Abstract
In this paper, we prove that every f -biharmonic map from a complete Rieman- nian manifold into a Riemannian manifold with non-positive sectional curvature,satisfying some condition, is f -harmonic. Also we present some properties for the f -biharmonicity of submanifolds of S n , and we give the classification of f -biharmonic curves in 3-dimensional sphere.
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