Left-invariant metric f-structures on three-dimensional sol vable Lie groups
https://doi.org/10.29235/1561-2430-2025-61-2-95-105
Abstract
In the paper, we investigate three-dimensional solvable Lie groups from the point of view of the generalized Hermitian geometry. The corresponding three-dimensional solvable Lie algebras were firstly classified by G. M. Mubarakzyanov in 1963. Using the classification in somewhat different notations, we construct basic left-invariant metric f-structures of rank 2 on all three-dimensional solvable Lie groups equipped with the standard left-invariant Riemannian metric. It was proved that all the considered f-structures belong to one or several classes of generalized almost Hermitian structures. As a result, it gives the opportunity to present new examples of left-invariant Killling, nearly Kähler, generalized nearly Kähler and Hermitian f-structures on solvable Lie groups.
About the Authors
V. V. Balashchenko
Belarusian State University
Belarus
Belarus
Vitaly V. Balashchenko – Ph. D. (Physics and Mathematics), Associate Professor, Department of Geometry, Topology and Methods of Teaching Mathematics
4, Nezavisimosti Ave., 220030, Minsk
V. N. Kunitsa
Belarusian State University
Belarus
Belarus
Victoria N. Kunitsa – Postgraduate Student, Department of Geometry, Topology and Methods of Teaching Mathematics
4, Nezavisimosti Ave., 220030, Minsk
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