Special semi-reducible pseudo-Riemannian spaces
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2021
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Анотація

The paper contains necessary conditions allowing to reduce matrix tensors of pseudo-Riemannian spaces to special forms called semi-reducible, under assumption that the tensor defining tensor characteristic of semireducibility spaces, is idempotent.
The tensor characteristic is reduced to the spaces of constant curvature, Ricci-symmetric spaces and conformally flat pseudo-Riemannian spaces.

The obtained results can be applied for construction of examples of spaces belonging to special types of pseudo-Riemannian spaces.

The research is carried out locally in tensor shape, without limitations imposed on a sign of a metric.