On Ricci negative solvmanifolds and their nilradicals

Autores
Deré, Jonas; Lauret, Jorge Ruben
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the homogeneous case, the only curvature behavior which is still far from being understood is Ricci negative. In this paper, we study which nilpotent Lie algebras admit a Ricci negative solvable extension. Different unexpected behaviors were found. On the other hand, given a nilpotent Lie algebra, we consider the space of all the derivations such that the corresponding solvable extension has a metric with negative Ricci curvature. Using the nice convexity properties of the moment map for the variety of nilpotent Lie algebras, we obtain a useful characterization of such derivations and some applications.
Fil: Deré, Jonas. Katholikie Universiteit Leuven; Bélgica
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; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Materia
NEGATIVE
RICCI
SOLVMANIFOLD
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:11336/125070
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On Ricci negative solvmanifolds and their nilradicalsDeré, JonasLauret, Jorge RubenNEGATIVERICCISOLVMANIFOLDhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In the homogeneous case, the only curvature behavior which is still far from being understood is Ricci negative. In this paper, we study which nilpotent Lie algebras admit a Ricci negative solvable extension. Different unexpected behaviors were found. On the other hand, given a nilpotent Lie algebra, we consider the space of all the derivations such that the corresponding solvable extension has a metric with negative Ricci curvature. Using the nice convexity properties of the moment map for the variety of nilpotent Lie algebras, we obtain a useful characterization of such derivations and some applications.Fil: Deré, Jonas. Katholikie Universiteit Leuven; BélgicaFil: 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; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaWiley VCH Verlag2019-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/125070Deré, Jonas; Lauret, Jorge Ruben; On Ricci negative solvmanifolds and their nilradicals; Wiley VCH Verlag; Mathematische Nachrichten; 292; 7; 7-2019; 1462-14810025-584X1522-2616CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1709.10342info:eu-repo/semantics/altIdentifier/doi/10.1002/mana.201700455info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/10.1002/mana.201700455info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T12:23:57Zoai:ri.conicet.gov.ar:11336/125070instacron: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:34982025-10-29 12:23:58.016CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On Ricci negative solvmanifolds and their nilradicals
title On Ricci negative solvmanifolds and their nilradicals
spellingShingle On Ricci negative solvmanifolds and their nilradicals
Deré, Jonas
NEGATIVE
RICCI
SOLVMANIFOLD
title_short On Ricci negative solvmanifolds and their nilradicals
title_full On Ricci negative solvmanifolds and their nilradicals
title_fullStr On Ricci negative solvmanifolds and their nilradicals
title_full_unstemmed On Ricci negative solvmanifolds and their nilradicals
title_sort On Ricci negative solvmanifolds and their nilradicals
dc.creator.none.fl_str_mv Deré, Jonas
Lauret, Jorge Ruben
author Deré, Jonas
author_facet Deré, Jonas
Lauret, Jorge Ruben
author_role author
author2 Lauret, Jorge Ruben
author2_role author
dc.subject.none.fl_str_mv NEGATIVE
RICCI
SOLVMANIFOLD
topic NEGATIVE
RICCI
SOLVMANIFOLD
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the homogeneous case, the only curvature behavior which is still far from being understood is Ricci negative. In this paper, we study which nilpotent Lie algebras admit a Ricci negative solvable extension. Different unexpected behaviors were found. On the other hand, given a nilpotent Lie algebra, we consider the space of all the derivations such that the corresponding solvable extension has a metric with negative Ricci curvature. Using the nice convexity properties of the moment map for the variety of nilpotent Lie algebras, we obtain a useful characterization of such derivations and some applications.
Fil: Deré, Jonas. Katholikie Universiteit Leuven; Bélgica
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; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
description In the homogeneous case, the only curvature behavior which is still far from being understood is Ricci negative. In this paper, we study which nilpotent Lie algebras admit a Ricci negative solvable extension. Different unexpected behaviors were found. On the other hand, given a nilpotent Lie algebra, we consider the space of all the derivations such that the corresponding solvable extension has a metric with negative Ricci curvature. Using the nice convexity properties of the moment map for the variety of nilpotent Lie algebras, we obtain a useful characterization of such derivations and some applications.
publishDate 2019
dc.date.none.fl_str_mv 2019-07
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/11336/125070
Deré, Jonas; Lauret, Jorge Ruben; On Ricci negative solvmanifolds and their nilradicals; Wiley VCH Verlag; Mathematische Nachrichten; 292; 7; 7-2019; 1462-1481
0025-584X
1522-2616
CONICET Digital
CONICET
url http://hdl.handle.net/11336/125070
identifier_str_mv Deré, Jonas; Lauret, Jorge Ruben; On Ricci negative solvmanifolds and their nilradicals; Wiley VCH Verlag; Mathematische Nachrichten; 292; 7; 7-2019; 1462-1481
0025-584X
1522-2616
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1709.10342
info:eu-repo/semantics/altIdentifier/doi/10.1002/mana.201700455
info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/10.1002/mana.201700455
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 Wiley VCH Verlag
publisher.none.fl_str_mv Wiley VCH Verlag
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 12.589754

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