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

Abstract

We classify the connected pseudo-Riemannian manifolds of signature $(p,q)$ with $q\ge 5$ 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 $M$.

Cited by in corpus (2)

• Riemannian manifolds of dimension 7 whose skew-symmetric curvature operator has constant eigenvalues
• The Spectral Geometry of the Riemann Curvature Operator in the Higher Signature Setting