  In this paper we consider smooth oriented hypersurfaces in 2-step nilpotent
Lie groups with a left invariant metric and derive an expression for the
Laplacian of the Gauss map for such hypersurfaces in the general case and in
some particular cases. In the case of CMC-hypersurface in the
(2m+1)-dimensional Heisenberg group we also derive necessary and sufficient
conditions for the Gauss map to be harmonic and prove that for m=1 all
CMC-surfaces with the harmonic Gauss map are "cylinders".
