Geodesic
Four-dimensional locally homogeneous pseudo-Riemannian manifolds with a~nontrivial isotropy subgroup and an isotropic Schouten--Weil tensor
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Tome 223 (2023), pp. 50-65.

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The isotropic Schouten–Weyl tensor was previously studied in the case of three-dimensional Lie groups with a left-invariant Lorentzian metric. In the case of locally homogeneous pseudo-Riemannian spaces with a nontrivial isotropy subgroup, manifolds with an isotropic Weyl tensor were classified. In this paper, we obtain a classification of four-dimensional, locally homogeneous pseudo-Riemannian manifolds with an isotropic Schouten—Weyl tensor. Some results on the curvature tensors of similar manifolds are obtained.
Keywords: locally homogeneous space, isotropic Schouten–Weyl tensor, Lie algebra. 
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     title = {Four-dimensional locally homogeneous {pseudo-Riemannian} manifolds with a~nontrivial isotropy subgroup and an isotropic {Schouten--Weil} tensor},
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P. N. Klepikov. Four-dimensional locally homogeneous pseudo-Riemannian manifolds with a~nontrivial isotropy subgroup and an isotropic Schouten--Weil tensor. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Tome 223 (2023), pp. 50-65. http://geodesic.mathdoc.fr/item/INTO_2023_223_a4/

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