Propiedades conformes de productos deformados

Isothermal coordinate systems in Riemannian surfaces are generalized in a natural way by locally conformally flat manifolds. Although there is not a complete classification of this sort of manifolds when their dimension is greater than two, there exist some important results under suitable topological conditions. Among those a relevant role is played by Kuiper's Theorem: a compact simply connected locally conformally flat manifold is isometric to an Euclidean sphere. We are also interested in the following, due to Zhu: the universal cover of a complete locally conformally flat manifold with nonnegative Ricci curvature is in the conformal class of Rn, Sn or Sn¡1 £ R. In spite of these results, among many others, there is a lack of information concerning negative curvature.