Vector fields which are biharmonic maps

摘要

In this paper, an explicit expression of the bitension field of a vector field considered as a map from a Riemannian manifold (M, g) to its tangent bundle TM equipped with the Sasaki metric gs is provided. As a consequence, we show characterization theorem for a vector field to be biharmonic map. We prove non-existence results for left-invariant vector fields which are biharmonic without being harmonic maps and non-harmonic biharmonic maps respectively on uninaodular Lie groups of dimension three.