  A Riemannian manifold is called harmonic if its volume density function
expressed in polar coordinates centered at any point is radial. Flat and
rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz
Conjecture) is true for manifolds of nonnegative scalar curvature and for some
other classes of manifolds, but is not true in general: there exists a family
of homogeneous harmonic spaces, the Damek-Ricci spaces, containing noncompact
rank-one symmetric spaces, as well as infinitely many nonsymmetric examples. We
prove that a harmonic homogeneous manifold of nonpositive curvature is either
flat, or is isometric to a Damek-Ricci space.
