3-dimensional complete gradient Yamabe solitons with divergence-free Cotton tensor

TL;DR

This paper classifies 3D complete gradient Yamabe solitons with divergence-free Cotton tensor and explores conditions with nonpositive Ricci curvature along the potential function's gradient.

Contribution

It provides a classification of certain 3D Yamabe solitons with divergence-free Cotton tensor and Ricci curvature conditions, extending understanding of their geometric structure.

Findings

Classification of 3D complete gradient Yamabe solitons with divergence-free Cotton tensor.

Results on Yamabe solitons with nonpositive Ricci curvature in the gradient direction.

Insights into the geometric properties of these solitons.

Abstract

In this paper, we classify 3-dimensional complete gradient Yamabe solitons with divergence-free Cotton tensor. We also give some classifications of complete gradient Yamabe solitons with nonpositively curved Ricci curvature in the direction of the gradient of the potential function.