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.
The goal of this work is the application of the f-stress energy of differ-ential forms to study the generalized monotonicity formulae and generalizedvanishing theorems. We obtain some generalized monotonicity formulas forp-formsω∈Ap(ξ), which satisfy the generalizedf-conservation laws, withf∈C∞(M×R) satisfying some conditions
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