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  M0M0, if its Weyl tensor at every point is “the same” as the Weyl tensor of M0M0, up to a positive multiple. We prove that a Weyl homogeneous manifold MnMn, n⩾4n⩾4, modelled on an irreducible symmetric space M0M0 of type II or IV (on a compact simple Lie group with a bi-invariant metric or on its noncompact dual) is conformally equivalent to M0M0.