The twistor spinors of generic 2- and 3-distributions
arXiv:1004.3632 · doi:10.1007/s10455-010-9240-2
Abstract
Generic distributions on 5- and 6-manifolds give rise to conformal structures that were discovered by P. Nurowski resp. R. Bryant. We describe both as Fefferman-type constructions and show that for orientable distributions one obtains conformal spin structures. The resulting conformal spin geometries are then characterized by their conformal holonomy and equivalently by the existence of a twistor spinor which satisfies a genericity condition. Moreover, we show that given such a twistor spinor we can decompose a conformal Killing field of the structure. We obtain explicit formulas relating conformal Killing fields, almost Einstein structures and twistor spinors.
26 pages
References in corpus (4)
- Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds - Characterization and Killing-Field Decomposition
- Invariant Prolongation of BGG-Operators in Conformal Geometry
- Free 3-distributions: holonomy, Fefferman constructions and dual distributions
- Inclusions between parabolic geometries