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We prove a Liouville-type theorem for biharmonic maps from a completeRiemannian manifold of dimension $n$ that has a lower bound on its Riccicurvature and positive injectivity radius into a Riemannian manifold whosesectional curvature is bounded from above. Under these geometric assumptions weshow that if the $L^p$-norm of the tension field is bounded and the $n$-energyof the map is sufficiently small then every biharmonic map must be harmonic,where $2<p<n$.

A Liouville-type theorem for biharmonic maps between complete Riemannian manifolds with small energies