Free $n$-distributions: holonomy, sub-Riemannian structures, Fefferman constructions and dual distributions
| dc.creator | Armstrong, Stuart | |
| dc.date | 2007-06-29 | |
| dc.date.accessioned | 2026-07-07T08:13:09Z | |
| dc.date.available | 2026-07-07T08:13:09Z | |
| dc.description | This 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.description | First Draft | |
| dc.identifier | https://arxiv.org/abs/0706.4441 | |
| dc.identifier | http://arxiv.org/abs/0706.4441 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132702 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Metric Geometry | |
| dc.subject | 53B05, 53B15, 53B20, 32V99, 58J60, 58J70, 58A30 | |
| dc.title | Free $n$-distributions: holonomy, sub-Riemannian structures, Fefferman constructions and dual distributions | |
| dc.type | text |