Riemannian manifolds whose skew-symmetric curvature operator has constant eigenvalues

A Riemannian metric on a manifold is said to be IP if the eigenvalues of th e skew-symmetric curvature operator are pointwise constant, i.e. they depen d upon the point of the manifold but not upon the particular 2 plane in the tangent bundle at that point. We classify the IP metrics in dimensions m = 5, m = 6, and m greater than or equal to 9.