  Higher dimensional Einstein gravity in vacuum admits static black hole
solutions with an Einstein manifold of non constant curvature as a horizon.
This gives a much richer family of static black holes than in four dimensional
GR. However, as we show in this paper, the Gauss-Bonnet string theory
correction to Einstein gravity poses severe limitations on the geometry of a
horizon Einstein manifold. The additional stringy constraints rule out most of
the known examples of exotic black holes with a horizon of non constant
curvature.
