Complete k-curvature homogeneous pseudo-Riemannian manifolds 0-modeled on an indecomposible symmetric space

2005/04/04 by Peter Gilkey, Gilkey, Peter, Stana Nikčević +2
Mathematics · Physics and Astronomy · #53B20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53B20

paper · pdf · doi:10.48550/arxiv.math/0504050

arxiv created 2005/04/04 · openalex publication_date 2005/04/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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