Mohamed Ali Hammami, Hichem El Hendi, Mustapha Meghnafi

Some Remarks on the Bienergy of Pull-Back Vector Fields

abstract:
The problem studied in this paper is related to the bienergy of a pull-back vector field from a Riemannian manifold $(M,g)$ to its tangent bundle $TN$ equipped with the Sasaki metric $h^{s}$. We show that a pull-back vector field on a compact manifold $(M,g)$ is biharmonic if and only if it is harmonic. We also investigate the bienergy of a pull-back vector field, as a map from $(M,g)$ to $(TN,h^{s})$.

Mathematics Subject Classification: Primary 58E20; Secondary 53C20

Key words and phrases: Pull-back vector field, bienergy, Riemannian manifold