Liouville's theorem in conformal geometry

Lionville's theorem states that all conformal transformations of E '' and S '' (n >= 3) are restrictions of Mobius transformations. As a generalization, we determine all conformal mappings of semi-Riemannian manifolds preserving pointwise the Ricci tensor. It turns out that, up to isometrics, they are essentially of the same type as in the classical case but they can exist for metrics different from the Euclidean metric and spherical metric. (C) 2007 Elsevier Masson SAS. All rights reserved.