On the f-biharmonic Maps and Submanifolds

Abstract

Abstract. In this paper, we prove that every f -biharmonic map from a complete Riemannian 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.