The Classification of Rotationally symmetric hypersurfaces in the Heisenberg groups $H_{n}$
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915481419513856 |
|---|---|
| author | Chiu, Hung-Lin Lai, Sin-Hua Liu, Hsiao-Fan |
| author_facet | Chiu, Hung-Lin Lai, Sin-Hua Liu, Hsiao-Fan |
| contents | 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 $H_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04972 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Classification of Rotationally symmetric hypersurfaces in the Heisenberg groups $H_{n}$ Chiu, Hung-Lin Lai, Sin-Hua Liu, Hsiao-Fan Differential Geometry 53A10, 53C42, 53C22, 34A26 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 $H_n$. |
| title | The Classification of Rotationally symmetric hypersurfaces in the Heisenberg groups $H_{n}$ |
| topic | Differential Geometry 53A10, 53C42, 53C22, 34A26 |
| url | https://arxiv.org/abs/2509.04972 |