Small mass limit of a langevin equation on a manifold

We study damped geodesic motion of a particle of mass m on a Riemannian manifold, in the presence of an external force and noise. Lifting the resulting stochastic differential equation to the orthogonal frame bundle, we prove that, as m→ 0 , its solutions converge to solutions of a limiting equation which includes a noise-induced drift term. A very special case of the main result presents Brownian motion on the manifold as a limit of inertial systems.