Local existence of Ricci solitons
type: Item
instance of: scholarly article
title: Local existence of Ricci solitons
zbMATH Open document ID: 0870.53039
DOI: 10.1007/BF02567946
author: Thomas A. Ivey
published in: Manuscripta Mathematica
publication date: 1997-02-20T00:00:00Z
full work available at URL: https://eudml.org/doc/156221
review text: The author employs exterior differential systems to investigate the generalized soliton equation \({\mathcal L}_X g= -2 \text{Ric} g+g\) with the trace requirement \(\Sigma g^{ij} \Gamma^k_{ij} =0\) (to ensure the ellipticity in the Douglis-Nirenberg sense) for Riemannian metrics \(g\). The involutivity test is thoroughly analyzed and gives the result that, modulo diffeomorphisms, the \(n\)-dimensional soliton metrics locally depend on \(n(n+1)\) functions on \(n-1\) variables.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 58A15
zbMATH DE Number: 980686
zbMATH Keywords: exterior differential systems
zbMATH Keywords: generalized soliton equation
zbMATH Keywords: involutivity
reviewed by: Jan Chrastina
MaRDI profile type: Publication
cites work: Q5337785
cites work: Interior estimates for elliptic systems of partial differential equations
cites work: Déformations infinitesimales des espaces riemanniens localement symétriques. I
cites work: Déformations infinitésimales des structures conformes plates. (Infinitesimal deformations of conformally flat structures)
cites work: Three-manifolds with positive Ricci curvature
cites work: Four-manifolds with positive curvature operator
cites work: Q3812872
OpenAlex ID: W2001796373
description: scientific article; zbMATH DE number 980686