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

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.

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