Abstract
Because of the different possible forms (Segre types) of the Ricci operator, semi-symmetry assumption for the curvature of a Lorentzian manifold turns out to have very different consequences with respect to the Riemannian case. In fact, a semi-symmetric homogeneous Riemannian manifold is necessarily symmetric, while we find some three-dimensional homogeneous Lorentzian manifolds which are semi-symmetric but not symmetric. The complete classification of three-dimensional semi-symmetric homogeneous Lorentzian manifolds is obtained.
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Supported by funds of MURST (PRIN), GNSAGA and the University of Lecce.
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Calvaruso, G. Three-dimensional semi-symmetric homogeneous Lorentzian manifolds. Acta Math Hung 121, 157–170 (2008). https://doi.org/10.1007/s10474-008-7194-7
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DOI: https://doi.org/10.1007/s10474-008-7194-7