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This is an English translation of the following paper, published severalyears ago: Nikonorov Yu.G. On a characterization of critical points of thescalar curvature functional (Russian), Tr. Rubtsovsk. Ind. Inst., 7, 211-217(2000), Zbl. 0956.53033. All inserted footnotes provide additional informationrelated to the mentioned problem.

On a characterization of critical points of the scalar curvature functional