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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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