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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