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@article{1079822,
author = {Slovák, Jan and Schmalz, Gerd},
article_number = {5},
doi = {http://dx.doi.org/10.2478/s11533-012-0090-y},
keywords = {Cartan connection; Cartan curvature; Parabolic geometry; Fefferman construction},
language = {eng},
issn = {1895-1074},
journal = {Central European Journal of Mathematics},
title = {Free CR distributions},
volume = {10},
year = {2012}
}
TY - JOUR
ID - 1079822
AU - Slovák, Jan - Schmalz, Gerd
PY - 2012
TI - Free CR distributions
JF - Central European Journal of Mathematics
VL - 10
IS - 5
SP - 1896-1913
EP - 1896-1913
SN - 18951074
KW - Cartan connection
KW - Cartan curvature
KW - Parabolic geometry
KW - Fefferman construction
N2 - 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.
ER -
SLOVÁK, Jan and Gerd SCHMALZ. Free CR distributions. \textit{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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