  We prove a Liouville-type theorem for biharmonic maps from a complete
Riemannian manifold of dimension \(n\) that has a lower bound on its Ricci
curvature and positive injectivity radius into a Riemannian manifold whose
sectional curvature is bounded from above. Under these geometric assumptions we
show that if the $L^p$-norm of the tension field is bounded and the $n$-energy
of the map is sufficiently small then every biharmonic map must be harmonic,
where \(2<p<n\).
