Author/Authors :
Djaa, Mustapha University of Saida - Laboratory of Geometry, Analysis, Control and Applications,Department of Mathematics, ALGERIA , Elhendi, Hichem University of Saida - Laboratory of Geometry, Analysis, Control and Applications,Department of Mathematics, ALGERIA , Ouakkas, Seddik University of Saida - Laboratory of Geometry, Analysis, Control and Applications,Department of Mathematics, ALGERIA
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.
