  We exhibit a family of generalized plane wave manifolds of signature (2,2).
The geodesics in these manifolds extend for infinite time (i.e. they are
complete), they are spacelike and timelike Jordan Osserman, and they are
spacelike and timelike Jordan Ivanov-Petrova. Some are irreducible symmetric
spaces. Some are homogeneous spaces but not symmetric. Some are 1-curvature
homogeneous but not homogeneous. All are 0-modeled on the same irreducible
symmetric space. We determine the Killing vector fields for these manifolds.
