Intrinsic geometry of oriented congruences in three dimensions
| dc.creator | Hill, C Denson | |
| dc.creator | Nurowski, Pawel | |
| dc.date | 2008-08-13 | |
| dc.date.accessioned | 2026-07-07T09:56:29Z | |
| dc.date.available | 2026-07-07T09:56:29Z | |
| dc.description | Starting from the classical notion of an oriented congruence (i.e. a foliation by oriented curves) in $R^3$, we abstract the notion of an oriented congruence structure. This is a 3-dimensional CR manifold $(M,H, J)$ with a preferred splitting of the tangent space $TM=V\oplus H$. We find all local invariants of such structures using Cartan's equivalence method refining Cartan's classification of 3-dimensional CR structures. We use these invariants and perform Fefferman like constructions, to obtain interesting Lorentzian metrics in four dimensions, which include explicit Ricci-flat and Einstein metrics, as well as not conformally Einstein Bach-flat metrics. | |
| dc.identifier | https://arxiv.org/abs/0808.1843 | |
| dc.identifier | http://arxiv.org/abs/0808.1843 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166990 | |
| dc.subject | Differential Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 32V05; 53A55; 83C15 | |
| dc.title | Intrinsic geometry of oriented congruences in three dimensions | |
| dc.type | text |