Complete quasi-Yamabe gradient solitons with bounded scalar curvature

TL;DR

This paper classifies complete quasi-Yamabe gradient solitons with bounded scalar curvature, providing a comprehensive understanding of their structure under various curvature bounds.

Contribution

It offers a complete classification of nontrivial shrinking, steady, and expanding quasi-Yamabe gradient solitons with scalar curvature bounds.

Findings

Classified shrinking and steady quasi-Yamabe solitons with scalar curvature bounded below.

Classified expanding and steady quasi-Yamabe solitons with scalar curvature bounded above.

Enhanced understanding of the geometric structure of quasi-Yamabe solitons.

Abstract

In this paper, we classify complete, nontrivial shrinking and steady quasi-Yamabe gradient solitons whose scalar curvature is bounded below by the soliton constant. We also classify complete, nontrivial expanding and steady quasi-Yamabe gradient solitons whose scalar curvature is bounded above by the soliton constant.