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

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 Added by Peter B. Gilkey
 Publication date 2007
  fields
and research's language is English




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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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