| Title:
|
Remarks on Grassmannian Symmetric Spaces (English) |
| Author:
|
Zalabová, Lenka |
| Author:
|
Žádník, Vojtěch |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
5 |
| Year:
|
2008 |
| Pages:
|
569-585 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for $|1|$-graded parabolic geometries and for almost Grassmannian structures, in particular. As an application of two general constructions with parabolic geometries, we present an example of non-flat Grassmannian symmetric space. Next we observe there is a distinguished torsion-free affine connection preserving the Grassmannian structure so that, with respect to this connection, the Grassmannian symmetric space is an affine symmetric space in the classical sense. (English) |
| Keyword:
|
parabolic geometries |
| Keyword:
|
Weyl structures |
| Keyword:
|
almost Grassmannian structures |
| Keyword:
|
symmetric spaces |
| MSC:
|
53A40 |
| MSC:
|
53C05 |
| MSC:
|
53C15 |
| MSC:
|
53C35 |
| idZBL:
|
Zbl 1212.53054 |
| idMR:
|
MR2501585 |
| . |
| Date available:
|
2009-04-26T06:12:34Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128279 |
| . |
| 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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| . |
