Special solitons on 3-manifolds

TL;DR

This paper classifies special solitons on 3-manifolds, showing they are locally isometric to well-known spaces, thus advancing understanding of geometric structures in differential geometry.

Contribution

It provides a classification of 3-dimensional gradient Ricci and Yamabe solitons, identifying their local isometry to standard geometric models.

Findings

Pseudo-symmetric gradient Ricci solitons are locally isometric to standard spaces.

Nontrivial gradient Yamabe solitons are also classified into known geometries.

The work extends the understanding of solitons in 3D geometry.

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 $\mathbb{R} \times \mathbb{H}^{2}$.