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

Gilkey, Peter; Zhang, Tan

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

Authors

Description

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 $M$.