On the biharmonic vector fields

Authors: MUSTAPHA DJAA, HICHEM ELHENDI, SEDDIK OUAKKAS

Abstract: The problem studied in this paper is related to the biharmonicity of a vector field from a Riemannian manifold (M,g) to its tangent bundle TM equipped with the Sasaki metric g^s. We show that a vector field on a compact manifold is biharmonic if and only if is harmonic. We also investigate the biharmonicity of vector field of M, as a map from (M,g) to (TM,g^s).

Keywords: Horizontal lift, vertical lift, harmonic maps, biharmonic maps

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