Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow

Autores
Fernández Culma, Edison Alberto
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The aim of this paper is to study self-similar solutions to the symplectic curvature flow on 6-dimensional nilmanifolds. For this purpose, we focus our attention on the family of symplectic two- and three-step nilpotent Lie algebras admitting a minimal compatible metric and give a complete classification of these algebras together with their respective metric. Such a classification is given by using our generalization of Nikolayevsky’s nice basis criterion, which, for the convenience of the reader, will be repeated here in the context of canonical compatible metrics for geometric structures on nilmanifolds. By computing the Chern–Ricci operator (Formula presented.) in each case, we show that the above distinguished metrics define a soliton almost Kähler structure. Many illustrative examples are carefully developed.
Fil: Fernández Culma, Edison Alberto. 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; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Materia
Convexity Of the Moment Map
Geometric Structures on Nilmanifolds
Nice Basis
Nilpotent Lie Algebras
Self-Similar Solutions
Symplectic Curvature 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:11336/51389
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/51389
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature FlowFernández Culma, Edison AlbertoConvexity Of the Moment MapGeometric Structures on NilmanifoldsNice BasisNilpotent Lie AlgebrasSelf-Similar SolutionsSymplectic Curvature Flowhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The aim of this paper is to study self-similar solutions to the symplectic curvature flow on 6-dimensional nilmanifolds. For this purpose, we focus our attention on the family of symplectic two- and three-step nilpotent Lie algebras admitting a minimal compatible metric and give a complete classification of these algebras together with their respective metric. Such a classification is given by using our generalization of Nikolayevsky’s nice basis criterion, which, for the convenience of the reader, will be repeated here in the context of canonical compatible metrics for geometric structures on nilmanifolds. By computing the Chern–Ricci operator (Formula presented.) in each case, we show that the above distinguished metrics define a soliton almost Kähler structure. Many illustrative examples are carefully developed.Fil: Fernández Culma, Edison Alberto. 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; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaSpringer2015-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/51389Fernández Culma, Edison Alberto; Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow; Springer; The Journal Of Geometric Analysis; 25; 4; 10-2015; 2736-27581050-6926CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s12220-014-9534-xinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs12220-014-9534-xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:39:39Zoai:ri.conicet.gov.ar:11336/51389instacron: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 10:39:40.189CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow
title Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow
spellingShingle Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow
Fernández Culma, Edison Alberto
Convexity Of the Moment Map
Geometric Structures on Nilmanifolds
Nice Basis
Nilpotent Lie Algebras
Self-Similar Solutions
Symplectic Curvature Flow
title_short Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow
title_full Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow
title_fullStr Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow
title_full_unstemmed Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow
title_sort Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow
dc.creator.none.fl_str_mv Fernández Culma, Edison Alberto
author Fernández Culma, Edison Alberto
author_facet Fernández Culma, Edison Alberto
author_role author
dc.subject.none.fl_str_mv Convexity Of the Moment Map
Geometric Structures on Nilmanifolds
Nice Basis
Nilpotent Lie Algebras
Self-Similar Solutions
Symplectic Curvature Flow
topic Convexity Of the Moment Map
Geometric Structures on Nilmanifolds
Nice Basis
Nilpotent Lie Algebras
Self-Similar Solutions
Symplectic Curvature 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 The aim of this paper is to study self-similar solutions to the symplectic curvature flow on 6-dimensional nilmanifolds. For this purpose, we focus our attention on the family of symplectic two- and three-step nilpotent Lie algebras admitting a minimal compatible metric and give a complete classification of these algebras together with their respective metric. Such a classification is given by using our generalization of Nikolayevsky’s nice basis criterion, which, for the convenience of the reader, will be repeated here in the context of canonical compatible metrics for geometric structures on nilmanifolds. By computing the Chern–Ricci operator (Formula presented.) in each case, we show that the above distinguished metrics define a soliton almost Kähler structure. Many illustrative examples are carefully developed.
Fil: Fernández Culma, Edison Alberto. 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; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
description The aim of this paper is to study self-similar solutions to the symplectic curvature flow on 6-dimensional nilmanifolds. For this purpose, we focus our attention on the family of symplectic two- and three-step nilpotent Lie algebras admitting a minimal compatible metric and give a complete classification of these algebras together with their respective metric. Such a classification is given by using our generalization of Nikolayevsky’s nice basis criterion, which, for the convenience of the reader, will be repeated here in the context of canonical compatible metrics for geometric structures on nilmanifolds. By computing the Chern–Ricci operator (Formula presented.) in each case, we show that the above distinguished metrics define a soliton almost Kähler structure. Many illustrative examples are carefully developed.
publishDate 2015
dc.date.none.fl_str_mv 2015-10
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/11336/51389
Fernández Culma, Edison Alberto; Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow; Springer; The Journal Of Geometric Analysis; 25; 4; 10-2015; 2736-2758
1050-6926
CONICET Digital
CONICET
url http://hdl.handle.net/11336/51389
identifier_str_mv Fernández Culma, Edison Alberto; Soliton Almost Kähler Structures on 6-Dimensional Nilmanifolds for the Symplectic Curvature Flow; Springer; The Journal Of Geometric Analysis; 25; 4; 10-2015; 2736-2758
1050-6926
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s12220-014-9534-x
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs12220-014-9534-x
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/zip
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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