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.