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arXiv · 1406.2444

Umbilicity and characterization of Pansu spheres in the Heisenberg group

Jih-Hsin Cheng·Hung-Lin Chiu·Jenn-Fang Hwang·Paul Yang
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Abstract

For $n\geq 2$ we define a notion of umbilicity for hypersurfaces in the Heisenberg group $H_{n}$. 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 $H_{n}$ up to Heisenberg translations.

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Jih-Hsin Cheng, Hung-Lin Chiu, Jenn-Fang Hwang, Paul Yang. 2014-06-10. Umbilicity and characterization of Pansu spheres in the Heisenberg group. https://arxiv.org/abs/1406.2444

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