The twistor spinors of generic 2- and 3-distributions

Details The twistor spinors of generic 2- and 3-distributions The twistor spinors of generic 2- and 3-distributions

2010-04-21

arxiv.org/abs/1004.3632v1

Annals of Global Analysis and Geometry, 2011, Volume 39, Number 4, pp. 403-425 [Some formulas corrected]

Mathematics

Differential Geometry

26 pages

Scientific paper

10.1007/s10455-010-9240-2

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.

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