Variational status of a class of fully nonlinear curvature prescription problems
Variational status of a class of fully nonlinear curvature prescription problems
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DOI：
10.1007/s00526-007-0141-6
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发表时间：
2006-10
影响因子：
2.1
通讯作者：
T. Branson;A. Gover
中科院分区：
文献类型：
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作者：
T. Branson;A. Gover
通过保角变换，使Schouten张量σk(P)的第k个初等对称多项式为常数，是Yamabe问题的推广。在紧黎曼流形上，我们证明了：对于3阶≤k≤n，当且仅当结构是局部共形平坦的时，该方程是一个具有某种作用的欧拉-拉格朗日方程.
Prescribing, by conformal transformation, thekth-elementary symmetric polynomial of the Schouten tensor σk(P) to be constant is a generalisation of the Yamabe problem. On compact Riemanniann-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.