  We give sufficient conditions for the essential self-adjointness of perturbed
biharmonic operators acting on sections of a Hermitian vector bundle over a
Riemannian manifold with additional assumptions, such as lower semi-bounded
Ricci curvature or bounded sectional curvature. In the case of lower
semi-bounded Ricci curvature, we formulate our results in terms of the
completeness of the metric that is conformal to the original one, via a
conformal factor that depends on a minorant of the perturbing potential $V$. In
the bounded sectional curvature situation, we are able to relax the growth
condition on the minorant of $V$ imposed in an earlier article. In this
context, our growth condition on the minorant of $V$ is consistent with the
literature on the self-adjointness of perturbed biharmonic operators on
$\mathbb{R}^n$.
