The problem of the correctness of Schur's theorem

This paper considers the problem of the correctness of Schur's theorem for an $n$-dimensional Riemannian space $V_n$. We show that in the general case it is not correct, that is, it may happen that, for an arbitrarily small variation of the curvature of the space due to rotations of two-dimensional elements of area at points of a given domain, the variation of the curvature from point to point of the domain is arbitrarily large.
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