Rotationally symmetric gradient Yamabe solitons

Abstract

This short note deals with compact and complete and non-compact gradient Yamabe solitons (M, g, f) such that it has metric of constant scalar curvature. Firstly, we give a new proof of triviality for gradient compact Yamabe solitons. Also, under some integral conditions, we are able to improve a result due to Ma and Miquel (Ann Global Anal Geom 42:195–205, 2012). Finally, we obtain that the Yamabe metric becomes rotationally symmetric. Results for k-Yamabe solitons are also obtained here.