Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/109170
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Type: Journal article
Title: The ambient obstruction tensor and conformal holonomy
Author: Leistner, T.
Lischewski, A.
Citation: Pacific Journal of Mathematics, 2017; 290(2):403-436
Publisher: Mathematical Sciences Publishers
Issue Date: 2017
ISSN: 0030-8730
0030-8730
Statement of
Responsibility: 
Thomas Leistner and Andree Lischewski
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.
Keywords: Fefferman-Graham ambient metric, obstruction tensor, conformal holonomy, exceptional conformal structures, normal conformal Killing forms
Rights: © 2017 Mathematical Sciences Publishers
DOI: 10.2140/pjm.2017.290.403
Grant ID: http://purl.org/au-research/grants/arc/FT110100429
http://purl.org/au-research/grants/arc/DP120104582
Published version: http://dx.doi.org/10.2140/pjm.2017.290.403
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Mathematical Sciences publications

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