The Alekseevskii conjecture in low dimensions

Autores
Arroyo, Romina Melisa; Lafuente, Ramiro Augusto
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The long-standing Alekseevskii conjecture states that a connected homogeneous Einstein space G / K of negative scalar curvature must be diffeomorphic to Rn. This was known to be true only in dimensions up to 5, and in dimension 6 for non-semisimple G. In this work we prove that this is also the case in dimensions up to 10 when G is not semisimple. For arbitrary G, besides 5 possible exceptions, we show that the conjecture holds up to dimension 8.
Fil: Arroyo, Romina Melisa. 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
Fil: Lafuente, Ramiro Augusto. Westfalische Wilhelms Universitat; Alemania
Materia
ALEKSEEVSKII CONJECTURE
LOW DIMENSIONS
EINSTEIN METRICS
NON-COMPACT HOMOGENEOUS SPACES
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:11336/59984
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/59984
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The Alekseevskii conjecture in low dimensionsArroyo, Romina MelisaLafuente, Ramiro AugustoALEKSEEVSKII CONJECTURELOW DIMENSIONSEINSTEIN METRICSNON-COMPACT HOMOGENEOUS SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The long-standing Alekseevskii conjecture states that a connected homogeneous Einstein space G / K of negative scalar curvature must be diffeomorphic to Rn. This was known to be true only in dimensions up to 5, and in dimension 6 for non-semisimple G. In this work we prove that this is also the case in dimensions up to 10 when G is not semisimple. For arbitrary G, besides 5 possible exceptions, we show that the conjecture holds up to dimension 8.Fil: Arroyo, Romina Melisa. 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: Lafuente, Ramiro Augusto. Westfalische Wilhelms Universitat; AlemaniaSpringer2017-02info: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/11336/59984Arroyo, Romina Melisa; Lafuente, Ramiro Augusto; The Alekseevskii conjecture in low dimensions; Springer; Mathematische Annalen; 367; 1-2; 2-2017; 283-3090025-5831CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s00208-016-1386-1info:eu-repo/semantics/altIdentifier/doi/10.1007/s00208-016-1386-1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:29:43Zoai:ri.conicet.gov.ar:11336/59984instacron: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:34982025-10-22 11:29:43.977CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Alekseevskii conjecture in low dimensions
title The Alekseevskii conjecture in low dimensions
spellingShingle The Alekseevskii conjecture in low dimensions
Arroyo, Romina Melisa
ALEKSEEVSKII CONJECTURE
LOW DIMENSIONS
EINSTEIN METRICS
NON-COMPACT HOMOGENEOUS SPACES
title_short The Alekseevskii conjecture in low dimensions
title_full The Alekseevskii conjecture in low dimensions
title_fullStr The Alekseevskii conjecture in low dimensions
title_full_unstemmed The Alekseevskii conjecture in low dimensions
title_sort The Alekseevskii conjecture in low dimensions
dc.creator.none.fl_str_mv Arroyo, Romina Melisa
Lafuente, Ramiro Augusto
author Arroyo, Romina Melisa
author_facet Arroyo, Romina Melisa
Lafuente, Ramiro Augusto
author_role author
author2 Lafuente, Ramiro Augusto
author2_role author
dc.subject.none.fl_str_mv ALEKSEEVSKII CONJECTURE
LOW DIMENSIONS
EINSTEIN METRICS
NON-COMPACT HOMOGENEOUS SPACES
topic ALEKSEEVSKII CONJECTURE
LOW DIMENSIONS
EINSTEIN METRICS
NON-COMPACT HOMOGENEOUS SPACES
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 long-standing Alekseevskii conjecture states that a connected homogeneous Einstein space G / K of negative scalar curvature must be diffeomorphic to Rn. This was known to be true only in dimensions up to 5, and in dimension 6 for non-semisimple G. In this work we prove that this is also the case in dimensions up to 10 when G is not semisimple. For arbitrary G, besides 5 possible exceptions, we show that the conjecture holds up to dimension 8.
Fil: Arroyo, Romina Melisa. 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
Fil: Lafuente, Ramiro Augusto. Westfalische Wilhelms Universitat; Alemania
description The long-standing Alekseevskii conjecture states that a connected homogeneous Einstein space G / K of negative scalar curvature must be diffeomorphic to Rn. This was known to be true only in dimensions up to 5, and in dimension 6 for non-semisimple G. In this work we prove that this is also the case in dimensions up to 10 when G is not semisimple. For arbitrary G, besides 5 possible exceptions, we show that the conjecture holds up to dimension 8.
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/11336/59984
Arroyo, Romina Melisa; Lafuente, Ramiro Augusto; The Alekseevskii conjecture in low dimensions; Springer; Mathematische Annalen; 367; 1-2; 2-2017; 283-309
0025-5831
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59984
identifier_str_mv Arroyo, Romina Melisa; Lafuente, Ramiro Augusto; The Alekseevskii conjecture in low dimensions; Springer; Mathematische Annalen; 367; 1-2; 2-2017; 283-309
0025-5831
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s00208-016-1386-1
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00208-016-1386-1
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 12.982451

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