Last week I've wonder about embedding manifolds, after a little research, I knew about the Campbell-Magaard theorem and its generalisation.

This theorem asserts that a Riemannian n-manifold can be embedded in a Euclidean one of dimension n+d, with d between 1 and n(n-1).

Nonetheless, if the condition of plane (bulk) manifold is relaxed, to Ricci-flat (or Einstein, et cetera), then, d=1.

Some papers on the subject are gr-qc/0109076 and gr-qc/0111058, by F. Dahia and C. Romero.

Oscar.