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On Nurowski’s conformal structure associated to a generic rank two distribution in dimension five. (English) Zbl 1172.53014
The authors introduce the notion of a generalized contact form for a generic distribution of rank two on a manifold \(M\) of dimension five. For this form they associate a generalized Reeb field and a partial connection. In this setting they give an explicit construction of a pseudo-Riemannian manifold \(M\) having a split signature, and prove that a change of the generalized contact form yields only a conformal rescaling of the pseudo-Riemannian metric. Consequently the corresponding conformal class is intrinsic to the generalized contact form. This conformal class is then related to the canonical Cartan connection associated to the original distribution, and this allows them to prove that it coincides with conformal class of P. Nurowski [J. Geom. Phys. 55, No. 1, 19–49 (1986)]. Contents include: Introduction (containing a nice overview of the topic); A canonical conformal structure; The relationship to Nurowski’s construction; and References (thirteen items).

MSC:
53A30 Conformal differential geometry (MSC2010)
53A40 Other special differential geometries
53B15 Other connections
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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References:
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