Variational status of a class of fully nonlinear curvature prescription problems

Details Variational status of a class of fully nonlinear curvature prescription problems Variational status of a class of fully nonlinear curvature prescription problems

2006-10-26

arxiv.org/abs/math/0610773v1

Mathematics

Differential Geometry

11 pages

Scientific paper

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.

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