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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/91631
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