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Examples of signature (2,2) manifolds with commuting curvature operators
Miguel Brozos-Vazquez, Eduardo Garcia-Rio, Peter B. Gilkey and Ramon Vazquez-LorenzoAbstract
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.
- Received:
- 17.08.07
- Published:
- 17.08.07
- MSC Codes:
- 53C20
- Keywords:
- anti-self-dual, self-dual, conformal Osserman, Einstein, curvature--Jacobi--Ricci commuting, Osserman, Ricci operator