Weierstrass Representation for Surfaces in the Three-Dimensional Heisenberg Group |
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| Authors: | Qun CHEN and Hongbing QIU |
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| Institution: | 1. School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China
2. School of Mathematical Sciences,Fudan University,Shanghai 200433,China |
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| Abstract: | The authors define the Gauss map of surfaces in the three-dimensional Heisenberg group and give 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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| Keywords: | Heisenberg group Mean curvature Weierstrass representation |
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