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MiS Preprint

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.

Jun 7, 2005
Jun 7, 2005
MSC Codes:
affine curvature homogeneous, vanishing curvature invariants, holonomy, ivanov-petrova manifold, osserman manifold, szabo manifold

Related publications

2005 Journal Open Access
Peter B. Gilkey and Stana Nikcevic

Generalized plane wave manifolds

In: Kragujevac journal of mathematics, 28 (2005), pp. 113-138