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Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition

By Matthias Hammerl and Katja Sagerschnig

Abstract

Given a maximally non-integrable 2-distribution D on a 5-manifold M, it was discovered by P. Nurowski that one can naturally associate a conformal structure [g]_D of signature (2,3) on M. We show that those conformal structures [g]_D which come about by this construction are characterized by the existence of a normal conformal Killing 2-form which is locally decomposable and satisfies a genericity condition. We further show that every conformal Killing field of [g]_D can be decomposed into a symmetry of D and an almost Einstein scale of [g]_D

Topics: generic distributions, conformal geometry, tractor calculus, Fefferman construction, conformal Killing fields, almost Einstein scales, Mathematics, QA1-939, Science, Q, DOAJ:Mathematics, DOAJ:Mathematics and Statistics
Publisher: National Academy of Science of Ukraine
Year: 2009
DOI identifier: 10.3842/SIGMA.2009.081
OAI identifier: oai:doaj.org/article:3c38c28d07ed406482b080dbb038ee21
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