Affine Osserman connections and their Riemann extensions
The notion of an affine Osserman space is introduced, and certain properties of such spaces are studied. By interesting examples, such as that of the cotangent bundle equipped with the pseudo-Riemannian metric defined by the Riemann extension of a linear connection on the base, one establishes some relations between affine and pseudo-Riemannian Osserman spaces. Finally, the authors prove the surprising result that, for arbitrary signature, a pseudo-Riemannian manifold is simultaneously timelike and spacelike Osserman.
scientific article; zbMATH DE number 1367711
scientific article