### Electronic Research Archive

2020, Issue 1: 157-163. doi: 10.3934/era.2020010

# Ricci solitons of the $\mathbb{H}^{2} \times \mathbb{R}$ Lie group

• Received: 01 October 2019 Revised: 01 February 2020
• 53C50, 53B30

• In this work we consider the three-dimensional Lie group denoted by $\mathbb{H}^{2} \times \mathbb{R}$, equipped with left-invariant Riemannian metric. The existence of non-trivial (i.e., not Einstein) Ricci solitons on three-dimensional Lie group $\mathbb{H}^{2} \times \mathbb{R}$ is proved. Moreover, we show that there are not gradient Ricci solitons.

Citation: Lakehal Belarbi. Ricci solitons of the $\mathbb{H}^{2} \times \mathbb{R}$ Lie group[J]. Electronic Research Archive, 2020, 28(1): 157-163. doi: 10.3934/era.2020010

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• In this work we consider the three-dimensional Lie group denoted by $\mathbb{H}^{2} \times \mathbb{R}$, equipped with left-invariant Riemannian metric. The existence of non-trivial (i.e., not Einstein) Ricci solitons on three-dimensional Lie group $\mathbb{H}^{2} \times \mathbb{R}$ is proved. Moreover, we show that there are not gradient Ricci solitons.

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