On homogeneous Ricci solitons

Autores
Lafuente, Ramiro Augusto; Lauret, Jorge Ruben
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space Graphic of all homogeneous spaces of dimension n with a q-dimensional isotropy, which is equivalent to the Ricci flow for homogeneous manifolds. We prove that algebraic solitons (i.e. the Ricci operator is a multiple of the identity plus a derivation) are precisely the fixed points of the system, and that a homogeneous Ricci soliton is isometric to an algebraic soliton if and only if the corresponding bracket flow solution is not chaotic, in the sense that its ω-limit set consists of a single point. We also geometrically characterize algebraic solitons among homogeneous Ricci solitons as those for which the Ricci flow solution is simultaneously diagonalizable.
Fil: Lafuente, Ramiro Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentina
Fil: Lauret, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentina
Materia
Soliton
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/8499
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/8499
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network_name_str CONICET Digital (CONICET)
spelling On homogeneous Ricci solitonsLafuente, Ramiro AugustoLauret, Jorge RubenSolitonhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space Graphic of all homogeneous spaces of dimension n with a q-dimensional isotropy, which is equivalent to the Ricci flow for homogeneous manifolds. We prove that algebraic solitons (i.e. the Ricci operator is a multiple of the identity plus a derivation) are precisely the fixed points of the system, and that a homogeneous Ricci soliton is isometric to an algebraic soliton if and only if the corresponding bracket flow solution is not chaotic, in the sense that its ω-limit set consists of a single point. We also geometrically characterize algebraic solitons among homogeneous Ricci solitons as those for which the Ricci flow solution is simultaneously diagonalizable.Fil: Lafuente, Ramiro Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; ArgentinaFil: Lauret, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; ArgentinaOxford University Press2013-06-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/8499Lafuente, Ramiro Augusto; Lauret, Jorge Ruben; On homogeneous Ricci solitons; Oxford University Press; Quarterly Journal Of Mathematics; 65; 2; 02-6-2013; 399-4190033-5606enginfo:eu-repo/semantics/altIdentifier/doi/10.1093/qmath/hat028info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/abstract/j/crelle.2015.2015.issue-699/crelle-2013-0044/crelle-2013-0044.xmlinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1109.6556v2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:48:31Zoai:ri.conicet.gov.ar:11336/8499instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:48:31.914CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On homogeneous Ricci solitons
title On homogeneous Ricci solitons
spellingShingle On homogeneous Ricci solitons
Lafuente, Ramiro Augusto
Soliton
title_short On homogeneous Ricci solitons
title_full On homogeneous Ricci solitons
title_fullStr On homogeneous Ricci solitons
title_full_unstemmed On homogeneous Ricci solitons
title_sort On homogeneous Ricci solitons
dc.creator.none.fl_str_mv Lafuente, Ramiro Augusto
Lauret, Jorge Ruben
author Lafuente, Ramiro Augusto
author_facet Lafuente, Ramiro Augusto
Lauret, Jorge Ruben
author_role author
author2 Lauret, Jorge Ruben
author2_role author
dc.subject.none.fl_str_mv Soliton
topic Soliton
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space Graphic of all homogeneous spaces of dimension n with a q-dimensional isotropy, which is equivalent to the Ricci flow for homogeneous manifolds. We prove that algebraic solitons (i.e. the Ricci operator is a multiple of the identity plus a derivation) are precisely the fixed points of the system, and that a homogeneous Ricci soliton is isometric to an algebraic soliton if and only if the corresponding bracket flow solution is not chaotic, in the sense that its ω-limit set consists of a single point. We also geometrically characterize algebraic solitons among homogeneous Ricci solitons as those for which the Ricci flow solution is simultaneously diagonalizable.
Fil: Lafuente, Ramiro Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentina
Fil: Lauret, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentina
description We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space Graphic of all homogeneous spaces of dimension n with a q-dimensional isotropy, which is equivalent to the Ricci flow for homogeneous manifolds. We prove that algebraic solitons (i.e. the Ricci operator is a multiple of the identity plus a derivation) are precisely the fixed points of the system, and that a homogeneous Ricci soliton is isometric to an algebraic soliton if and only if the corresponding bracket flow solution is not chaotic, in the sense that its ω-limit set consists of a single point. We also geometrically characterize algebraic solitons among homogeneous Ricci solitons as those for which the Ricci flow solution is simultaneously diagonalizable.
publishDate 2013
dc.date.none.fl_str_mv 2013-06-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/8499
Lafuente, Ramiro Augusto; Lauret, Jorge Ruben; On homogeneous Ricci solitons; Oxford University Press; Quarterly Journal Of Mathematics; 65; 2; 02-6-2013; 399-419
0033-5606
url http://hdl.handle.net/11336/8499
identifier_str_mv Lafuente, Ramiro Augusto; Lauret, Jorge Ruben; On homogeneous Ricci solitons; Oxford University Press; Quarterly Journal Of Mathematics; 65; 2; 02-6-2013; 399-419
0033-5606
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1093/qmath/hat028
info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/abstract/j/crelle.2015.2015.issue-699/crelle-2013-0044/crelle-2013-0044.xml
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1109.6556v2
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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