Triviality, Rotational Symmetry, and Classification of Complete Expanding Gradient Yamabe Solitons

TL;DR

This paper classifies all nontrivial complete expanding gradient Yamabe solitons based on their scalar curvature relative to the soliton constant, providing a comprehensive understanding of their geometric structure.

Contribution

It offers a complete classification of nontrivial complete expanding gradient Yamabe solitons under different scalar curvature conditions.

Findings

Classified solitons when scalar curvature exceeds the soliton constant.

Classified solitons when scalar curvature is less than the soliton constant.

Provided a rigorous analysis of scalar curvature in these solitons.

Abstract

In this paper, we rigorously analyze the scalar curvature of complete expanding gradient Yamabe solitons. We completely classify nontrivial complete expanding gradient Yamabe solitons in both cases: when the scalar curvature is greater than the soliton constant and when it is less than the soliton constant.