2011/09/20 by Matthias Hammerl, Hammerl, Matthias, Katja Sagerschnig +1
Mathematics · #35N10 #53A30 #53B15 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #math.DG #msc:35N10 #msc:53A30 #msc:53B15
paper · pdf · doi:10.48550/arxiv.1109.4231
arxiv created 2011/09/20 · openalex publication_date 2011/09/20 · arxiv updated 2011/09/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We treat a non-normal Fefferman-type construction based on an inclusion \SL(n+1)\embed\Spin(n+1,n+1). The construction associates a split signature (n,n)-conformal spin structure to a projective structure of dimension n. For n≥ 3 the induced conformal Cartan connection is shown to be normal if and only if it is flat. The main technical work of this article consists in showing that in the non-flat case the normalised conformal Cartan connection still allows a parallel (pure) spin-tractor and thus a corresponding (pure) twistor spinor on the conformal space. The Fefferman-type construction presented here is an alternative approach to study a construction of Dunajski-Tod