On the geometrical properties of hypercomplex four-dimensional Lorentzian Lie groups
| Autor: | Mehri Nasehi, Mansour Aghasi |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Georgian Mathematical Journal. 28:281-290 |
| ISSN: | 1572-9176 1072-947X |
| DOI: | 10.1515/gmj-2019-2064 |
| Popis: | In this paper we first classify left-invariant generalized Ricci solitons on four-dimensional hypercomplex Lie groups equipped with three families of left-invariant Lorentzian metrics. Then, on these Lorentzian spaces, we explicitly calculate the energy of an arbitrary left-invariant vector field X and determine the exact form of all left-invariant unit time-like vector fields which are spatially harmonic. Furthermore, we give a complete and explicit description of all homogeneous structures on these spaces in both Riemannian and Lorentzian cases and determine some of their types. The existence of Einstein four-dimensional hypercomplex Lorentzian Lie groups is proved and it is shown that although the results concerning Einstein-like metrics, conformally flatness and some equations in the Riemannian case are much richer than their Lorentzian analogues, in the Lorentzian case, there exist some new critical points of energy functionals, homogeneous structures and geodesic vectors which do not exist in the Riemannian case. |
| Databáze: | OpenAIRE |
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