Examples of signature (2,2) manifolds with commuting curvature operators
arXiv:0708.2770 · doi:10.1088/1751-8113/40/43/021
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.
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