  We investigate harmonic maps in the context of isometric embeddings when the
target space is Ricci-flat and has codimension one. With the help of the
Campbell-Magaard theorem we show that any $n$-dimensional ($n\geqslant 3$)
Lorentzian manifold can be isometrically and harmonically embedded in a
(n+1)-dimensional semi-Riemannian Ricci-flat space. We then extend our analysis
to the case when the target space is an Einstein space. Finally, as an example,
we work out the harmonic and isometric embedding of a
Friedmann-Robertson-Walker spacetime in a five-dimensional Ricci-flat space and
proceed to obtain a general scheme to minimally embed any vacuum solution of
general relativity in Ricci-flat spaces with codimension one.
