On a conjecture of Fefferman and Graham
An embedding of codimension 2 of an arbitrary real-analytic manifold \(M\) of even dimension into a Ricci-flat regular tubular neighborhood \(N=U(M)\) is constructed. This result generalizes a theorem of Fefferman and Graham (1985) concerning odd dimensional manifolds \(M\). A family of formal solutions of the embedding problem involving logarithms and square-roots is obtained by means of PDEs with respect to coordinates of a regular neighborhood. The formal solution is convergent and contains \(n(n+1)\) arbitrary coefficients.
scientific article; zbMATH DE number 2081968