| Title:
|
Parallel and totally geodesic hypersurfaces of 5-dimensional 2-step homogeneous nilmanifolds (English) |
| Author:
|
Nasehi, Mehri |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
547-559 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study parallel and totally geodesic hypersurfaces of two-step homogeneous nilmanifolds of dimension five. We give the complete classification and explicitly describe parallel and totally geodesic hypersurfaces of these spaces. Moreover, we prove that two-step homogeneous nilmanifolds of dimension five which have one-dimensional centre never admit parallel hypersurfaces. Also we prove that the only two-step homogeneous nilmanifolds of dimension five which admit totally geodesic hypersurfaces have three-dimensional centre. (English) |
| Keyword:
|
hypersurface |
| Keyword:
|
totally geodesic hypersurface |
| Keyword:
|
parallel geodesic hypersurfaces |
| Keyword:
|
two-step homogeneous nilmanifold |
| MSC:
|
53C30 |
| MSC:
|
53C42 |
| idZBL:
|
Zbl 06604485 |
| idMR:
|
MR3519620 |
| DOI:
|
10.1007/s10587-016-0274-x |
| . |
| Date available:
|
2016-06-16T13:03:32Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145742 |
| . |
| Reference:
|
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