Variational status of a class of fully nonlinear curvature prescription problems

Branson, Thomas P.; Gover, A. Rod
June 2008
Calculus of Variations & Partial Differential Equations;Jun2008, Vol. 32 Issue 2, p253
Academic Journal
Prescribing, by conformal transformation, the kth-elementary symmetric polynomial of the Schouten tensor s 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.


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