  This paper deals with an inverse problem for a non-self-adjoint Schr\"odinger
equation on a compact Riemannian manifold. Our goal is to stably determine a
real vector field from the dynamical Dirichlet-to Neumann map. We establish in
dimension n greater than 2, an H\"older type stability estimate for the inverse
problem under study. The proof is mainly based on the reduction to an
equivalent problem for an electro-magnetic Schr\"odinger equation and the use
of a Carleman estimate designed for elliptic operators.
