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Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group
We study immersed, connected, umbilic hypersurfaces in the Heisenberg group
with We show that such a hypersurface, if closed, must
be rotationally invariant up to a Heisenberg translation. Moreover, we prove
that, among others, Pansu spheres are the only such spheres with positive
constant sigma-k curvature up to Heisenberg translations.Comment: 28 pages, 6 figure
Umbilicity and characterization of Pansu spheres in the Heisenberg group
For we define a notion of umbilicity for hypersurfaces in the
Heisenberg group . We classify umbilic hypersurfaces in some cases, and
prove that Pansu spheres are the only umbilic spheres with positive constant
(or horizontal)-mean curvature in up to Heisenberg translations.Comment: 32 pages, 2 figures; in Crelle's journal, 201
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