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

Document Type : Original Article

Authors

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

2 Department of Pure Mathematics, Faculty of mathematics, University of Kashan, Kashan, Iran

Abstract

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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References

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AUT Journal of Mathematics and Computing
Volume 5, Issue 4
2024
Pages 305-319

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