Some geometrical properties of the Oscillator group
Differential Geometry
2021-10-11 v2
Abstract
We consider the oscillator group equipped with a bi-invariant Lorentzian metric, and then some geometrical properties of this group i.e. homogeneous Ricci solitons and harmonicity properties of invariant vector fields are obtained. We also determine all vector fields which are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also determined, and the energy of critical points is explicitly calculated.
Keywords
Cite
@article{arxiv.1604.04369,
title = {Some geometrical properties of the Oscillator group},
author = {Yadollah Aryanejad},
journal= {arXiv preprint arXiv:1604.04369},
year = {2021}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1412.6336, arXiv:1410.7626