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Title: Free CR distributions
Contributor(s): Schmalz, Gerd  (author)orcid ; Slovak, Jan (author)
Publication Date: 2012
DOI: 10.2478/s11533-012-0090-y
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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 n² 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+n²)-dimensional submanifolds in C n+n² 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.
Publication Type: Journal Article
Source of Publication: Central European Journal of Mathematics, 10(5), p. 1896-1913
Publisher: Versita
Place of Publication: Poland
ISSN: 1644-3616
Field of Research (FOR): 010102 Algebraic and Differential Geometry
010111 Real and Complex Functions (incl Several Variables)
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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