Abstract
We study the Lorentzian manifolds M1, M2, M3, and M4 obtained by small changes of the standard Euclidean metric on ℝ4 with the punctured origin O. The spaces M1 and M4 are closed isotropic space-time models. The manifolds M3 and M4 (respectively, M1 and M2) are geodesically (non)complete; M1 are M4 are globally hyperbolic, while M2 and M3 are not chronological. We found the Lie algebras of isometry and homothety groups for all manifolds; the curvature, Ricci, Einstein, Weyl, and energy-momentum tensors. It is proved that M1 and M4 are conformally flat, while M2 and M3 are not conformally flat and their Weyl tensor has the first Petrov type.
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The author was supported by the Ministry of Education and Science of the Russian Federation (Grant 1.3087.2017/4.6).
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Berestovskii, V.N. Lorentzian Manifolds Close to Euclidean Space. Sib Math J 60, 235–248 (2019). https://doi.org/10.1134/S0037446619020058
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DOI: https://doi.org/10.1134/S0037446619020058