  We develop a geometric and explicit construction principle that generates
classes of Poincare-Einstein manifolds, and more generally almost Einstein
manifolds. Almost Einstein manifolds satisfy a generalisation of the Einstein
condition; they are Einstein on an open dense subspace and, in general, have a
conformal scale singularity set that is a conformal infinity for the Einstein
metric. In particular, the construction may be applied to yield families of
compact Poincare-Einstein manifolds, as well as classes of almost Einstein
manifolds that are compact without boundary. We obtain classification results
which show that the construction essentially exhausts a class of almost
Einstein (and Poincare-Einstein) manifold. We develop the general theory of
fixed conformal structures admitting multiple compatible almost Einstein
structures. We also show that, in a class of cases, these are canonically
related to a family of constant mean curvature totally umbillic embedded
hypersurfaces.
