Biharmonic Maps into a Riemannian Manifold of Non-positive Curvature
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.