Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-25T00:42:33.322Z Has data issue: false hasContentIssue false
  • English
  • Français

The canonical Cartan bundle and connection in CR geometry

Published online by Cambridge University Press:  01 March 2009

MARC HERZLICH
MARC HERZLICH*
Affiliation:
Institut de Mathématiques et Modélisation de Montpellier, UMR 5149 CNRS – Université Montpellier II, France. e-mail: herzlich@math.univ-montp2.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

We give a simple differential geometric description of the canonical Cartan (or tractor) bundle and connection in CR geometry, thus offering an alternative definition to the usual abstract Lie algebraic approach.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 2 , March 2009 , pp. 415 - 434
Copyright
Copyright © Cambridge Philosophical Society 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bailey, T. N., Eastwood, M. G. and Gover, A. R.Thomas' structure bundle for confomal, projective, and related structures. Rocky Mountain J. Math. 24 (1994), 61–103.CrossRefGoogle Scholar
[2]Calderbank, D. M. J., Diemer, T. and Souček, V.Ricci-corrected derivatives and invariant differential operators. Diff. Geom. Appl. 23 (2005), 149–175.CrossRefGoogle Scholar
[3]Čap, A.Parabolic geometries, CR-tractors, and the Fefferman construction. Diff. Geom. Appl. 17 (2002), 123–138.CrossRefGoogle Scholar
[4]Čap, A.Correspondence spaces and twistor spaces for parabolic geometries. J. Reine Angew. Math. 582 (2005), 143–172.CrossRefGoogle Scholar
[5]Čap, A. and Gover, A. R.Tractor calculi for parabolic geometries. Trans. Amer. Math. Soc. 354 (2002), 1511–1548.CrossRefGoogle Scholar
[6]Čap, A. and Gover, A. R.Standard tractors and the conformal ambient metric construction. Ann. Global Anal. Geom. 24 (2003), 231–259.CrossRefGoogle Scholar
[7]Čap, A. and Schichl, H.Parabolic geometries and canonical Cartan connection. Hokkaido Math. J. 29 (2000), 453–505.CrossRefGoogle Scholar
[8]Čap, A. and Slovák, J.Weyl structures for parabolic geometries. Math. Scand. 93 (2003), 53–90.CrossRefGoogle Scholar
[9]Cartan, E.Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes. Ann. Mat. Pura Appl. 11 (1932), 17–90.CrossRefGoogle Scholar
[10]Cartan, E.Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes. Ann. Sc. Norm. Sup. Pisa, Ser. II, 1 (1932), 333–354.Google Scholar
[11]Chern, S.-S. and Moser, J. K.Real hypersurfaces in complex manifolds. Acta Math. 133 (1974), 219–271.CrossRefGoogle Scholar
[12]David, L.Weyl connections and curvature properties of CR manifolds. Ann. Glob. Anal. Geom. 26 (2004), 59–72.CrossRefGoogle Scholar
[13]Farris, F.An intrinsic construction of Fefferman's CR metric. Pacific J. Math. 123 (1986), 33–45.CrossRefGoogle Scholar
[14]Gauduchon, P. Connexion canonique et structures de Weyl en géométrie conforme. Unpublished lecture notes. (1990).Google Scholar
[15]Gover, A. R. and Graham, C. R.CR invariant powers of the sub-Laplacian. J. Reine Angew. Math. 583 (2005), 1–27.CrossRefGoogle Scholar
[16]Lee, J. M.The Fefferman metric and pseudohermitian invariants. Trans. Amer. Math. Soc. 296 (1986), 411–429.Google Scholar
[17]Lee, J. M.Pseudo–Einstein structures on CR manifolds. Amer. J. Math. 110 (1988), 157–178.CrossRefGoogle Scholar
[18]Tanaka, N.A Differential Geometric Study on Strongly Pseudo-Convex Manifolds (Kinokuniya Press, 1975).Google Scholar
[19]Webster, S.Pseudo-hermitian structure on a real hypersurface. J. Diff. Geom. 13 (1978), 25–41.Google Scholar