On the symplectic curvature flow for locally homogeneous manifolds

Recently, J. Streets and G. Tian introduced a natural way to evolve an almost-Kähler manifold called the symplectic curvature flow, in which the metric, the symplectic structure and the almost-complex structure are all evolving. We study in this paper different aspects of the flow on locally homogen...

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Detalles Bibliográficos
Autores: Lauret, Jorge Ruben, Will, Cynthia Eugenia
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/59793
Acceso en línea:http://hdl.handle.net/11336/59793
Access Level:acceso abierto
Palabra clave:symplectic Geometry
curvature flow
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling On the symplectic curvature flow for locally homogeneous manifoldsLauret, Jorge RubenWill, Cynthia Eugeniasymplectic Geometrycurvature flowhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Recently, J. Streets and G. Tian introduced a natural way to evolve an almost-Kähler manifold called the symplectic curvature flow, in which the metric, the symplectic structure and the almost-complex structure are all evolving. We study in this paper different aspects of the flow on locally homogeneous manifolds, including long-time existence, solitons, regularity and convergence. We develop in detail two large classes of Lie groups, which are relatively simple from a structural point of view but yet geometrically rich and exotic: solvable Lie groups with a codimension one abelian normal subgroup and a construction attached to each left symmetric algebra. As an application, we exhibit a soliton structure on most of symplectic surfaces which are Lie groups. A family of ancient solutions which develop a finite time singularity was found; neither their Chern scalar nor their scalar curvature are monotone along the flow and they converge in the pointed sense to a (non-Kähler) shrinking soliton solution on the same Lie group.Fil: Lauret, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Will, Cynthia Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaInternational Press Boston2017-02info: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/11336/59793Lauret, Jorge Ruben; Will, Cynthia Eugenia; On the symplectic curvature flow for locally homogeneous manifolds; International Press Boston; Journal Of Symplectic Geometry; 15; 1; 2-2017; 1-491527-5256CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.intlpress.com/site/pub/pages/journals/items/jsg/content/vols/0015/0001/a001/index.htmlinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1405.6065info:eu-repo/semantics/altIdentifier/doi/10.4310/JSG.2017.v15.n1.a1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:06:42Zoai:ri.conicet.gov.ar:11336/59793instacron: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:34982024-05-08 14:06:43.121CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the symplectic curvature flow for locally homogeneous manifolds
title On the symplectic curvature flow for locally homogeneous manifolds
spellingShingle On the symplectic curvature flow for locally homogeneous manifolds
Lauret, Jorge Ruben
symplectic Geometry
curvature flow
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short On the symplectic curvature flow for locally homogeneous manifolds
title_full On the symplectic curvature flow for locally homogeneous manifolds
title_fullStr On the symplectic curvature flow for locally homogeneous manifolds
title_full_unstemmed On the symplectic curvature flow for locally homogeneous manifolds
title_sort On the symplectic curvature flow for locally homogeneous manifolds
dc.creator.none.fl_str_mv Lauret, Jorge Ruben
Will, Cynthia Eugenia
author Lauret, Jorge Ruben
author_facet Lauret, Jorge Ruben
Will, Cynthia Eugenia
author_role author
author2 Will, Cynthia Eugenia
author2_role author
dc.subject.none.fl_str_mv symplectic Geometry
curvature flow
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic symplectic Geometry
curvature flow
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description Recently, J. Streets and G. Tian introduced a natural way to evolve an almost-Kähler manifold called the symplectic curvature flow, in which the metric, the symplectic structure and the almost-complex structure are all evolving. We study in this paper different aspects of the flow on locally homogeneous manifolds, including long-time existence, solitons, regularity and convergence. We develop in detail two large classes of Lie groups, which are relatively simple from a structural point of view but yet geometrically rich and exotic: solvable Lie groups with a codimension one abelian normal subgroup and a construction attached to each left symmetric algebra. As an application, we exhibit a soliton structure on most of symplectic surfaces which are Lie groups. A family of ancient solutions which develop a finite time singularity was found; neither their Chern scalar nor their scalar curvature are monotone along the flow and they converge in the pointed sense to a (non-Kähler) shrinking soliton solution on the same Lie group.
publishDate 2017
dc.date.none.fl_str_mv 2017-02
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/11336/59793
Lauret, Jorge Ruben; Will, Cynthia Eugenia; On the symplectic curvature flow for locally homogeneous manifolds; International Press Boston; Journal Of Symplectic Geometry; 15; 1; 2-2017; 1-49
1527-5256
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59793
identifier_str_mv Lauret, Jorge Ruben; Will, Cynthia Eugenia; On the symplectic curvature flow for locally homogeneous manifolds; International Press Boston; Journal Of Symplectic Geometry; 15; 1; 2-2017; 1-49
1527-5256
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.intlpress.com/site/pub/pages/journals/items/jsg/content/vols/0015/0001/a001/index.html
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1405.6065
info:eu-repo/semantics/altIdentifier/doi/10.4310/JSG.2017.v15.n1.a1
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 International Press Boston
publisher.none.fl_str_mv International Press Boston
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,811543

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