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arXiv · 0708.2770

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

M. Brozos-Vazquez·E. Garcia-Rio·P. Gilkey·R. Vazquez-Lorenzo
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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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M. Brozos-Vazquez, E. Garcia-Rio, P. Gilkey, R. Vazquez-Lorenzo. 2007-08-21. Examples of signature (2,2) manifolds with commuting curvature operators. https://doi.org/10.1088/1751-8113/40/43/021

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