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Abstract
The paper treats two pseudo-Riemannian spaces having common geodesic lines. Certain algebraic and differential conditions are imposed on the Riemann tensor of one of the spaces, while an operation of lowering indices and a calculation of the covariant derivative is carried out with respect to metrics and connection objects of the another space. In order to study the objects we introduce a special supplementary tensor. It is proven that, when the additional conditions are true, then either the spaces do not admit non-trivial mappings or the spaces are equidistant spaces. We apply tensor methods without limitations imposed on the sign of the metric under question.
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