Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 5 4 2024 10 01 Generalized Lorentzian Ricci solitons on 3-dimensional Lie groups associated to the Bott Connection 305 319 5195 10.22060/ajmc.2023.22329.1153 EN Ghodratallah Fasihi Ramandi Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran Shahroud Azami Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran Vahid Pirhadi Department of Pure Mathematics, Faculty of mathematics, University of Kashan, Kashan, Iran Journal Article 2023 04 11 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. https://ajmc.aut.ac.ir/article_5195_b34a3973e7012a6572e01bf73f68e064.pdf