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 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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0090-y,
author = {Gerd Schmalz and Jan Slov\'ak},
title = {Free CR distributions},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1896-1913},
zbl = {1262.32039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0090-y}
}
Gerd Schmalz; Jan Slovák. Free CR distributions. Open Mathematics, Tome 10 (2012) pp. 1896-1913. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0090-y/
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