Curvature homogeneous hypersurfaces in space forms
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916730064863232 |
|---|---|
| author | Bryant, Robert Florit, Luis Ziller, Wolfgang |
| author_facet | Bryant, Robert Florit, Luis Ziller, Wolfgang |
| contents | We classify curvature homogeneous hypersurfaces in S^4 and H^4. In higher dimesnsion one only has the FKM examples and an isolate one by Tsukada of a hypersurface in H^5.
Besides some simple examples, we show that there exists an isolated hypersurface with a circle of symmetries and and a one parameter family admitting no continuous symmetries. Outside the set of minimal points, which only exists in the case of S^4, every example is locally and up to covers of this form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curvature homogeneous hypersurfaces in space forms Bryant, Robert Florit, Luis Ziller, Wolfgang Differential Geometry 53C40, 53B25, 53C30 We classify curvature homogeneous hypersurfaces in S^4 and H^4. In higher dimesnsion one only has the FKM examples and an isolate one by Tsukada of a hypersurface in H^5. Besides some simple examples, we show that there exists an isolated hypersurface with a circle of symmetries and and a one parameter family admitting no continuous symmetries. Outside the set of minimal points, which only exists in the case of S^4, every example is locally and up to covers of this form. |
| title | Curvature homogeneous hypersurfaces in space forms |
| topic | Differential Geometry 53C40, 53B25, 53C30 |
| url | https://arxiv.org/abs/2404.02302 |