Weierstrass representation for surfaces in the three-dimensional Heisenberg group

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.

Keywords

Heisenberg group / Mean curvature / Weierstrass representation

References

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