| Title:
|
A construction of non-flat non-homogeneous symmetric parabolic geometries (English) |
| Author:
|
Gregorovič, Jan |
| Author:
|
Zalabová, Lenka |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
52 |
| Issue:
|
5 |
| Year:
|
2016 |
| Pages:
|
291-302 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct series of examples of non-flat non-homogeneous parabolic geometries that carry a symmetry of the parabolic geometry at each point. (English) |
| Keyword:
|
parabolic geometries |
| Keyword:
|
geodesic symmetries |
| Keyword:
|
non-flat non-homogeneous examples |
| Keyword:
|
construction |
| Keyword:
|
generalized flag manifolds |
| MSC:
|
53B15 |
| MSC:
|
53C10 |
| MSC:
|
53C30 |
| MSC:
|
58J70 |
| idZBL:
|
Zbl 06674905 |
| idMR:
|
MR3610864 |
| DOI:
|
10.5817/AM2016-5-291 |
| . |
| Date available:
|
2016-12-20T21:55:27Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145936 |
| . |
| Reference:
|
[1] Čap, A., Slovák, J.: Parabolic Geometries: Background and general theory.Math. Surveys Monogr., vol. 154, AMS, 2009. MR 2532439, 10.1090/surv/154/03 |
| Reference:
|
[2] Gregorovič, J.: General construction of symmetric parabolic structures.Differential Geom. Appl. 38 (5) (2012), 450–476. Zbl 1350.53068, MR 2966647, 10.1016/j.difgeo.2012.06.006 |
| Reference:
|
[3] Gregorovič, J., Zalabová, L.: Notes on symmetric conformal geometries.Arch. Math. (Brno) 51 (5) (2015), 287–296. Zbl 1374.53080, MR 3449109, 10.5817/AM2015-5-287 |
| Reference:
|
[4] Gregorovič, J., Zalabová, L.: On automorphisms with natural tangent action on homogeneous parabolic geometries.J. Lie Theory 25 (2015), 677–715. MR 3384992 |
| Reference:
|
[5] Gregorovič, J., Zalabová, L.: Geometric properties of homogeneous parabolic geometries with generalized symmetries.Differential Geom. Appl. 49 (2016), 388–422. Zbl 1352.53020, MR 3573842, 10.1016/j.difgeo.2016.09.008 |
| Reference:
|
[6] Zalabová, L.: Parabolic symmetric spaces.Ann. Global Anal. Geom. 37 (2) (2010), 125–141. Zbl 1188.53026, MR 2578261, 10.1007/s10455-009-9177-5 |
| Reference:
|
[7] Zalabová, L.: A non-homogeneous, symmetric contact projective structure.Cent. Eur. J. Math. 12 (6) (2014), 879–886. Zbl 1302.53058, MR 3179989 |
| . |
