  We prove a volume-rigidity theorem for fuchsian representations of
fundamental groups of hyperbolic k-manifolds into Isom(H^n). Namely, we show
that if M is a complete hyperbolic k-manifold with finite volume, then the
volume of any representation of its fundamental group into Isom(H^n), 3 <= k <=
n, is less than the volume of M, and the volume is maximal if and only if the
representation is discrete, faithful and ``k-fuchsian''.
