Algebraic curvature tensors for indefinite metrics whose skew-symmetric curvature operator has constant Jordan normal form

Peter Gilkey, Tan Zhang

英文摘要：

We classify the connected pseudo-Riemannian manifolds of signature $(p,q)$ with $q\ge5$ so that at each point of $M$ the skew-symmetric curvature operator has constant rank 2 and constant Jordan normal form on the set of spacelike 2 planes and so that the skew-symmetric curvature operator is not nilpotent for at least one point of $M$.

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