  Let $\Gamma$ be a nonuniform lattice acting on real hyperbolic n-space. We
show that in dimension greater than or equal to 4, the volume of a
representation is constant on each connected component of the representation
variety of $\Gamma$ in SO(n,1). Furthermore, in dimensions 2 and 3, there is a
semialgebraic subset of the representation variety such that the volume of a
representation is constant on connected components of the semialgebraic subset.
Our approach gives a new proof of the local rigidity theorem for nonuniform
hyperbolic lattices and the analogue of Soma's theorem, which shows that the
number of orientable hyperbolic manifolds dominated by a closed, connected,
orientable 3-manifold is finite, for noncompact 3-manifolds.
