Free CR distributions

Gerd Schmalz; Jan Slovák

Open Mathematics (2012)

  • Volume: 10, Issue: 5, page 1896-1913
  • ISSN: 2391-5455

Abstract

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There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n 2 are among the very few possibilities of the so-called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n+1,n)/P with a suitable parabolic subgroup P. We study the geometric properties of such real (2n+n 2)-dimensional submanifolds in ℂ n + n 2 for all n > 1. In particular, we show that the fundamental invariant is of torsion type, we provide its explicit computation, and we discuss an analogy to the Fefferman construction of a circle bundle in the hypersurface type CR geometry.

How to cite

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Gerd Schmalz, and Jan Slovák. "Free CR distributions." Open Mathematics 10.5 (2012): 1896-1913. <http://eudml.org/doc/269158>.

@article{GerdSchmalz2012,
abstract = {There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n 2 are among the very few possibilities of the so-called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n+1,n)/P with a suitable parabolic subgroup P. We study the geometric properties of such real (2n+n 2)-dimensional submanifolds in $\mathbb \{C\}^\{n + n^2 \} $ for all n > 1. In particular, we show that the fundamental invariant is of torsion type, we provide its explicit computation, and we discuss an analogy to the Fefferman construction of a circle bundle in the hypersurface type CR geometry.},
author = {Gerd Schmalz, Jan Slovák},
journal = {Open Mathematics},
keywords = {Cartan connection; Cartan curvature; Parabolic geometry; Fefferman construction; parabolic geometry},
language = {eng},
number = {5},
pages = {1896-1913},
title = {Free CR distributions},
url = {http://eudml.org/doc/269158},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Gerd Schmalz
AU - Jan Slovák
TI - Free CR distributions
JO - Open Mathematics
PY - 2012
VL - 10
IS - 5
SP - 1896
EP - 1913
AB - There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n 2 are among the very few possibilities of the so-called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n+1,n)/P with a suitable parabolic subgroup P. We study the geometric properties of such real (2n+n 2)-dimensional submanifolds in $\mathbb {C}^{n + n^2 } $ for all n > 1. In particular, we show that the fundamental invariant is of torsion type, we provide its explicit computation, and we discuss an analogy to the Fefferman construction of a circle bundle in the hypersurface type CR geometry.
LA - eng
KW - Cartan connection; Cartan curvature; Parabolic geometry; Fefferman construction; parabolic geometry
UR - http://eudml.org/doc/269158
ER -

References

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  8. [8] Šilhan J., A real analog of Kostant’s version of the Bott-Borel-Weil theorem, J. Lie Theory, 2004, 14(2), 481–499 Zbl1090.17010
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