2010/04/21 by Matthias Hammerl, Katja Sagerschnig · 2 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:35N10 #msc:53A30 #msc:53B15
paper · pdf · doi:10.1007/s10455-010-9240-2
published as Annals of Global Analysis and Geometry, 2011, Volume 39, Number 4, pp. 403-425 [Some formulas corrected] · 26 pages
arxiv created 2010/04/21 · openalex publication_date 2010/12/14 · arxiv updated 2011/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.