From infinitesimal harmonic transformations to Ricci solitons
Result description
A Ricci soliton is a Riemannian metric g on a manifold together with a vector field ksí that are related in terms of the Lie derivative and the Ricci tensor of the metric by -2Ric=L ksí g+2lambdag for some constant lambda; Einstein manifolds are a particular case. The concept of Ricci soliton is related to harmonic mappings, namely, the vector field ksí making g into a metric of the Ricci soliton is necessarily an infinitesimal harmonic transformation. Moreover, on a compact manifold, the field ksí is gradient, ksí=gradF. The authors give examples of infinitesimal harmonic transformations and prove existence theorems for Ricci solitons on compact and non-compact manifolds.
Keywords
Riemannian manifoldinfinitesimal harmonic transformationRicci soliton
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
From infinitesimal harmonic transformations to Ricci solitons
Original language description
A Ricci soliton is a Riemannian metric g on a manifold together with a vector field ksí that are related in terms of the Lie derivative and the Ricci tensor of the metric by -2Ric=L ksí g+2lambdag for some constant lambda; Einstein manifolds are a particular case. The concept of Ricci soliton is related to harmonic mappings, namely, the vector field ksí making g into a metric of the Ricci soliton is necessarily an infinitesimal harmonic transformation. Moreover, on a compact manifold, the field ksí is gradient, ksí=gradF. The authors give examples of infinitesimal harmonic transformations and prove existence theorems for Ricci solitons on compact and non-compact manifolds.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
GAP201/11/0356: Riemannian, pseudo-Riemannian and affine differential geometry
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematica Bohemica
ISSN
0862-7959
e-ISSN
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Volume of the periodical
138
Issue of the periodical within the volume
1
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
12
Pages from-to
25-36
UT code for WoS article
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EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2013