(Almost) Ricci Solitons in Lorentzian–Sasakian Hom-Lie Groups

Autor:	Esmaeil Peyghan, Leila Nourmohammadifar, Akram Ali, Ion Mihai
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	hom-Lie groups Lorentzian almost contact hom-Lie algebras Lorentzian–Sasakian structures (almost) Ricci solitons Mathematics QA1-939
Zdroj:	Axioms, Vol 13, Iss 10, p 693 (2024)
Druh dokumentu:	article
ISSN:	2075-1680
DOI:	10.3390/axioms13100693
Popis:	We study Lorentzian contact and Lorentzian–Sasakian structures in Hom-Lie algebras. We find that the three-dimensional sl(2,R) and Heisenberg Lie algebras provide examples of such structures, respectively. Curvature tensor properties in Lorentzian–Sasakian Hom-Lie algebras are investigated. If v is a contact 1-form, conditions under which the Ricci curvature tensor is v-parallel are given. Ricci solitons for Lorentzian–Sasakian Hom-Lie algebras are also studied. It is shown that a Ricci soliton vector field ζ is conformal whenever the Lorentzian–Sasakian Hom-Lie algebra is Ricci semisymmetric. To illustrate the use of the theory, a two-parameter family of three-dimensional Lorentzian–Sasakian Hom-Lie algebras which are not Lie algebras is given and their Ricci solitons are computed.
Databáze:	Directory of Open Access Journals
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