Umbilicity and characterization of Pansu spheres in the Heisenberg group

For n ≥ 2 we define a notion of umbilicity for hypersurfaces in the Heisenberg group Hn. We classify umbilic hypersurfaces in some cases, and prove that Pansu spheres are the only umbilic spheres with positive constant p(or horizontal)-mean curvature in Hn up to Heisenberg translations.