| Title:
|
Riemannian symmetries in flag manifolds (English) |
| Author:
|
Piu, Paola |
| Author:
|
Remm, Elisabeth |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
48 |
| Issue:
|
5 |
| Year:
|
2012 |
| Pages:
|
387-398 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Flag manifolds are in general not symmetric spaces. But they are provided with a structure of $\mathbb{Z}_2^k$-symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. The conditions for a metric adapted to the $\mathbb{Z}_2^2$-symmetric structure to be naturally reductive are detailed for the flag manifold $SO(5)/SO(2)\times SO(2) \times SO(1)$. (English) |
| Keyword:
|
$\mathbb{Z}_2^k$-symmetric space |
| Keyword:
|
flag manifolds |
| Keyword:
|
Riemannian metrics |
| MSC:
|
53C30 |
| idMR:
|
MR3007620 |
| DOI:
|
10.5817/AM2012-5-387 |
| . |
| Date available:
|
2012-12-17T14:03:37Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143113 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Bouyakoub, A., Goze, M., Remm, E.: On Riemannian non symmetric spaces and flag manifolds.arXiv:math/0609790. MR 2114414 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
