Variations of entropies and deformations of flat conformal structures on compact hyperbolic manifords

We study the link between variations of entropy on a compact hyperbolic man ifold M and infinitesimal flat conformal deformations of M. We remark that the entropy of the Liouville measure increases in the direction of these de formations. We then explain a new construction of infinitesimal flat confor mal deformations by bending along totally geodesic hypersurfaces of M which allows us to extend a theorem of L. Flaminio.