Mustapha DJAA, Hichem ELHENDI, Seddik OUAKKAS

On the biharmonic vector fields

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 gs. 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,gs).

Anahtar Kelimeler:

Horizontal lift, vertical lift, harmonic maps, biharmonic maps

On the biharmonic vector fields

Keywords:

Horizontal lift, vertical lift, harmonic maps, biharmonic maps,

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Mustapha DJAA, Hichem ELHENDI, Seddik OUAKKAS Laboratory of Geometry, Analysis, Control and Applications. Department of Mathematics. University of Saida, BP 138 ”20000”, Saida-ALGERIA e-mail: Djaamustapha@Hotmail.com e-mail: Lgaca Saida2009@Hotmail.com e-mail: Souakkas@Yahoo.fr