GRADIENT YAMABE SOLITONS WITH CONFORMAL VECTOR FIELD

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.