Variational status of a class of fully nonlinear curvature prescription problems

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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.
11 pages

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Differential Geometry, Analysis of PDEs, Primary 53C20; Secondary 53J50, 35J60,35K55, 53A30

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http://salesiana.dossiersoluciones.com/handle/123456789/118111

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610773
 http://arxiv.org/abs/math/0610773

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arXiv