Benoît Daniel
Published 2006-06-13, updated 2010-03-24Version 2
We study the Gauss map of minimal surfaces in the Heisenberg group $\mathrm{Nil}_3$ endowed with a left-invariant Riemannian metric. We prove that the Gauss map of a nowhere vertical minimal surface is harmonic into the hyperbolic plane $\mathbb{H}^2$. Conversely, any nowhere antiholomorphic harmonic map into $\mathbb{H}^2$ is the Gauss map of a nowhere vertical minimal surface. Finally, we study the image of the Gauss map of complete nowhere vertical minimal surfaces.
Comments: 17 pages, redaction improved.
Journal: Int. Math. Res. Not. IMRN 2011 (2011), no. 3, 674-695
On the Gauss map of finite geometric type surfaces
Gauss maps of surfaces in 3-dimentional Heisenberg group
Half-space theorem, embedded minimal annuli and minimal graphs in the Heisenberg group
![QR code for arXiv:math/0606299 [math.DG]](http://oss.arxitics.com/images/favicon.svg)