Variational status of a class of fully nonlinear curvature prescription problems

By T. Branson, A. Gover. 2006

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Prescribing, by conformal transformation, the kth-elementary symmetric polynomial of the Schouten tensor σk(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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/903f011ee9af904aceb354db06af017adda5391c