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MiS Preprint

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

Miguel Brozos-Vazquez, Eduardo Garcia-Rio, Peter B. Gilkey and Ramon Vazquez-Lorenzo


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, these properties are related to the Ricci tensor of the affine structure.

Aug 17, 2007
Aug 17, 2007
MSC Codes:
anti-self-dual, self-dual, conformal Osserman, Einstein, curvature--Jacobi--Ricci commuting, Osserman, Ricci operator

Related publications

2007 Repository Open Access
Miguel Brozos-Vazquez, Peter B. Gilkey, Eduardo Garcia-Rio and Ramon Vazquez-Lorenzo

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

In: Journal of physics / A, 40 (2007) 43, pp. 13149-13159