Three Dimensional Lorentz homogeneous spaces and the Petrov classification

Details Three Dimensional Lorentz homogeneous spaces and the Petrov classification Three Dimensional Lorentz homogeneous spaces and the Petrov classification

2012-03-03

arxiv.org/abs/1203.0625v1

Physics

Mathematical Physics

39 pages, 16 tables; adapted from master's thesis

Scientific paper

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.

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