Twistorial examples of Riemannian almost product manifolds and their Gil-Medrano and Naveira types

Abstract: Non-trivial examples of Riemannian almost product structures are constructed on the product bundle of the positive and negative twistor spaces of an oriented Riemannian four-manifold. The Gil-Medrano and Naveira types of these structures are determined and a geometric interpretation of the corresponding classes is given.