Three Dimensional Lorentz homogeneous spaces and the Petrov classification
arXiv:1203.0625
Abstract
In this note, we verify the classification of local geometries given by A.Z. Petrov. First, we determine criteria for identifying a given 3D Lorentz homogeneous space in Petrov's classification. Then, we identify all inequivalent 1D subalgebras of all real 4D Lie algebras and determine which of these give rise to a homogeneous space admitting an invariant Lorentz metric.
39 pages, 16 tables; adapted from master's thesis