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Article Dans Une Revue Advances in Mathematics Année : 2004

On a conjecture of Fefferman and Graham

Résumé

In 1985, Fefferman and Graham have constructed a local embedding of an arbitrary real-analytic manifold, of odd dimension $n$, into a Ricci-flat manifold of dimension $n+2$ admitting a homothety. They conjectured that their result remains valid in even dimensions, if logarithms are allowed in the expansion of the metric. In this paper, we (i) prove that such expansions exist and converge and (ii) establish the degree of non-uniqueness of the solution in terms of the coefficients in the expansion.

Dates et versions

hal-00002569 , version 1 (17-08-2004)

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Satyanad Kichenassamy. On a conjecture of Fefferman and Graham. Advances in Mathematics, 2004, 184, pp.268-288. ⟨10.1016/S0001-8708(03)00145-2⟩. ⟨hal-00002569⟩
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