The curvature homogeneity bound for Lorentzian four-manifolds
| dc.creator | Milson, Robert | |
| dc.creator | Pelavas, Nicos | |
| dc.date | 2007-11-24 | |
| dc.date | 2008-06-21 | |
| dc.date.accessioned | 2026-07-07T09:45:40Z | |
| dc.date.available | 2026-07-07T09:45:40Z | |
| dc.description | We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or CH_3 for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, CH_2 manifolds that are not homogeneous. The resulting metrics belong to the class of null electromagnetic radiation, type N solutions on an anti-de Sitter background. These findings prove that the four-dimensional Lorentzian Singer number $k_{1,3}=3$, falsifying some recent conjectures by Gilkey. We also prove that invariant classification for these proper CH_2 solutions requires $\nabla^{(7)}R$, and that these are the unique metrics requiring the seventh order. | |
| dc.description | 24 pages, streamlined version | |
| dc.identifier | https://arxiv.org/abs/0711.3851 | |
| dc.identifier | http://arxiv.org/abs/0711.3851 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163274 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | Differential Geometry | |
| dc.title | The curvature homogeneity bound for Lorentzian four-manifolds | |
| dc.type | text |