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.
References in corpus (4)
- Completeness, Ricci blowup, the Osserman and the conformal Osserman condition for Walker signature (2,2) manifolds
- Four-dimensional Riemannian manifolds with commuting higher order Jacobi operators
- Jacobi--Tsankov manifolds which are not 2-step nilpotent
- Pseudo-Riemannian manifolds with Commuting Jacobi Operators