Osserman and Conformally Osserman Manifolds with Warped and Twisted Product Structure

Abstract

We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman manifolds which can be written as a twisted product are those of constant curvature. Pseudo-Riemannian versions of those results are also considered, showing that four-dimensional conformally Osserman warped products are locally conformally flat. The result however fails in higher dimensions where there exist conformally Osserman products which are not locally conformally flat.