The Gauss map of Minimal graphs in the Heisenberg group

In this paper we study some geometric properties of surfaces in the Heisenberg group, ${\mathcal{H}}_3\mathrm{.}$ We obtain, using the Gauss map for Lie groups, a partial classification of minimal graphs in ${\mathcal{H}}_3\mathrm{.}$ We also proof the non existence of umbilical surfaces in ${\mathcal{H}}_3\mathrm{.}$