The twistor spinors of generic 2- and 3-distributions |
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Authors: | Matthias Hammerl Katja Sagerschnig |
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Institution: | 1.Faculty of Mathematics,University of Vienna,Wien,Austria;2.Institute of Mathematics,Polish Academy of Sciences,Warszawa,Poland |
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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. |
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Keywords: | |
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