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.
Aryanejad, Y. (2020). Some geometrical properties of the oscillator group. Caspian Journal of Mathematical Sciences, 9(2), 284-293. doi: 10.22080/cjms.2020.17566.1441
MLA
Yadollah Aryanejad. "Some geometrical properties of the oscillator group". Caspian Journal of Mathematical Sciences, 9, 2, 2020, 284-293. doi: 10.22080/cjms.2020.17566.1441
HARVARD
Aryanejad, Y. (2020). 'Some geometrical properties of the oscillator group', Caspian Journal of Mathematical Sciences, 9(2), pp. 284-293. doi: 10.22080/cjms.2020.17566.1441
VANCOUVER
Aryanejad, Y. Some geometrical properties of the oscillator group. Caspian Journal of Mathematical Sciences, 2020; 9(2): 284-293. doi: 10.22080/cjms.2020.17566.1441
)