Variedades de Osserman e Ivanov-Petrova en dimensión cuatro

Relating algebraic properties of the Riemannian curvature tensor to the underlying geometry of the manifold is a central problem in diferential geometry. Due to the dificulties in dealing with the full curvature tensor, the investigation usually derives to the consideration of the algebraic structure of certain natural operators, the Jacobi operator and the skew-symmetric curvature operator being typical examples. Properties of the Jacobi operator have been broadly studied since it measures the geodesic deviation.The skew-symmetric curvature operator is the part of the curvature tensor describing the behavior of circles. Geodesics and circles are classical objects in geometry and physics, the later being preserved by Mäobius transformations and thus related to the conformal structure.