| Title:
|
Local reflexion spaces (English) |
| Author:
|
Gregorovič, Jan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
48 |
| Issue:
|
5 |
| Year:
|
2012 |
| Pages:
|
323-332 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A reflexion space is generalization of a symmetric space introduced by O. Loos in [4]. We generalize locally symmetric spaces to local reflexion spaces in the similar way. We investigate, when local reflexion spaces are equivalently given by a locally flat Cartan connection of certain type. (English) |
| Keyword:
|
local reflexion space |
| Keyword:
|
flat Cartan geometry |
| Keyword:
|
local infinitesimal automorphisms |
| MSC:
|
53C10 |
| MSC:
|
53C35 |
| idMR:
|
MR3007615 |
| DOI:
|
10.5817/AM2012-5-323 |
| . |
| Date available:
|
2012-12-17T13:57:21Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143108 |
| . |
| Reference:
|
[1] Alekseevsky, D. V., Michor, P. W.: Differential geometry of $\mathfrak{g}$–manifolds.Differential Geom. Appl. 5 (1995), 371–403. MR 1362865, 10.1016/0926-2245(95)00023-2 |
| Reference:
|
[2] Čap, A., Slovák, J.: Parabolic Geometries I: Background and General Theory.Math. Surveys Monogr. 154 (2009). Zbl 1183.53002, MR 2532439 |
| Reference:
|
[3] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Springer Verlag, Berlin–Heidelberg, 1993. MR 1202431 |
| Reference:
|
[4] Loos, O.: Spiegelungsräume und homogene symmetrische Räume.Math. Z. 99 (1967), 141–170. Zbl 0148.17403, MR 0212742, 10.1007/BF01123745 |
| Reference:
|
[5] Loos, O.: An intrinsic characterization of fibre bundles associated with homogeneous spaces defined by Lie group automorphisms.Abh. Math. Sem. Univ. Hamburg 37 (1972), 160–179. Zbl 0239.55018, MR 0307124, 10.1007/BF02999694 |
| Reference:
|
[6] Sharpe, R. W.: Differential Geometry, Cartan’s Generalization of Klein’s Erlangen Program.Springer Verlag, New York, 1997. Zbl 0876.53001, MR 1453120 |
| . |
