Publication details

Free CR distributions

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Authors

SLOVÁK Jan SCHMALZ Gerd

Year of publication 2012
Type Article in Periodical
Magazine / Source Central European Journal of Mathematics
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.2478/s11533-012-0090-y
Field General mathematics
Keywords Cartan connection; Cartan curvature; Parabolic geometry; Fefferman construction
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Description 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.
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