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Критерий псевдоримановости слоения с трансверсальной линейной связностью.

We find necessary and sufficient conditions for a foliation of codimension $q$ on $n$-dimensional manifold with transverse linear connection to admit a transverse invariant pseudo-Riemannian metric of a given signature which is parallel with the respect to the indicated connection. In particular, we obtain a criterion for a foliation with transverse linear connection to be Riemannian foliation.