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

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

2007-08-21

arxiv.org/abs/0708.2770v1

Mathematics

Differential Geometry

Scientific paper

10.1088/1751-8113/40/43/021

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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