A note on the uniqueness of the canonical connection of a naturally reductive space

Autores
Olmos, Carlos Enrique; Reggiani, Silvio Nicolás
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere, a compact Lie group with a bi-invariant metric or its symmetric dual. In particular, the canonical connection is unique for the hyperbolic space when the dimension is different from three. We also prove that the canonical connection on the sphere is unique for the symmetric presentation. Finally, we compute the full isometry group (connected component) of a compact and locally irreducible naturally reductive space.
Fil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Materia
Canonical Connection
Reductive Space
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:11336/10985
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A note on the uniqueness of the canonical connection of a naturally reductive spaceOlmos, Carlos EnriqueReggiani, Silvio NicolásCanonical ConnectionReductive Spacehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere, a compact Lie group with a bi-invariant metric or its symmetric dual. In particular, the canonical connection is unique for the hyperbolic space when the dimension is different from three. We also prove that the canonical connection on the sphere is unique for the symmetric presentation. Finally, we compute the full isometry group (connected component) of a compact and locally irreducible naturally reductive space.Fil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); ArgentinaFil: Reggiani, Silvio Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); ArgentinaSpringer Wien2013-12info: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/11336/10985Olmos, Carlos Enrique; Reggiani, Silvio Nicolás; A note on the uniqueness of the canonical connection of a naturally reductive space; Springer Wien; Monatshefete Fur Mathematik; 172; 3-4; 12-2013; 379-3860026-9255enginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00605-013-0554-6info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs00605-013-0554-6info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:28:27Zoai:ri.conicet.gov.ar:11336/10985instacron: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:34982025-10-15 15:28:28.181CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A note on the uniqueness of the canonical connection of a naturally reductive space
title A note on the uniqueness of the canonical connection of a naturally reductive space
spellingShingle A note on the uniqueness of the canonical connection of a naturally reductive space
Olmos, Carlos Enrique
Canonical Connection
Reductive Space
title_short A note on the uniqueness of the canonical connection of a naturally reductive space
title_full A note on the uniqueness of the canonical connection of a naturally reductive space
title_fullStr A note on the uniqueness of the canonical connection of a naturally reductive space
title_full_unstemmed A note on the uniqueness of the canonical connection of a naturally reductive space
title_sort A note on the uniqueness of the canonical connection of a naturally reductive space
dc.creator.none.fl_str_mv Olmos, Carlos Enrique
Reggiani, Silvio Nicolás
author Olmos, Carlos Enrique
author_facet Olmos, Carlos Enrique
Reggiani, Silvio Nicolás
author_role author
author2 Reggiani, Silvio Nicolás
author2_role author
dc.subject.none.fl_str_mv Canonical Connection
Reductive Space
topic Canonical Connection
Reductive Space
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 extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere, a compact Lie group with a bi-invariant metric or its symmetric dual. In particular, the canonical connection is unique for the hyperbolic space when the dimension is different from three. We also prove that the canonical connection on the sphere is unique for the symmetric presentation. Finally, we compute the full isometry group (connected component) of a compact and locally irreducible naturally reductive space.
Fil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
description We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere, a compact Lie group with a bi-invariant metric or its symmetric dual. In particular, the canonical connection is unique for the hyperbolic space when the dimension is different from three. We also prove that the canonical connection on the sphere is unique for the symmetric presentation. Finally, we compute the full isometry group (connected component) of a compact and locally irreducible naturally reductive space.
publishDate 2013
dc.date.none.fl_str_mv 2013-12
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/11336/10985
Olmos, Carlos Enrique; Reggiani, Silvio Nicolás; A note on the uniqueness of the canonical connection of a naturally reductive space; Springer Wien; Monatshefete Fur Mathematik; 172; 3-4; 12-2013; 379-386
0026-9255
url http://hdl.handle.net/11336/10985
identifier_str_mv Olmos, Carlos Enrique; Reggiani, Silvio Nicolás; A note on the uniqueness of the canonical connection of a naturally reductive space; Springer Wien; Monatshefete Fur Mathematik; 172; 3-4; 12-2013; 379-386
0026-9255
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00605-013-0554-6
info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs00605-013-0554-6
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 Wien
publisher.none.fl_str_mv Springer Wien
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 13.22299

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