Some characterizations of gradient Yamabe solitons

Abstract

In this article we have proved that a gradient Yamabe soliton satisfying some additional conditions must be of constant scalar curvature. Later, we have showed that in a gradient expanding Yamabe soliton with non-negative scalar curvature if the potential function satisfies an integral condition then it is isometric to the Euclidean space Rn, and for steady case with the same condition the potential function becomes harmonic. Also we have proved that, in a compact gradient Yamabe soliton, the potential function agrees with the Hodge-de Rham potential up to a constant.