On Nurowski's conformal structure associated to a generic rank two distribution in dimension five

Abstract

For a generic distribution of rank two on a manifold $M$ of dimension five, we introduce the notion of a generalized contact form. To such a form we associate a generalized Reeb field and a partial connection. From these data, we explicitly constructed a pseudo--Riemannian metric on $M$ of split signature. We prove that a change of the generalized contact form only leads to a conformal rescaling of this metric, so the corresponding conformal class is intrinsic to the distribution. In the second part of the article, we relate this conformal class to the canonical Cartan connection associated to the distribution. This is used to prove that it coincides with the conformal class constructed by Nurowski.

AMSLaTeX, 23 pages

References in corpus (3)

• Differential equations and conformal structures
• Ricci-corrected derivatives and invariant differential operators
• Two constructions with parabolic geometries

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• Analytic torsion of generic rank two distributions in dimension five
• Homogeneous Real (2,3,5) Distributions with Isotropy
• The ambient obstruction tensor and conformal holonomy
• Analytic torsion of nilmanifolds with (2,3,5) distributions
• Regularized determinants of the Rumin complex in irreducible unitary representations of the (2,3,5) nilpotent Lie group