Examples of signature (2, 2) manifolds with commuting curvature operators

2007/08/21 by M. Brozos-Vazquez, Miguel Brozos‐Vázquez, Eduardo García‐Río +5
Mathematics · #Curvature #Geology #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Mathematics #Pure mathematics #Scalar curvature #Sectional curvature #Signature (topology) #math.DG #msc:53C20

paper · pdf · doi:10.1088/1751-8113/40/43/021

arxiv created 2007/08/21 · openalex publication_date 2007/10/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We exhibit Walker manifolds of signature (2,2) with various commutativity properties for the Ricci operator, the skew-symmetric curvature operator, and the Jacobi operator. If the Walker metric is a Riemannian extension of an underlying affine structure A, these properties are related to the Ricci tensor of A.

Citations

• Jacobi--Tsankov manifolds which are not 2-step nilpotent
• Four-dimensional Riemannian manifolds with commuting higher order Jacobi operators
• Dynamics of antimembranes in the maximally supersymmetric eleven-dimensional pp wave
• Self-dual supergravity theories in 2 + 2 dimensions
• Screen bundles of Lorentzian manifolds and some generalisations of pp-waves
• GRAVITATION AND DUALITY SYMMETRY