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

Given a maximally non-integrable $2$-distribution $\mathcal D$ on a $5$-manifold $M$, it was discovered by P. Nurowski that one can naturally associate a conformal structure $[g]_{\mathcal D}$ of signature $(2,3)$ on $M$. We show that those conformal structures $[g]_{\mathcal D}$ 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 $[g]_{\mathcal D}$ can be decomposed into a symmetry of $\mathcal D$ and an almost Einstein scale of $[g]_{\mathcal D}$.