Free CR distributions
| Authors | |
|---|---|
| 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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