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arXiv · 2509.04972

The Classification of Rotationally symmetric hypersurfaces in the Heisenberg groups $H_{n}$

Hung-Lin Chiu·Sin-Hua Lai·Hsiao-Fan Liu
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Abstract

In this paper, we show the fundamental theorems for rotationally symmetric hypersurfaces, and thus, together with the earlier results in [3] and [4], provide a complete classification of umbilic hypersurfaces in the Heisenberg groups $H_{n}$. In addition, we give a complete description of generating curves for rotationally symmetric hypersurfaces with constant $p$-mean curvature $H=c$ (including $H=0$) in the Heisenberg group $H_{n}$. We also establish the validity of Alexandrov's theorem for rotationally symmetric hypersurfaces in $H_n$.

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Hung-Lin Chiu, Sin-Hua Lai, Hsiao-Fan Liu. 2025-09-05. The Classification of Rotationally symmetric hypersurfaces in the Heisenberg groups $H_{n}$. https://arxiv.org/abs/2509.04972

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