The ambient obstruction tensor and conformal holonomy

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.

26 pages. In Version 2 results for analytic conformal structures are generalised to smooth conformal structures

References in corpus (7)

• Almost conformally Einstein manifolds and obstructions
• Normal Conformal Killing Forms
• The twistor spinors of generic 2- and 3-distributions
• On Nurowski's conformal structure associated to a generic rank two distribution in dimension five
• Explicit ambient metrics and holonomy
• A Projective-to-Conformal Fefferman-Type Construction
• Conformal Holonomy Equals Ambient Holonomy