| Title:
|
Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space (English) |
| Author:
|
Wang, Qiaoling |
| Author:
|
Xia, Changyu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
435-445 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study the topological and metric rigidity of hypersurfaces in ${\mathbb H}^{n+1}$, the $(n+1)$-dimensional hyperbolic space of sectional curvature $-1$. We find conditions to ensure a complete connected oriented hypersurface in ${\mathbb H}^{n+1}$ to be diffeomorphic to a Euclidean sphere. We also give sufficient conditions for a complete connected oriented closed hypersurface with constant norm of the second fundamental form to be totally umbilic. (English) |
| Keyword:
|
rigidity |
| Keyword:
|
hypersurfaces |
| Keyword:
|
topology |
| Keyword:
|
hyperbolic space |
| MSC:
|
53C20 |
| MSC:
|
53C24 |
| MSC:
|
53C40 |
| MSC:
|
53C42 |
| idZBL:
|
Zbl 1174.53318 |
| idMR:
|
MR2309976 |
| . |
| Date available:
|
2009-09-24T11:46:52Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128182 |
| . |
| Reference:
|
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| Reference:
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| . |
