Rigidity and nonexistence of complete spacelike hypersurfaces in the steady state space
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_ | 1866912196734222336 |
|---|---|
| author | Barboza, Weiller F. C. de Lima, Henrique F. Velásquez, Marco Antonio L. |
| author_facet | Barboza, Weiller F. C. de Lima, Henrique F. Velásquez, Marco Antonio L. |
| contents | We study complete spacelike hypersurfaces immersed in an open region of the de Sitter space $\mathbb{S}^{n+1}_{1}$ which is known as the steady state space $\mathcal{H}^{n+1}$. In this setting, under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we prove that they must be spacelike hyperplanes of $\mathcal{H}^{n+1}$. Nonexistence results concerning these spacelike hypersurfaces are also given. Our approach is based on a suitable extension of the Omori-Yau's generalized maximum principle due to Al\'ıas, Impera and Rigoli in [5]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11614 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity and nonexistence of complete spacelike hypersurfaces in the steady state space Barboza, Weiller F. C. de Lima, Henrique F. Velásquez, Marco Antonio L. Differential Geometry We study complete spacelike hypersurfaces immersed in an open region of the de Sitter space $\mathbb{S}^{n+1}_{1}$ which is known as the steady state space $\mathcal{H}^{n+1}$. In this setting, under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we prove that they must be spacelike hyperplanes of $\mathcal{H}^{n+1}$. Nonexistence results concerning these spacelike hypersurfaces are also given. Our approach is based on a suitable extension of the Omori-Yau's generalized maximum principle due to Al\'ıas, Impera and Rigoli in [5]. |
| title | Rigidity and nonexistence of complete spacelike hypersurfaces in the steady state space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2501.11614 |