Four-dimensional Osserman metrics of neutral signature

2008/04/02 by Eduardo García‐Río, E. Garcia-Rio, P. Gilkey +9
Mathematics · #53C20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.DG #msc:53C20

paper · pdf · doi:10.48550/arxiv.0804.0436

arxiv created 2008/04/02 · openalex publication_date 2008/04/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the algebraic context, we show that null Osserman, spacelike Osserman, and timelike Osserman are equivalent conditions for a model of signature (2,2). We also classify the null Jordan Osserman models of signature (2,2). In the geometric context, we show that a pseudo-Riemannian manifold of signature (2,2) is null Jordan Osserman if and only if either it has constant sectional curvature or it is locally a complex space form.

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• Completeness, Ricci blowup, the Osserman and the conformal Osserman condition for Walker signature (2,2) manifolds