Complete k-curvature homogeneous pseudo-Riemannian manifolds

2004/05/02 by Peter Gilkey, P. Gilkey, Gilkey, P. +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53B20

paper · pdf · doi:10.48550/arxiv.math/0405024

arxiv created 2004/05/02 · arxiv updated 2009/12/01

Abstract

For any k which is at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not k+1-affine curvature homogeneous, and hence not locally homogeneous. All the local scalar Weyl invariants of these manifolds vanish. These manifolds are Ricci flat, Osserman, and Ivanov-Petrova.

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