2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64292Let E be a natural operator associated to the curvature tensor of a pseudo-Riemannian manifold. This survey article studies when the spectrum, or more generally the real Jordan normal form, of E is constant on the natural domain of definition. It deals with results for the Jacobi operator, the higher order Jacobi operator, the Szabo operator, and the skew-symmetric curvature operator. Some results in the complex setting are presented as well for the skew-symmetric curvature operator.Differential GeometryMathematical Physics53B20text