Generalized Lorentz Ricci solitons on $3$-dimensional Lie groups associated to Bott connection

Document Type : Original Article


1 Department of Pure Mathematics, Faculty of Basic Sciences, Imam Khomeini International University, Qazvin, Iran

2 Department of Mathematics, University of Kashan, Kashan, Iran


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.


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