  Prescribing, 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.
