On left invariant CR structures on SU ( 2 )

Andreas Čap

Archivum Mathematicum (2006)

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

Abstract

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There is a well known one–parameter family of left invariant CR structures on S U ( 2 ) ≅ 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.

How to cite

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Čap, 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

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  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. (1932) Zbl0005.37401MR1553196
  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. Zbl1102.53013MR2152362
  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. Zbl1120.53013MR2287124
  4. Čap A., Infinitesimal automorphisms and deformations of parabolic geometries, preprint math.DG/050835. Zbl1161.32020MR2390330
  5. Čap A., Gover A. R., Tractor calculi for parabolic geometries, Trans. Amer. Math. Soc. 354 (2002), 1511–1548. Zbl0997.53016MR1873017
  6. Čap A., Schichl H., Parabolic geometries and canonical Cartan connections, Hokkaido Math. J. 29 No.3 (2000), 453–505. Zbl0996.53023MR1795487
  7. 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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