In this paper we prove that any complete n-dimensional conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product R x 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.

On the global structure of conformal gradient solitons with nonnegative Ricci tensor

MANTEGAZZA, Carlo Maria;MAZZIERI, LORENZO
2012

Abstract

In this paper we prove that any complete n-dimensional conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product R x 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/11189
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