The twistor spinors of generic 2- and 3-distributions

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

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Cited by in corpus (21)

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• The Geometry of Almost Einstein (2,3,5) Distributions
• On 5-manifolds admitting rank two distributions of Cartan type
• Analytic torsion of generic rank two distributions in dimension five
• Pure spinors, intrinsic torsion and curvature in odd dimensions
• Para-Kähler-Einstein 4-manifolds and non-integrable twistor distributions
• A non-normal Fefferman-type construction of split-signature conformal structures admitting twistor spinors
• A Projective-to-Conformal Fefferman-Type Construction
• Conformal superalgebras via tractor calculus
• Towards a Classification of pseudo-Riemannian Geometries Admitting Twistor Spinors
• First BGG operators on homogeneous conformal geometries
• Charged Conformal Killing Spinors
• The ambient obstruction tensor and conformal holonomy
• Homogeneous Real (2,3,5) Distributions with Isotropy
• Analytic torsion of nilmanifolds with (2,3,5) distributions
• Regularized determinants of the Rumin complex in irreducible unitary representations of the (2,3,5) nilpotent Lie group
• Normal BGG solutions and polynomials
• Transitive conformal holonomy groups