Ricci flow of homogeneous manifolds

Autores
Lauret, Jorge Ruben
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present in this paper a general approach to study the Ricci flow on homogeneous manifolds. Our main tool is a dynamical system defined on a subset Hq,n of the variety of (q+n)-dimensional Lie algebras, parameterizing the space of all simply connected homogeneous spaces of dimension n with a q-dimensional isotropy, which is proved to be equivalent in a precise sense to the Ricci flow. The approach is useful to better visualize the possible (nonflat) pointed limits of Ricci flow solutions, under diverse rescalings, as well as to determine the type of the possible singularities. Ancient solutions arise naturally from the qualitative analysis of the evolution equation. We develop two examples in detail: a 2-parameter subspace of H1,3 reaching most of 3-dimensional geometries, and a 2-parameter family in H0,n of left-invariant metrics on n-dimensional compact and non-compact semisimple Lie groups.
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
Materia
Ricci Flow
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:11336/8988
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Ricci flow of homogeneous manifoldsLauret, Jorge RubenRicci Flowhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present in this paper a general approach to study the Ricci flow on homogeneous manifolds. Our main tool is a dynamical system defined on a subset Hq,n of the variety of (q+n)-dimensional Lie algebras, parameterizing the space of all simply connected homogeneous spaces of dimension n with a q-dimensional isotropy, which is proved to be equivalent in a precise sense to the Ricci flow. The approach is useful to better visualize the possible (nonflat) pointed limits of Ricci flow solutions, under diverse rescalings, as well as to determine the type of the possible singularities. Ancient solutions arise naturally from the qualitative analysis of the evolution equation. We develop two examples in detail: a 2-parameter subspace of H1,3 reaching most of 3-dimensional geometries, and a 2-parameter family in H0,n of left-invariant metrics on n-dimensional compact and non-compact semisimple Lie groups.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); ArgentinaSpringer2013-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/8988Lauret, Jorge Ruben; Ricci flow of homogeneous manifolds; Springer; Mathematische Zeitschrift; 274; 1-2; 3-2013; 373-4030025-5874enginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00209-012-1075-zinfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs00209-012-1075-zinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:45:23Zoai:ri.conicet.gov.ar:11336/8988instacron: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:34982025-09-29 10:45:23.334CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Ricci flow of homogeneous manifolds
title Ricci flow of homogeneous manifolds
spellingShingle Ricci flow of homogeneous manifolds
Lauret, Jorge Ruben
Ricci Flow
title_short Ricci flow of homogeneous manifolds
title_full Ricci flow of homogeneous manifolds
title_fullStr Ricci flow of homogeneous manifolds
title_full_unstemmed Ricci flow of homogeneous manifolds
title_sort Ricci flow of homogeneous manifolds
dc.creator.none.fl_str_mv Lauret, Jorge Ruben
author Lauret, Jorge Ruben
author_facet Lauret, Jorge Ruben
author_role author
dc.subject.none.fl_str_mv Ricci Flow
topic Ricci Flow
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 present in this paper a general approach to study the Ricci flow on homogeneous manifolds. Our main tool is a dynamical system defined on a subset Hq,n of the variety of (q+n)-dimensional Lie algebras, parameterizing the space of all simply connected homogeneous spaces of dimension n with a q-dimensional isotropy, which is proved to be equivalent in a precise sense to the Ricci flow. The approach is useful to better visualize the possible (nonflat) pointed limits of Ricci flow solutions, under diverse rescalings, as well as to determine the type of the possible singularities. Ancient solutions arise naturally from the qualitative analysis of the evolution equation. We develop two examples in detail: a 2-parameter subspace of H1,3 reaching most of 3-dimensional geometries, and a 2-parameter family in H0,n of left-invariant metrics on n-dimensional compact and non-compact semisimple Lie groups.
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
description We present in this paper a general approach to study the Ricci flow on homogeneous manifolds. Our main tool is a dynamical system defined on a subset Hq,n of the variety of (q+n)-dimensional Lie algebras, parameterizing the space of all simply connected homogeneous spaces of dimension n with a q-dimensional isotropy, which is proved to be equivalent in a precise sense to the Ricci flow. The approach is useful to better visualize the possible (nonflat) pointed limits of Ricci flow solutions, under diverse rescalings, as well as to determine the type of the possible singularities. Ancient solutions arise naturally from the qualitative analysis of the evolution equation. We develop two examples in detail: a 2-parameter subspace of H1,3 reaching most of 3-dimensional geometries, and a 2-parameter family in H0,n of left-invariant metrics on n-dimensional compact and non-compact semisimple Lie groups.
publishDate 2013
dc.date.none.fl_str_mv 2013-03
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/11336/8988
Lauret, Jorge Ruben; Ricci flow of homogeneous manifolds; Springer; Mathematische Zeitschrift; 274; 1-2; 3-2013; 373-403
0025-5874
url http://hdl.handle.net/11336/8988
identifier_str_mv Lauret, Jorge Ruben; Ricci flow of homogeneous manifolds; Springer; Mathematische Zeitschrift; 274; 1-2; 3-2013; 373-403
0025-5874
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00209-012-1075-z
info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs00209-012-1075-z
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
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 13.070432

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