Communications of the
Korean Mathematical Society CKMS

The purpose of this paper is to investigate the geometry of complete gradient Yamabe soliton $(M^n ,g, f, \lambda)$ with constant scalar curvature admitting a non-homothetic conformal vector field $V$ leaving the potential vector field invariant. We show that in such manifolds the potential function $f$ is constant and the scalar curvature of $g$ is determined by its soliton scalar. Considering the locally conformally flat case and conformal vector field $V$, without constant scalar curvature assumption, we show that $g$ has constant curvature and determines the potential function $f$ explicitly.

Keywords: Yamabe soliton, constant scalar curvature, conformal vector field

MSC numbers: 53C21, 53C44