# On left invariant CR structures on $\mathrm{SU}\left(2\right)$

Archivum Mathematicum (2006)

- Volume: 042, Issue: 5, page 185-195
- ISSN: 0044-8753

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topČap, Andreas. "On left invariant CR structures on ${\rm SU}(2)$." Archivum Mathematicum 042.5 (2006): 185-195. <http://eudml.org/doc/249794>.

@article{Čap2006,

abstract = {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.},

author = {Čap, Andreas},

journal = {Archivum Mathematicum},

keywords = {Cartan connection; CR structure; curvature; tractor bundle; tractor connection},

language = {eng},

number = {5},

pages = {185-195},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {On left invariant CR structures on $\{\rm SU\}(2)$},

url = {http://eudml.org/doc/249794},

volume = {042},

year = {2006},

}

TY - JOUR

AU - Čap, Andreas

TI - On left invariant CR structures on ${\rm SU}(2)$

JO - Archivum Mathematicum

PY - 2006

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 042

IS - 5

SP - 185

EP - 195

AB - 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.

LA - eng

KW - Cartan connection; CR structure; curvature; tractor bundle; tractor connection

UR - http://eudml.org/doc/249794

ER -

## References

top- 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. (1932) Zbl0005.37401MR1553196
- 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. Zbl1102.53013MR2152362
- 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. Zbl1120.53013MR2287124
- Čap A., Infinitesimal automorphisms and deformations of parabolic geometries, preprint math.DG/050835. Zbl1161.32020MR2390330
- Čap A., Gover A. R., Tractor calculi for parabolic geometries, Trans. Amer. Math. Soc. 354 (2002), 1511–1548. Zbl0997.53016MR1873017
- Čap A., Schichl H., Parabolic geometries and canonical Cartan connections, Hokkaido Math. J. 29 No.3 (2000), 453–505. Zbl0996.53023MR1795487
- Gover A. R., Graham C. R., CR invariant powers of the sub-Laplacian, J. Reine Angew. Math. 583 (2005), 1–27. Zbl1076.53048MR2146851

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