On curvature homogeneous 4D Lorentzian manifolds

2007/02/28 by Robert Milson, Milson, R., Nicos Pelavas +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.gr-qc/0702152

openalex publication_date 2007/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or \CH₃ for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, \CH₂ manifolds that are not homogeneous.

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