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

Abstract

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 $[g{]}_{\mathcal{D}}$.

Misprints in Theorem B are corrected

References in corpus (3)

• On Nurowski's conformal structure associated to a generic rank two distribution in dimension five
• Invariant Prolongation of BGG-Operators in Conformal Geometry
• Almost Einstein and Poincare-Einstein manifolds in Riemannian signature