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

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

2007-10-11

arxiv.org/abs/0710.2208v1

J. Geom. Phys. 59 (2009) 901-912

Mathematics

Differential Geometry

AMSLaTeX, 23 pages

Scientific paper

10.1016/j.geomphys.2009.04.001

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.

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