Ricci-Yamabe solitons on the Lie group $H_{2} \times \mathbb{R}$

Abstract

In this paper, we study Ricci-Yamabe and gradient Yamabe solitons on the Lie group $H_{2}\times \mathbb{R}$ with a left-invariant metric. We prove that the kind of the Ricci-Yamabe soliton is only related with one variable existing in the definition.