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Generalized plane wave manifolds
Peter B. Gilkey and Stana Nikcevic
We show that generalized plane wave manifolds are complete, strongly geodesically convex, Osserman, Szabo, and Ivanov-Petrova. We show their holonomy groups are nilpotent and that all the local Weyl scalar invariants of these manifolds vanish. We construct isometry invariants which are not of Weyl type. Given k, we exhibit manifolds in this family which are k-curvature homogeneous but not locally homogeneous. We also exhibit a manifold which is weakly 1-curvature homogeneous but not 1-curvature homogeneous.