On the rigidity of hyperbolic cone-manifolds

Starting with a compact hyperbolic cone-manifold of dimension n >= 3, we study the deformations of the metric with the aim of getting Einstein cone-manifolds. If the singular locus is a closed codimension 2 submanifold and all cone angles are smaller than 2 pi, we show that there is no non-trivial infinitesimal Einstein deformations preserving the cone angles. (c) 2005 Academie des sciences. Published by Elsevier SAS. All rights reserved.