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Conformal structures associated to generic rank 2 distributions on 5-manifolds – characterization and Killing-field decomposition. (English) Zbl 1191.53016
Summary: 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 to \({\mathcal D}\) a conformal structure \([g]_{\mathcal D}\) of signature \((2,3)\) on \(M\). We show that these conformal structures \([g]_{\mathcal D}\) obtained 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 \([g]_{\mathcal D}\).

MSC:
53A55 Differential invariants (local theory), geometric objects
34A26 Geometric methods in ordinary differential equations
35N10 Overdetermined systems of PDEs with variable coefficients
53A30 Conformal differential geometry (MSC2010)
53B15 Other connections
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
58A30 Vector distributions (subbundles of the tangent bundles)
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