Algebraic curvature tensors for indefinite metrics whose skew-symmetric curvature operator has constant Jordan normal form

2002/05/08 by Peter Gilkey, Gilkey, Peter, Tan Zhang +1 · 1 citation
Mathematics · Physics and Astronomy · #53A15 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53A15

paper · pdf · doi:10.48550/arxiv.math/0205079

arxiv created 2002/05/08 · openalex publication_date 2002/05/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the connected pseudo-Riemannian manifolds of signature (p,q) with q≥5 so that at each point of M the skew-symmetric curvature operator has constant rank 2 and constant Jordan normal form on the set of spacelike 2 planes and so that the skew-symmetric curvature operator is not nilpotent for at least one point of M.

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• The Spectral Geometry of the Riemann Curvature Operator in the Higher Signature Setting

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