Szabo Osserman IP Pseudo-Riemannian manifolds
  We construct a family of pseudo-Riemannian manifolds so that the skew-symmetric curvature operator, the Jacobi operator, and the Szabo operator have constant eigenvalues on their domains of definition. This provides new and non-trivial examples of Osserman, Szabo, and IP manifolds. We also study when the associated Jordan normal form of these operators is constant. 
Peter Gilkey, Raina Ivanova, Tan Zhang