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On curvature homogeneous 4D Lorentzian manifolds

R. Milson·N. Pelavas
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Abstract

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.

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R. Milson, N. Pelavas. 2007-11-27. On curvature homogeneous 4D Lorentzian manifolds. https://arxiv.org/abs/gr-qc/0702152

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