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
2011-01-01
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:
| File | Dimensione | Formato | |
|---|---|---|---|
|
confsol.pdf
accesso aperto
Tipologia:
Altro materiale allegato
Licenza:
Sola lettura
Dimensione
300.63 kB
Formato
Adobe PDF
|
300.63 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
