  We classify noncompact homogeneous spaces which are Einstein and
asymptotically harmonic. This completes the classification of Riemannian
harmonic spaces in the homogeneous case: Any simply connected homogeneous
harmonic space is flat, or rank-one symmetric, or a nonsymmetric Damek-Ricci
space. Independently, Y. Nikolayevsky has obtained the latter classification
under the additional assumption of nonpositive sectional curvatures.
