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We consider biharmonic maps  from a complete Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. Assume that  satisfies . If for such a ,  and  where  is the tension field of , then we show that  is harmonic. For a biharmonic submanifold, we obtain that the above assumption  is not necessary. These results give affirmative partial answers to the global version of generalized Chen’s conjecture.

Biharmonic maps from a complete Riemannian manifold into a non-positively curved manifold