ar X iv : 0 80 4 . 27 45 v 1 [ m at h . D G ] 1 7 A pr 2 00 8 UNIVERSAL RECURSIVE FORMULAS FOR Q - CURVATURE
نویسنده
چکیده
We discuss recursive formulas for Branson’sQ-curvatures. The formulas present Q-curvatures of any order in terms of lower order Qcurvatures and lower order GJMS-operators. These presentations are universal in the sense that the recursive structure does not depend on the dimension of the underlying space. We give proofs for Q4 and Q6 for general metrics, and for Q8 for conformally flat metrics. The general case is conjectural. We display explicit formulas for Q-curvatures of order up to 16. The high order cases are tested for round spheres of even dimension and Einstein metrics. A part of the structure of the universal recursive formulas is described in terms of a generating function. The results rest on the theory of residue families ([25]).
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ar X iv : 0 80 4 . 27 45 v 2 [ m at h . D G ] 8 S ep 2 00 8 UNIVERSAL RECURSIVE FORMULAS FOR Q - CURVATURE
We discuss recursive formulas for Branson’s Q-curvatures. These formulas present Q-curvatures of any order on manifolds of even dimension in terms of lower order Q-curvatures and lower order GJMS-operators. They are universal in the sense that their formulation does not depend on the dimension of the underlying space. We introduce two algorithms of different nature for the computation of the co...
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