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

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.

Keywords

• generic distributions
• conformal geometry
• tractor calculus
• Fefferman construction
• conformal Killing fields
• almost Einstein scales