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

• Main Authors: Matthias Hammerl, Katja Sagerschnig
• Format: Article
• Language: English
• Published: National Academy of Science of Ukraine 2009-08-01
• Series: Symmetry, Integrability and Geometry: Methods and Applications
• Subjects: generic distributions; conformal geometry; tractor calculus; Fefferman construction; conformal Killing fields; almost Einstein scales
• Online Access: http://dx.doi.org/10.3842/SIGMA.2009.081

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.