| Title:
|
Notes on symmetric conformal geometries (English) |
| Author:
|
Gregorovič, Jan |
| Author:
|
Zalabová, Lenka |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
51 |
| Issue:
|
5 |
| Year:
|
2015 |
| Pages:
|
287-296 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In particular, we show that each symmetric conformal geometry is either locally flat or covered by a pseudo-Riemannian symmetric space, where the covering is a conformal map. We construct examples of locally flat symmetric conformal geometries that are not pseudo-Riemannian symmetric spaces. (English) |
| Keyword:
|
conformal geometry |
| Keyword:
|
symmetric space |
| Keyword:
|
parallel Weyl tensor |
| MSC:
|
53A30 |
| MSC:
|
53C35 |
| idZBL:
|
Zbl 06537731 |
| idMR:
|
MR3449109 |
| DOI:
|
10.5817/AM2015-5-287 |
| . |
| Date available:
|
2016-01-11T10:08:36Z |
| Last updated:
|
2017-02-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144771 |
| . |
| Reference:
|
[1] Čap, A., Melnick, K.: Essential Killing fields of parabolic geometries: projective and conformal structures.Central European Journal of Mathematics 11 (12) (2013), 2053–2061. Zbl 1286.53017, MR 3111705 |
| Reference:
|
[2] Čap, A., Slovák, J.: Parabolic Geometries: Background and general theory.Math. Surveys and Monogr., vol. 154, Amer. Math. Soc., 2009. MR 2532439, 10.1090/surv/154/03 |
| Reference:
|
[3] Derdzinski, A., Roter, W.: Projectively flat surfaces, null parallel distributions, and conformally symmetric manifolds.Tohoku Math. J. 59 (4) (2007), 565–602. Zbl 1146.53014, MR 2404206, 10.2748/tmj/1199649875 |
| Reference:
|
[4] Gregorovič, J.: Classification of invariant AHS-structures on semisimple locally symmetric spaces.Central European Journal of Mathematics 11 (12) (2013), 2062–2075. Zbl 1300.53054, MR 3111706 |
| Reference:
|
[5] Gregorovič, J., Zalabová, L.: On automorphisms with natural tangent action on homogeneous parabolic geometries.J. Lie Theory 25 (2015), 677–715. MR 3384992 |
| Reference:
|
[6] Kruglikov, B., The, D.: The gap phenomenon in parabolic geometries.arXiv:1303.1307. |
| Reference:
|
[7] Zalabová, L.: Symmetries of parabolic geometries.Differential Geom. Appl. 27 (5) (2009), 605–622. Zbl 1187.53036, MR 2567839, 10.1016/j.difgeo.2009.03.001 |
| Reference:
|
[8] 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:
|
[9] Zalabová, L.: A non–homogeneous, symmetric contact projective structure.Central European Journal of Mathematics 12 (6) (2014), 879–886. Zbl 1302.53058, MR 3179989 |
| . |
