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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:
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 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


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