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On the geometry of three-dimensional pseudo-Riemannian homogeneous spaces. I. (Russian. English summary) Zbl 1451.53067
The author investigates conditions for which the Ricci curvature tensor vanishes on pseudo-Riemannian homogeneous spaces (P-RHSs) of dimension three, also, the author looks for conditions allowing P-RHSs to be Einstein manifolds and conditions for which each point of a P-RHS has a neighborhood that can be mapped to a flat space through a suitable transformation. Furthermore, the author provides explicitly the associated Levi-Cevita connections, curvature/torsion tensors, holonomy algebras, scalar curvatures, Ricci tensors.

MSC:
53C30 Differential geometry of homogeneous manifolds
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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References:
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