Prescribing, by conformal transformation, the kth-elementary symmetric polynomial of the Schouten tensor σ k (P) to be constant is a generalisation of the Yamabe problem. On compact Riemannian n-manifolds we show that, for 3 ≤ k ≤ n, this prescription equation is an Euler–Lagrange equation of some action if and only if the structure is locally conformally flat.
