Stanilov-Tsankov-Videv Theory - Brozos-Vázquez, M.; Fiedler, B.; García-Río, E.; Gilkey, P.; Nikcevic, S.; Stanilov, G.; Tsankov, Y.; Vázquez-Lorenzo, R.; Videv, V. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
We survey some recent results concerning Stanilov-Tsankov-Videv theory, conformal Osserman geometry, and Walker geometry which relate algebraic properties of the curvature operator to the underlying geometry of the manifold.