Complete minimal hypersurfaces in $\mathbb H^5$ with constant scalar curvature and zero Gauss-Kronecker curvature
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916585543827456 |
|---|---|
| author | Cui, Qing Zhang, Boyuan |
| author_facet | Cui, Qing Zhang, Boyuan |
| contents | We show that any complete minimal hypersurface in the five-dimensional hyperbolic space $\mathbb H^5$, endowed with constant scalar curvature and vanishing Gauss-Kronecker curvature, must be totally geodesic. Cheng-Peng [3] recently conjecture that any complete minimal hypersurface with constant scalar curvature in $\mathbb H^4$ is totally geodesic. Our result partially confirms this conjecture in five dimensional setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complete minimal hypersurfaces in $\mathbb H^5$ with constant scalar curvature and zero Gauss-Kronecker curvature Cui, Qing Zhang, Boyuan Differential Geometry We show that any complete minimal hypersurface in the five-dimensional hyperbolic space $\mathbb H^5$, endowed with constant scalar curvature and vanishing Gauss-Kronecker curvature, must be totally geodesic. Cheng-Peng [3] recently conjecture that any complete minimal hypersurface with constant scalar curvature in $\mathbb H^4$ is totally geodesic. Our result partially confirms this conjecture in five dimensional setting. |
| title | Complete minimal hypersurfaces in $\mathbb H^5$ with constant scalar curvature and zero Gauss-Kronecker curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2501.16232 |