Abstract
For every 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-mean (or horizontal-mean) curvature in Hn up to Heisenberg translations.
Original language | English (US) |
---|---|
Pages (from-to) | 203-235 |
Number of pages | 33 |
Journal | Journal fur die Reine und Angewandte Mathematik |
Volume | 2015 |
DOIs | |
State | Published - 2015 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics