Document Type : Research Articles
Department of Mathematics, Payame noor University, P.O. Box 19395-3697, Tehran, Iran.
We consider the oscillator group equipped with a biinvariant Lorentzian metric. Some geometrical properties of this space and the harmonicity properties of left-invariant vector fields on this space are determined. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. Left-invariant vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated.