A sharp lower bound for the scalar curvature of certain steady gradient Ricci solitons
type: Item
instance of: scholarly article
title: A sharp lower bound for the scalar curvature of certain steady gradient Ricci solitons
zbMATH Open document ID: 1277.53041
DOI: 10.1090/S0002-9939-2013-11675-8
author: Eduardo García-Río
author: Manuel Fernández-López
published in: Proceedings of the American Mathematical Society
publication date: 2013-07-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1104.1889
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C44
zbMATH DE Number: 6183794
zbMATH Keywords: gradient Ricci soliton
zbMATH Keywords: scalar curvature
MaRDI profile type: Publication
arXiv ID: 1104.1889
cites work: Recent Progress on Ricci Solitons
cites work: Q3435052
cites work: Lower bounds for the scalar curvatures of noncompact gradient Ricci solitons
cites work: Maximum principles and gradient Ricci solitons
cites work: Local existence of Ricci solitons
cites work: Rigidity of gradient Ricci solitons
cites work: On the potential function of gradient steady Ricci solitons
OpenAlex ID: W2050845825
review text: A steady Ricci soliton is a Riemannian manifold \((M, g)\) which has a smooth vector field \(X\) such that \( L_X g + 2\mathrm{ Ric}(g) =0\), where \(L_X\) is the Lie derivative with respect to \(X\) and \(\mathrm{Ric}(g)\) denotes the Ricci tensor of \(g\). In the present paper the authors show a sharp lower bound for the scalar curvature of a steady gradient Ricci soliton in terms of the hyperbolic secant of the distance from a fixed point \(O \in M\) under the assumption that \(2 |\mathrm{Ric} (g) |^2 \leq\mathrm{Scal}(g)\). They prove that this condition is satisfied by every steady gradient Ricci soliton with nonnegative sectional curvature.
reviewed by: Anna Fino
description: scientific article; zbMATH DE number 6183794