Generalized Lorentzian Ricci solitons on 3-dimensional Lie groups associated to the Bott Connection

	Generalized Lorentzian Ricci solitons on 3-dimensional Lie groups associated to the Bott Connection
AUT Journal of Mathematics and Computing
مقاله 2، دوره 5، شماره 4، 2024، صفحه 305-319 اصل مقاله (410.6 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2023.22329.1153
نویسندگان
Ghodratallah Fasihi Ramandi^* ¹؛ Shahroud Azami²؛ Vahid Pirhadi³
¹Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
²Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
³Department of Pure Mathematics, Faculty of mathematics, University of Kashan, Kashan, Iran
چکیده
In this paper, we investigate which one of the non-isometric left-invariant Lorentz metrics $g$ on $3$-dimensional Lie groups satisfies the generalized Ricci soliton equation $a{\rm Ric}^B [g] + \dfrac{b}{2}{\cal L}_{ X}^B g +cX^\flat\otimes X^\flat = \lambda g$ associated to the Bott connection $\nabla^B$, here ${X}$ is a vector field and $\lambda , a, b, c$ are real constants such that $c\neq 0$. A complete classification of this structure on $3$-dimensional Lorentzian Lie groups will be presented.
کلیدواژه‌ها
Left-invariant Lorentz metric‎؛ Generalized Ricci soliton؛ ‎ Pseudo-Riemannian metric‎؛ Lie group
مراجع

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