Classification of three dimensional complete gradient Yamabe solitons

TL;DR

This paper classifies 3-dimensional complete gradient Yamabe solitons, showing that nontrivial steady solutions are rotationally symmetric, thereby advancing understanding of their geometric structure.

Contribution

It provides a complete classification of nontrivial 3D gradient Yamabe solitons, highlighting their rotational symmetry in the steady case, which was previously unknown.

Findings

Nontrivial steady gradient Yamabe solitons in 3D are rotationally symmetric.

Complete classification of nontrivial 3D gradient Yamabe solitons.

Advances understanding of geometric properties of Yamabe solitons.

Abstract

In this paper, we classify nontrivial 3-dimensional complete gradient Yamabe solitons. In particular, we show that any nontrivial non-flat 3-dimensional complete steady gradient Yamabe soliton is rotationally symmetric.