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Publication details
Free CR distributions
Authors | |
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Year of publication | 2012 |
Type | Article in Periodical |
Magazine / Source | Central European Journal of Mathematics |
MU Faculty or unit | |
Citation | |
Doi | http://dx.doi.org/10.2478/s11533-012-0090-y |
Field | General mathematics |
Keywords | Cartan connection; Cartan curvature; Parabolic geometry; Fefferman construction |
Attached files | |
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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