2×R and gives a representation formula for surfaces of prescribed mean curvature.Furthermore,a second order partial differential equation for the Gauss map is obtained and it is shown that this equation is the complete integrability condition of the representation. |
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