2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118111Prescribing, by conformal transformation, the kth-elementary symmetric polynomial of the Schouten tensor $P$ to be constant is a generalisation of the Yamabe problem. On compact Riemannian n-manifolds we show that, for k between and including 3 and n, this prescription equation is an Euler-Lagrange equation of some action if and only if the structure is locally conformally flat.11 pagesDifferential GeometryAnalysis of PDEsPrimary 53C20; Secondary 53J50, 35J60,35K55, 53A30text