Curvature Homogeneous Spacelike Jordan Osserman Pseudo-riemannian Manifolds

Let s ≥ 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s, s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric space. They are spacelike Jordan Osserman with a Jacobi operator which is nilpotent of order 3; they are not timelike Jordan Osserman. They are k-spacelike higher order Jordan Osserman for 2 ≤ k ≤ s; they are k-timelike higher order Jordan Osserman for s + 2 ≤ k ≤ 2s, and they are not k-timelike higher order Jordan Osserman for 2 ≤ s ≤ s + 1.