| Title:
|
On left invariant CR structures on ${\rm SU}(2)$ (English) |
| Author:
|
Čap, Andreas |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
5 |
| Year:
|
2006 |
| Pages:
|
185-195 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
There is a well known one–parameter family of left invariant CR structures on $SU(2)\cong S^3$. We show how purely algebraic methods can be used to explicitly compute the canonical Cartan connections associated to these structures and their curvatures. We also obtain explicit descriptions of tractor bundles and tractor connections. (English) |
| MSC:
|
32Vxx |
| MSC:
|
53Cxx |
| idZBL:
|
Zbl 1164.32304 |
| idMR:
|
MR2322406 |
| . |
| Date available:
|
2008-06-06T22:49:23Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108026 |
| . |
| Reference:
|
[1] Cartan E.: Sur la géométrie pseudo-conforme des hypersurfaces de l’espace de deux variables complexes.Ann. Mat. Pura Appl., IV. Ser. 11 (1932), 17–90. Zbl 0005.37401, MR 1553196 |
| Reference:
|
[2] Čap A.: Automorphism groups of parabolic geometries.in: Proceedings of the 24th Winter School on Geometry and Physics, Srni 2004, Rend. Circ. Mat. Palermo (2) Suppl. 75 (2005), 233–239. Zbl 1102.53013, MR 2152362 |
| Reference:
|
[3] Čap A.: Two constructions with parabolic geometries.Proceedings of the 25th Winter School on Geometry and Physics, Srni 2005, Rend. Circ. Mat. Palermo (2) Suppl. 79 (2006), 11–38, preprint math.DG/0504389. Zbl 1120.53013, MR 2287124 |
| Reference:
|
[4] Čap A.: Infinitesimal automorphisms and deformations of parabolic geometries.preprint math.DG/050835. Zbl 1161.32020, MR 2390330 |
| Reference:
|
[5] Čap A., Gover A. R.: Tractor calculi for parabolic geometries.Trans. Amer. Math. Soc. 354 (2002), 1511–1548. Zbl 0997.53016, MR 1873017 |
| Reference:
|
[6] Čap A., Schichl H.: Parabolic geometries and canonical Cartan connections.Hokkaido Math. J. 29 No.3 (2000), 453–505. Zbl 0996.53023, MR 1795487 |
| Reference:
|
[7] Gover A. R., Graham C. R.: CR invariant powers of the sub-Laplacian.J. Reine Angew. Math. 583 (2005), 1–27. Zbl 1076.53048, MR 2146851 |
| . |
