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 |
Appears in Collections: | Aurora harvest 3 Mathematical Sciences publications |
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hdl_109170.pdf | Published version | 456.6 kB | Adobe PDF | View/Open |
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