Self-adjointness of perturbed biharmonic operators on Riemannian manifolds

We give a sufficient condition for the essential self-adjointness of a perturbed biharmonic-type operator acting on sections of a Hermitian vector bundle on a geodesically complete Riemannian manifold with Ricci curvature bounded from below by a (possibly unbounded) non-positive function depending on the distance from a reference point. We also establish the separation property in the case when the corresponding operator acts on functions.