Free $n$-distributions: holonomy, sub-Riemannian structures, Fefferman constructions and dual distributions

dc.creatorArmstrong, Stuart
dc.date2007-06-29
dc.date.accessioned2026-07-07T08:13:09Z
dc.date.available2026-07-07T08:13:09Z
dc.descriptionThis paper analyses the parabolic geometries generated by a free $n$-distribution in the tangent space of a manifold. It shows that certain holonomy reductions of the associated normal Tractor connections, imply preferred connections with special properties, along with Riemannian or sub-Riemannian structures on the manifold. It constructs examples of these holonomy reductions in the simplest cases. The main results, however, lie in the free 3-distributions. In these cases, there are normal Fefferman constructions over CR and Lagrangian contact structures corresponding to holonomy reductions to SO(4,2) and SO(3,3), respectively. There is also a fascinating construction of a `dual' distribution when the holonomy reduces to $G_2'$.
dc.descriptionFirst Draft
dc.identifierhttps://arxiv.org/abs/0706.4441
dc.identifierhttp://arxiv.org/abs/0706.4441
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132702
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subjectMetric Geometry
dc.subject53B05, 53B15, 53B20, 32V99, 58J60, 58J70, 58A30
dc.titleFree $n$-distributions: holonomy, sub-Riemannian structures, Fefferman constructions and dual distributions
dc.typetext

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