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@article{905449,
author = {Doubrov, Boris and Slovák, Jan},
article_location = {Boston},
article_number = {3},
keywords = {Cartan connections; Fefferman construction; free distributions; spinorial geometry; normality conditions},
language = {eng},
issn = {1558-8599},
journal = {Pure and Applied Mathematics Quarterly},
title = {Inclusions between parabolic geometries},
volume = {6},
year = {2010}
}
TY - JOUR
ID - 905449
AU - Doubrov, Boris - Slovák, Jan
PY - 2010
TI - Inclusions between parabolic geometries
JF - Pure and Applied Mathematics Quarterly
VL - 6
IS - 3
SP - 755-780
EP - 755-780
PB - Int. Press
SN - 15588599
KW - Cartan connections
KW - Fefferman construction
KW - free distributions
KW - spinorial geometry
KW - normality conditions
N2 - Some of the well known Fefferman like constructions of parabolic geometries end up with a new structure on the same manifold. In this paper, we classify all such cases with the help of the classical Onishchik's lists [10] and we treat the only new series of inclusions in detail, providing the spinorial structures on the manifolds with generic free distributions. Our technique relies on the cohomological understanding of the canonical normal Cartan connections for parabolic geometries and the classical computations with exterior forms. Apart of the complete discussion of the distributions from the geometrical point of view and the new functorial construction of the inclusion into the spinorial geometry, we also discuss the normality problem of the resulting spinorial connections. In particular, there is a non-trivial subclass of distributions providing normal spinorial connections directly by the construction.
ER -
DOUBROV, Boris and Jan SLOVÁK. Inclusions between parabolic geometries. \textit{Pure and Applied Mathematics Quarterly}. Boston: Int. Press, 2010, vol.~6, No~3, p.~755-780. ISSN~1558-8599.
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