Biharmonic maps into a Riemannian manifold of non-positive curvature
  We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We show that if the domain is complete and the target of non-positive curvature, then such a map is harmonic. We then give applications to isometric immersions and horizontally conformal submersions. 
Nobumitsu Nakauchi, Hajime Urakawa and Sigmundur Gudmundsson
math.DG