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The ambient obstruction tensor and conformal holonomy

2015/11/30 by Thomas Leistner, Andree Lischewski · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal map #Conformal symmetry #Connection (principal bundle) #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Holonomy #Mathematical analysis #Mathematical physics #Mathematics #Pure mathematics #Spinor #Tensor (intrinsic definition) #Twistor theory #Weyl transformation #math.DG #msc:53A30 #msc:53C29

paper · pdf · doi:10.2140/pjm.2017.290.403

published in Pacific Journal of Mathematics 290(2), 403-436 (Mathematical Sciences Publishers) · 26 pages. In Version 2 results for analytic conformal structures are generalised to smooth conformal structures

arxiv created 2016/09/05 · openalex publication_date 2017/07/25 · arxiv updated 2018/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

For a conformal manifold, we describe a new relation between the ambient obstruction tensor of Fefferman and Graham and the holonomy of the normal conformal Cartan connection. This relation allows us to prove several results on the vanishing and the rank of the obstruction tensor, for example for conformal structures admitting twistor spinors or normal conformal Killing forms. As our main tool we introduce the notion of a conformal holonomy distribution and show that its integrability is closely related to the exceptional conformal structures in dimensions five and six that were found by Nurowski and Bryant.

Citations