Some uniqueness results for Ricci solitons
type: Item
instance of: scholarly article
title: Some uniqueness results for Ricci solitons
zbMATH Open document ID: 1397.53061
published in: Illinois Journal of Mathematics
publication date: 2018-09-06T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ijm/1534924833
review text: The aim of this paper is to describe the relationship between different Ricci soliton structures on a fixed Riemannian manifold. In particular, the author proves that every complete Ricci soliton endowed with a non-Killing homothetic vector field has non-negative scalar curvature and a finite fundamental group.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 6932510
zbMATH Keywords: Ricci soliton
zbMATH Keywords: Killing vector field
zbMATH Keywords: fundamental group
author: João F. Silva Filho
reviewed by: Gabriel Eduard Vilcu
MaRDI profile type: Publication
cites work: Conformality of Riemannian manifolds to spheres
cites work: Some applications of the Hodge-de Rham decomposition to Ricci solitons
cites work: Q3110183
cites work: Three-dimensional Ricci solitons which project to surfaces
cites work: Homogeneous Ricci almost solitons
cites work: The geometry of closed conformal vector fields on Riemannian spaces
cites work: Closed conformal vector fields and Lagrangian submanifolds in complex space forms.
cites work: Strong uniqueness of the Ricci flow
cites work: Sur la réductibilité d'un espace de Riemann
cites work: Generic properties of homogeneous Ricci solitons
cites work: Ricci solitons: The equation point of view
cites work: Q4873981
cites work: Noncompact shrinking four solitons with nonnegative curvature
cites work: Conformal transformations of Riemannian manifolds
cites work: Conformal changes of Riemannian metrics
cites work: Q3312869
cites work: Q5485637
cites work: Q4371081
cites work: On gradient Ricci solitons with symmetry
cites work: Rigidity of gradient Ricci solitons
cites work: Explicit description of three-dimensional homogeneous Ricci solitons
cites work: Lagrangian submanifolds of \(C^n\) with conformal Maslov form and the Whitney sphere
cites work: Riemannian manifolds admitting a certain conformal transformation group
cites work: Closed conformal vector fields
cites work: Complete Riemannian Manifolds and Some Vector Fields
cites work: Complete shrinking Ricci solitons have finite fundamental group
description: scientific article; zbMATH DE number 6932510