Closed Biconservative Hypersurfaces in Spheres
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909451773018112 |
|---|---|
| author | Montaldo, Stefano Oniciuc, Cezar Pampano, Alvaro |
| author_facet | Montaldo, Stefano Oniciuc, Cezar Pampano, Alvaro |
| contents | We characterise the profile curves of non-CMC biconservative rotational hypersurfaces of space forms $N^n(ρ)$ as $p$-elastic curves, for a suitable rational number $p\in[1/4,1)$ which depends on the dimension $n$ of the ambient space. Analysing the closure conditions of these $p$-elastic curves, we prove the existence of a discrete biparametric family of non-CMC closed (i.e., compact without boundary) biconservative hypersurfaces in $\mathbb{S}^n(ρ)$. None of these hypersurfaces can be embedded in $\mathbb{S}^n(ρ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_11169 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Closed Biconservative Hypersurfaces in Spheres Montaldo, Stefano Oniciuc, Cezar Pampano, Alvaro Differential Geometry We characterise the profile curves of non-CMC biconservative rotational hypersurfaces of space forms $N^n(ρ)$ as $p$-elastic curves, for a suitable rational number $p\in[1/4,1)$ which depends on the dimension $n$ of the ambient space. Analysing the closure conditions of these $p$-elastic curves, we prove the existence of a discrete biparametric family of non-CMC closed (i.e., compact without boundary) biconservative hypersurfaces in $\mathbb{S}^n(ρ)$. None of these hypersurfaces can be embedded in $\mathbb{S}^n(ρ)$. |
| title | Closed Biconservative Hypersurfaces in Spheres |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2201.11169 |