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).
Horizontal lift, vertical lift, harmonic maps, biharmonic maps
DJAA, MUSTAPHA; ELHENDI, HICHEM; and OUAKKAS, SEDDIK
"On the biharmonic vector fields,"
Turkish Journal of Mathematics: Vol. 36:
3, Article 12.
Available at: https://journals.tubitak.gov.tr/math/vol36/iss3/12