Weyl–Schouten theorem

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The Weyl–Schouten theorem in mathematics (named after Hermann Weyl and Jan Arnoldus Schouten) says that a Riemannian manifold of dimension n with n ≥ 3 is conformally flat if and only if the Schouten tensor is a Codazzi tensor for n = 3, or the Weyl tensor vanishes for n > 3.