A note on (anti-)self dual quasi Yamabe gradient soliton

TL;DR

This paper proves that (anti-)self dual quasi Yamabe solitons with positive sectional curvature are rotationally symmetric, extending previous results, and shows that certain gradient Yamabe solitons have a warped product structure under specific conditions.

Contribution

It generalizes existing results by establishing rotational symmetry of (anti-)self dual quasi Yamabe solitons with positive curvature and describes the structure of half conformally flat gradient Yamabe solitons.

Findings

(Anti-)self dual quasi Yamabe solitons with positive curvature are rotationally symmetric.

Half conformally flat gradient Yamabe solitons with non-critical potential functions have a warped product structure.

Abstract

In this note we prove that a (anti-)self dual quasi Yamabe soliton with positive sectional curvature is rotationally symmetric. This generalizes a recent result of G. Huang and H. Li in dimension four. Whence, (anti-) self dual gradient Yamabe solitons with positive sectional curvature is rotationally symmetric. We also prove that half conformally flat gradient Yamabe soliton has a special warped product structure provided that the potential function has no critical point.