Inclusions between parabolic geometries

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Authors

DOUBROV Boris SLOVÁK Jan

Year of publication 2010
Type Article in Periodical
Magazine / Source Pure and Applied Mathematics Quarterly
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords Cartan connections; Fefferman construction; free distributions; spinorial geometry; normality conditions
Attached files
Description 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.
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