In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product × N n-1, or globally conformally equivalent to the Euclidean space Rn or to the round sphere Rn. 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.
On the Global Structure of Conformal Gradient Solitons with Nonnegative Ricci Tensor
Mantegazza, Carlo;Catino, Giovanni;Mazzieri, Lorenzo
2011
Abstract
In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product × N n-1, or globally conformally equivalent to the Euclidean space Rn or to the round sphere Rn. 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.File in questo prodotto:
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