Special solitons on 3-manifolds

Abstract

In this paper, we study solitons on $3$-dimensional manifolds. In particular, we show that $3$-dimensional pseudo-symmetric gradient Ricci solitons and nontrivial gradient Yamabe solitons are locally isometric to either ${\mathbb{R}}^3$, ${\mathbb{S}}^3$, ${\mathbb{H}}^3$, $\mathbb{R}\times {\mathbb{S}}^2$ or $\mathbb{R}\times {\mathbb{H}}^2$.