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| Weierstrass Representation for Surfaces in the Three-Dimensional Heisenberg Group |
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Citation： |
Qun CHEN,Hongbing QIU.Weierstrass Representation for Surfaces in the Three-Dimensional Heisenberg Group[J].Chinese Annals of Mathematics B,2010,31(1):119~132 |
| Page view： 1951
Net amount： 1197 |
Authors： |
Qun CHEN; Hongbing QIU; |
Foundation： |
the National Natural Science Foundation of China (No. 10571068, 10871149)
and the Research Fund for the Doctoral Program of Higher Education (No. 200804860046). |
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| Abstract： |
The authors define the Gauss map of surfaces in the three-dimensional Heisen-
berg 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 represen-
tation. |
Keywords： |
Heisenberg group, Mean curvature, Weierstrass representation |
Classification： |
53B25, 53C40 |
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