On the Global Structure of Conformal Gradient Solitons With Nonnegative Ricci Tensor

In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product ℝ × N n-1 , or globally conformally equivalent to the Euclidean space ℝ n or to the round sphere 𝕊 n . In particular, we show that any complete, noncompact, gradient Yamabe-type soliton with positive Ricci tensor is rotationally symmetric, whenever the potential function is nonconstant.