SLOVÁK, Jan and Gerd SCHMALZ. Free CR distributions. Central European Journal of Mathematics. 2012, vol. 10, No 5, p. 1896-1913. ISSN 1895-1074. doi:10.2478/s11533-012-0090-y.
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Basic information
Original name Free CR distributions
Name in Czech Volné CR distribuce
Authors SLOVÁK, Jan (203 Czech Republic, guarantor, belonging to the institution) and Gerd SCHMALZ (276 Germany).
Edition Central European Journal of Mathematics, 2012, 1895-1074.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher Poland
Confidentiality degree is not subject to a state or trade secret
Impact factor Impact factor: 0.405
RIV identification code RIV/00216224:14310/12:00057986
Organization unit Faculty of Science
Doi http://dx.doi.org/10.2478/s11533-012-0090-y
UT WoS 000306731000020
Keywords in English Cartan connection; Cartan curvature; Parabolic geometry; Fefferman construction
Tags AKR, rivok
Tags International impact, Reviewed
Changed by Changed by: prof. RNDr. Jan Slovák, DrSc., učo 1424. Changed: 3. 1. 2013 14:30.
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 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.
Abstract (in Czech)
Článek studuje výjimečné geometrie zděděné automaticky na generických plochách vysoké kodimenze v CR varietách. Využívá obecnou teorii parabolických geometrií k jejich studiu a podává také konstrukci analogickou k Feffermanově bandlu kružnic v případě kodimenze jedna.
Links
GA201/08/0397, research and development projectName: Algebraické metody v geometrii a topologii
Investor: Czech Science Foundation, Standard Projects
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