| Title:
|
New characterizations of linear Weingarten hypersurfaces immersed in the hyperbolic space (English) |
| Author:
|
Aquino, Cícero P. |
| Author:
|
de Lima, Henrique F. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
201-209 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we deal with complete linear Weingarten hypersurfaces immersed in the hyperbolic space $\mathbb{H}^{n+1}$, that is, complete hypersurfaces of $\mathbb{H}^{n+1}$ whose mean curvature $H$ and normalized scalar curvature $R$ satisfy $R=aH+b$ for some $a$, $b\in \mathbb{R}$. In this setting, under appropriate restrictions on the mean curvature and on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of $\mathbb{H}^{n+1}$. Furthermore, a rigidity result concerning the compact case is also given. (English) |
| Keyword:
|
hyperbolic space |
| Keyword:
|
linear Weingarten hypersurfaces |
| Keyword:
|
totally umbilical hypersurfaces |
| Keyword:
|
hyperbolic cylinders |
| MSC:
|
53A10 |
| MSC:
|
53B30 |
| MSC:
|
53C42 |
| MSC:
|
53C50 |
| idZBL:
|
Zbl 06537725 |
| idMR:
|
MR3434603 |
| DOI:
|
10.5817/AM2015-4-201 |
| . |
| Date available:
|
2015-11-30T09:58:12Z |
| Last updated:
|
2016-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144480 |
| . |
| Reference:
|
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