Algebraic curvature tensors whose skew-symmetric curvature operator has constant rank 2

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64011Let R be an algebraic curvature tensor for a non-degenerate inner product of signature(p,q) where q>4. If $π$ is a spacelike 2 plane, let $R(π)$ be the associated skew-symmetric curvature operator. We classify the algebraic curvature tensors so R(-) has constant rank 2 and show these are geometrically realizable by hypersurfaces in flat spaces. We also classify the Ivanov-Petrova algebraic curvature tensors of rank 2; these are the algebraic curvature tensors of constant rank 2 such that the complex Jordan normal form of R(-) is constant.Differential Geometry53B20Algebraic curvature tensors whose skew-symmetric curvature operator has constant rank 2text