Ricci solitons on compact three-manifolds
type: Item
instance of: scholarly article
title: Ricci solitons on compact three-manifolds
zbMATH Open document ID: 0788.53034
DOI: 10.1016/0926-2245(93)90008-O
published in: Differential Geometry and its Applications
publication date: 1994-05-30T00:00:00Z
review text: In this short article we show that there are no compact three-dimensional Ricci solitons other than spaces of constant curvature. This generalizes a result obtained for surfaces by \textit{R. S. Hamilton} [Contemp. Math. 71, 237-262 (1988; Zbl 0663.53031)]. The proof involves a careful analysis of the ODE for the curvature which is associated to the Ricci flow.
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 527412
zbMATH Keywords: Ricci flow
zbMATH Keywords: Ricci solitons
zbMATH Keywords: spaces of constant curvature
zbMATH Keywords: curvature
Wikidata QID: Q115362719
author: Thomas A. Ivey
reviewed by: Thomas A. Ivey
MaRDI profile type: Publication
cites work: The Ricci flow on the 2-sphere
cites work: Three-manifolds with positive Ricci curvature
cites work: Four-manifolds with positive curvature operator
cites work: Q3812872
cites work: Q3713107
cites work: The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature
description: scientific article; zbMATH DE number 527412