| Title:
|
Uniqueness of the stereographic embedding (English) |
| Author:
|
Eastwood, Michael |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
50 |
| Issue:
|
5 |
| Year:
|
2014 |
| Pages:
|
265-271 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification. (English) |
| Keyword:
|
stereographic |
| Keyword:
|
conformal circles |
| Keyword:
|
compactification |
| MSC:
|
53A30 |
| MSC:
|
53C22 |
| idZBL:
|
Zbl 06487011 |
| idMR:
|
MR3303776 |
| DOI:
|
10.5817/AM2014-5-265 |
| . |
| Date available:
|
2015-01-07T14:51:25Z |
| Last updated:
|
2016-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144069 |
| . |
| Reference:
|
[1] Bailey, T.N., Eastwood, M.G.: Conformal circles and parametrizations of curves in conformal manifolds.Proc. Amer. Math. Soc. 108 (1990), 215–221. Zbl 0684.53016, MR 0994771, 10.1090/S0002-9939-1990-0994771-7 |
| Reference:
|
[2] Cartan, É.: Les espaces à connexion conforme.Ann. Soc. Polon. Math. (1923), 171–221. |
| Reference:
|
[3] Francès, C.: Rigidity at the boundary for conformal structures and other Cartan geometries.arXiv:0806:1008. |
| Reference:
|
[4] Francès, C.: Sur le groupe d’automorphismes des géométries paraboliques de rang 1.Ann. Sci. École Norm. Sup. 40 (2007), 741–764. Zbl 1135.53016, MR 2382860 |
| Reference:
|
[5] : The Maple program: http://www.maplesoft.com.ple program: http://www.maplesoft.com. |
| Reference:
|
[6] Tod, K.P.: Some examples of the behaviour of conformal geodesics.J. Geom. Phys. 62 (2012), 1778–1792. Zbl 1245.53042, MR 2925827, 10.1016/j.geomphys.2012.03.010 |
| Reference:
|
[7] Yano, K.: The Theory of Lie Derivatives and its Applications.North-Holland 1957. Zbl 0077.15802, MR 0088769 |
| . |
