Abstract
We completely classify three-dimensional homogeneous Lorentzian manifolds, equipped with Einstein-like metrics. Similarly to the Riemannian case (E. Abbena et al., Simon Stevin Quart J Pure Appl Math 66:173–182, 1992), if (M, g) is a three-dimensional homogeneous Lorentzian manifold, the Ricci tensor of (M, g) being cyclic-parallel (respectively, a Codazzi tensor) is related to natural reductivity (respectively, symmetry) of (M, g). However, some exceptional examples arise.
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The author is supported by funds of MURST, GNSAGA and the University of Lecce.
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Calvaruso, G. Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds. Geom Dedicata 127, 99–119 (2007). https://doi.org/10.1007/s10711-007-9163-7
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DOI: https://doi.org/10.1007/s10711-007-9163-7