Negative Ricci curvature on some non-solvable Lie groups

Autores
Will, Cynthia Eugenia
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show that for any non-trivial representation (V, π) of u(2) with the center acting as multiples of the identity, the semidirect product u(2) ⋉ πV admits a metric with negative Ricci curvature that can be explicitly obtained. It is proved that u(2) ⋉ πV degenerates to a solvable Lie algebra that admits a metric with negative Ricci curvature. An n-dimensional Lie group with compact Levi factor SU (2) admitting a left invariant metric with negative Ricci is therefore obtained for any n≥ 7.
Fil: 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; Argentina
Materia
LIE GROUPS
RICCI CURVATURE
RIEMANNIAN METRICS
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:11336/59979
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Negative Ricci curvature on some non-solvable Lie groupsWill, Cynthia EugeniaLIE GROUPSRICCI CURVATURERIEMANNIAN METRICShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We show that for any non-trivial representation (V, π) of u(2) with the center acting as multiples of the identity, the semidirect product u(2) ⋉ πV admits a metric with negative Ricci curvature that can be explicitly obtained. It is proved that u(2) ⋉ πV degenerates to a solvable Lie algebra that admits a metric with negative Ricci curvature. An n-dimensional Lie group with compact Levi factor SU (2) admitting a left invariant metric with negative Ricci is therefore obtained for any n≥ 7.Fil: 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; ArgentinaSpringer2017-02info: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/11336/59979Will, Cynthia Eugenia; Negative Ricci curvature on some non-solvable Lie groups; Springer; Geometriae Dedicata; 186; 1; 2-2017; 181-1950046-5755CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10711-016-0185-xinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10711-016-0185-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 Técnicas2025-09-29T09:37:11Zoai:ri.conicet.gov.ar:11336/59979instacron: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 09:37:11.918CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Negative Ricci curvature on some non-solvable Lie groups
title Negative Ricci curvature on some non-solvable Lie groups
spellingShingle Negative Ricci curvature on some non-solvable Lie groups
Will, Cynthia Eugenia
LIE GROUPS
RICCI CURVATURE
RIEMANNIAN METRICS
title_short Negative Ricci curvature on some non-solvable Lie groups
title_full Negative Ricci curvature on some non-solvable Lie groups
title_fullStr Negative Ricci curvature on some non-solvable Lie groups
title_full_unstemmed Negative Ricci curvature on some non-solvable Lie groups
title_sort Negative Ricci curvature on some non-solvable Lie groups
dc.creator.none.fl_str_mv Will, Cynthia Eugenia
author Will, Cynthia Eugenia
author_facet Will, Cynthia Eugenia
author_role author
dc.subject.none.fl_str_mv LIE GROUPS
RICCI CURVATURE
RIEMANNIAN METRICS
topic LIE GROUPS
RICCI CURVATURE
RIEMANNIAN METRICS
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 show that for any non-trivial representation (V, π) of u(2) with the center acting as multiples of the identity, the semidirect product u(2) ⋉ πV admits a metric with negative Ricci curvature that can be explicitly obtained. It is proved that u(2) ⋉ πV degenerates to a solvable Lie algebra that admits a metric with negative Ricci curvature. An n-dimensional Lie group with compact Levi factor SU (2) admitting a left invariant metric with negative Ricci is therefore obtained for any n≥ 7.
Fil: 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; Argentina
description We show that for any non-trivial representation (V, π) of u(2) with the center acting as multiples of the identity, the semidirect product u(2) ⋉ πV admits a metric with negative Ricci curvature that can be explicitly obtained. It is proved that u(2) ⋉ πV degenerates to a solvable Lie algebra that admits a metric with negative Ricci curvature. An n-dimensional Lie group with compact Levi factor SU (2) admitting a left invariant metric with negative Ricci is therefore obtained for any n≥ 7.
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/11336/59979
Will, Cynthia Eugenia; Negative Ricci curvature on some non-solvable Lie groups; Springer; Geometriae Dedicata; 186; 1; 2-2017; 181-195
0046-5755
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59979
identifier_str_mv Will, Cynthia Eugenia; Negative Ricci curvature on some non-solvable Lie groups; Springer; Geometriae Dedicata; 186; 1; 2-2017; 181-195
0046-5755
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://link.springer.com/article/10.1007/s10711-016-0185-x
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10711-016-0185-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/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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