Hypersurfaces of any homogeneous $\mathbb{C}P^3$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917952131956736 |
|---|---|
| author | Liefsoens, Michaël |
| author_facet | Liefsoens, Michaël |
| contents | Hypersurfaces are studied and classified under multiple additional assumptions in any Riemannian homogeneous space $(\mathbb{C}P^3, g_a)$, including nearly Kähler $\mathbb{C}P^3$. Notably, all extrinsically homogeneous hypersurfaces are classified in all these spaces, with an explicit family of examples. Moreover, for nearly Kähler $\mathbb{C}P^3$, all Hopf hypersurfaces are classified. Finally, Codazzi-like hypersurfaces (and in particular parallel and totally geodesic hypersurfaces), totally umbilical hypersurfaces and constant sectional curvature hypersurfaces are proven to not exist in any homogeneous $\mathbb{C}P^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hypersurfaces of any homogeneous $\mathbb{C}P^3$ Liefsoens, Michaël Differential Geometry Hypersurfaces are studied and classified under multiple additional assumptions in any Riemannian homogeneous space $(\mathbb{C}P^3, g_a)$, including nearly Kähler $\mathbb{C}P^3$. Notably, all extrinsically homogeneous hypersurfaces are classified in all these spaces, with an explicit family of examples. Moreover, for nearly Kähler $\mathbb{C}P^3$, all Hopf hypersurfaces are classified. Finally, Codazzi-like hypersurfaces (and in particular parallel and totally geodesic hypersurfaces), totally umbilical hypersurfaces and constant sectional curvature hypersurfaces are proven to not exist in any homogeneous $\mathbb{C}P^3$. |
| title | Hypersurfaces of any homogeneous $\mathbb{C}P^3$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.08871 |