Complete k-curvature homogeneous pseudo-Riemannian manifolds 0-modeled   on an indecomposible symmetric space
  For k at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). The curvature tensor of these manifolds is modeled on that of an indecomposible symmetric space. All the local scalar Weyl curvature invariants of these manifolds vanish. 
Peter Gilkey and Stana Nikcevic