Examples of signature (2,2) manifolds with commuting curvature operators
Differential Geometry
2009-11-13 v1
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.
Keywords
Cite
@article{arxiv.0708.2770,
title = {Examples of signature (2,2) manifolds with commuting curvature operators},
author = {M. Brozos-Vazquez and E. Garcia-Rio and P. Gilkey and R. Vazquez-Lorenzo},
journal= {arXiv preprint arXiv:0708.2770},
year = {2009}
}