On the duality principle in pseudo-Riemannian Osserman manifolds

Abstract

Here we give a natural extension of the duality principle for the curvature tensor of pointwise pseudo-Riemannian Osserman manifolds. We proved that this extended duality principle holds under certain additional assumptions. Also, it is proved that duality principle holds for every four-dimensional Osserman manifold. © 2007 Elsevier Ltd. All rights reserved.