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 x Nn-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.