The index of symmetry of compact naturally reductive spaces

Autores
Olmos, Carlos Enrique; Reggiani, Silvio Nicolás; Tamaru, Hiroshi
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive spaces. In this case, the so-called leaf of symmetry turns out to be of the group type. We also study several examples where the leaf of symmetry is not of the group type. Interesting examples arise from the unit tangent bundle of the sphere of curvature 2, and two metrics in an Aloff-Wallach 7-manifold and the Wallach 24-manifold
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 Conicet - Córdoba; 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 Conicet - Córdoba; Argentina
Fil: Tamaru, Hiroshi. Hiroshima University; Japón
Materia
Index of Symmetry
Distribution of Symmetry
Naturally Reductive Space
Symmetric 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:11336/30184
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/30184
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network_name_str CONICET Digital (CONICET)
spelling The index of symmetry of compact naturally reductive spacesOlmos, Carlos EnriqueReggiani, Silvio NicolásTamaru, HiroshiIndex of SymmetryDistribution of SymmetryNaturally Reductive SpaceSymmetric Spacehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive spaces. In this case, the so-called leaf of symmetry turns out to be of the group type. We also study several examples where the leaf of symmetry is not of the group type. Interesting examples arise from the unit tangent bundle of the sphere of curvature 2, and two metrics in an Aloff-Wallach 7-manifold and the Wallach 24-manifoldFil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; 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 Conicet - Córdoba; ArgentinaFil: Tamaru, Hiroshi. Hiroshima University; JapónSpringer2014-08info: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/11336/30184Olmos, Carlos Enrique; Reggiani, Silvio Nicolás; Tamaru, Hiroshi; The index of symmetry of compact naturally reductive spaces; Springer; Mathematische Zeitschrift; 277; 3-4; 8-2014; 611-6280025-5874CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00209-013-1268-0info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00209-013-1268-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:58:41Zoai:ri.conicet.gov.ar:11336/30184instacron: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 11:58:42.204CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The index of symmetry of compact naturally reductive spaces
title The index of symmetry of compact naturally reductive spaces
spellingShingle The index of symmetry of compact naturally reductive spaces
Olmos, Carlos Enrique
Index of Symmetry
Distribution of Symmetry
Naturally Reductive Space
Symmetric Space
title_short The index of symmetry of compact naturally reductive spaces
title_full The index of symmetry of compact naturally reductive spaces
title_fullStr The index of symmetry of compact naturally reductive spaces
title_full_unstemmed The index of symmetry of compact naturally reductive spaces
title_sort The index of symmetry of compact naturally reductive spaces
dc.creator.none.fl_str_mv Olmos, Carlos Enrique
Reggiani, Silvio Nicolás
Tamaru, Hiroshi
author Olmos, Carlos Enrique
author_facet Olmos, Carlos Enrique
Reggiani, Silvio Nicolás
Tamaru, Hiroshi
author_role author
author2 Reggiani, Silvio Nicolás
Tamaru, Hiroshi
author2_role author
author
dc.subject.none.fl_str_mv Index of Symmetry
Distribution of Symmetry
Naturally Reductive Space
Symmetric Space
topic Index of Symmetry
Distribution of Symmetry
Naturally Reductive Space
Symmetric 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 introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive spaces. In this case, the so-called leaf of symmetry turns out to be of the group type. We also study several examples where the leaf of symmetry is not of the group type. Interesting examples arise from the unit tangent bundle of the sphere of curvature 2, and two metrics in an Aloff-Wallach 7-manifold and the Wallach 24-manifold
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 Conicet - Córdoba; 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 Conicet - Córdoba; Argentina
Fil: Tamaru, Hiroshi. Hiroshima University; Japón
description We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive spaces. In this case, the so-called leaf of symmetry turns out to be of the group type. We also study several examples where the leaf of symmetry is not of the group type. Interesting examples arise from the unit tangent bundle of the sphere of curvature 2, and two metrics in an Aloff-Wallach 7-manifold and the Wallach 24-manifold
publishDate 2014
dc.date.none.fl_str_mv 2014-08
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/11336/30184
Olmos, Carlos Enrique; Reggiani, Silvio Nicolás; Tamaru, Hiroshi; The index of symmetry of compact naturally reductive spaces; Springer; Mathematische Zeitschrift; 277; 3-4; 8-2014; 611-628
0025-5874
CONICET Digital
CONICET
url http://hdl.handle.net/11336/30184
identifier_str_mv Olmos, Carlos Enrique; Reggiani, Silvio Nicolás; Tamaru, Hiroshi; The index of symmetry of compact naturally reductive spaces; Springer; Mathematische Zeitschrift; 277; 3-4; 8-2014; 611-628
0025-5874
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/s00209-013-1268-0
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00209-013-1268-0
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 13.129756

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