Liouville and geodesic Ricci solitons
type: Item
instance of: scholarly article
title: Liouville and geodesic Ricci solitons
zbMATH Open document ID: 1183.53036
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2009-11-25T00:00:00Z
review text: A Riemannian manifold \((M, g)\) carries a Ricci soliton if \[ L_V g + 2 S_g + 2 \lambda g = 0, \] where \(S_g\) is its Ricci tensor, \(L_V\) is the Lie derivative operator with respect a vector field \(V\) and \(\lambda\) is a real scalar. The Ricci soliton is shrinking, steady or expanding according as \(\lambda\) is negative, zero or positive respectively. In this paper, the authors have proved that if \(M\) is Ricci flat then its tangent bundle carries a \(1\)-parameter family of shrinking Liouville Ricci solitons and if \(M\) is flat then its tangent bundle carries a steady geodesic Ricci soliton.
reviewed by: Krishan Lal Duggal
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C44
zbMATH DE Number: 5638300
zbMATH Keywords: Ricci soliton
zbMATH Keywords: Einstein metrics
zbMATH Keywords: Liouville vector field
zbMATH Keywords: geodesic spray
author: Mircea Crasmareanu
MaRDI profile type: Publication
full work available at URL: j.crma.2009.10.008
OpenAlex ID: W2065617516
Wikidata QID: Q125561216
cites work: Q5200652
cites work: Einstein manifolds
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cites work: Some classes of almost anti-Hermitian structures on the tangent bundle
cites work: A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold
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cites work: SOME GEOMETRIC STRUCTURES ON THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD
cites work: Q5427568
cites work: Q5678143
DOI: 10.1016/J.CRMA.2009.10.008
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description: scientific article; zbMATH DE number 5638300