Weyl homogeneous manifolds modelled on compact Lie groups

A Riemannian manifold is called Weyl homogeneous, if its Weyl conformal curvature tensor at any two points is "the same", up to a positive multiple. A Weyl homogeneous manifold is modelled on a homogeneous space M(0), if its Weyl tensor at every point is "the same" as the Weyl tensor of M(0), up to a positive multiple. We prove that a Weyl homogeneous manifold M(n), n >= 4, modelled on an irreducible symmetric space M(0) of type II or IV (on a compact simple Lie group with a hi-invariant metric or on its noncompact dual) is conformally equivalent to M(0). (C) 2010 Elsevier B.V. All rights reserved.