Calculus of Variations and Geometric Measure Theory

G. Catino - C. Mantegazza - L. Mazzieri

On the Global Structure of Conformal Gradient Solitons with Nonnegative Ricci Tensor

created by catino on 02 Sep 2011
modified by root on 06 Mar 2013


Published Paper

Inserted: 2 sep 2011
Last Updated: 6 mar 2013

Journal: Commun. Contemp. Math.
Volume: 14
Number: 6
Pages: 1250045 (12 pages)
Year: 2012


In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product $\mathbb{R}\times N^{n-1}$, or globally conformally equivalent to the Euclidean space $\mathbb{R}^{n}$ or to the round sphere $\mathbb{S}^{n}$. 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.