Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 081, 29 pages      arXiv:0908.0483      https://doi.org/10.3842/SIGMA.2009.081
Contribution to the Special Issue “Élie Cartan and Differential Geometry”

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

Matthias Hammerl and Katja Sagerschnig
Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austria

Received April 09, 2009, in final form July 28, 2009; Published online August 04, 2009; Misprints in Theorem B are corrected November 09, 2009

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.

Key words: generic distributions; conformal geometry; tractor calculus; Fefferman construction; conformal Killing fields; almost Einstein scales.

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