  We study some canonical differential operators on vector bundles over smooth,
complete Riemannian manifolds. Under very general assumptions, we show that
smooth, compactly supported sections are dense in the domains of these
operators. Furthermore, we show that smooth, compactly supported functions are
dense in second order Sobolev spaces on such manifolds under the sole
additional assumption that the Ricci curvature is uniformly bounded from below.
