Self‐adjointness of perturbed biharmonic operators on Riemannian manifolds

Abstract 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.