Invariant f-structures on the four-dimensional oscillator group - Balashchenko, Vitaly V.; Kunitsa, Victoria N. (Journal of the Belarusian State University. Mathematics and Informatics, 2025)
In this paper, we investigate the four-dimensional oscillator group from the point of view of the generalised Hermitian geometry. This solvable Lie group is a semi-direct product of the classical three-dimensional Heisenberg group by a real line. Using the corresponding Lie algebra, we construct and study six basic left-invariant metric f-structures of rank 2 on the oscillator group. As a result, it gives the opportunity to present new examples of left-invariant nearly Kähler, generalised nearly Kähler and Hermitian f-structures on solvable Lie groups.