Invariant Yang-Mills connections over non-reductive pseudo-Riemannian homogeneous spaces

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. Show more