Maximal totally geodesic submanifolds and index of symmetric spaces

Autores
Berndt, Jürgen; Olmos, Carlos Enrique
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let M be an irreducible Riemannian symmetric space. The index i(M) of M is the minimal codimension of a totally geodesic submanifold of M. In [1] we proved that i(M) is bounded from below by the rank rk(M) of M, that is, rk(M) ≤ i(M). In this paper we classify all irreducible Riemannian symmetric spaces M for which the equality holds, that is, rk(M) = i(M). In this context we also obtain an explicit classification of all non-semisimple maximal totally geodesic submanifolds in irreducible Riemannian symmetric spaces of noncompact type and show that they are closely related to irreducible symmetric R-spaces. We also determine the index of some symmetric spaces and classify the irreducible Riemannian symmetric spaces of noncompact type with i(M) ∈ {4, 5, 6}.
Fil: Berndt, Jürgen. King's College London; Reino Unido
Fil: Olmos, Carlos Enrique. 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
totally geodesic submanifolds
symmetric 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:11336/58456

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network_name_str CONICET Digital (CONICET)
spelling Maximal totally geodesic submanifolds and index of symmetric spacesBerndt, JürgenOlmos, Carlos Enriquetotally geodesic submanifoldssymmetric spaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let M be an irreducible Riemannian symmetric space. The index i(M) of M is the minimal codimension of a totally geodesic submanifold of M. In [1] we proved that i(M) is bounded from below by the rank rk(M) of M, that is, rk(M) ≤ i(M). In this paper we classify all irreducible Riemannian symmetric spaces M for which the equality holds, that is, rk(M) = i(M). In this context we also obtain an explicit classification of all non-semisimple maximal totally geodesic submanifolds in irreducible Riemannian symmetric spaces of noncompact type and show that they are closely related to irreducible symmetric R-spaces. We also determine the index of some symmetric spaces and classify the irreducible Riemannian symmetric spaces of noncompact type with i(M) ∈ {4, 5, 6}.Fil: Berndt, Jürgen. King's College London; Reino UnidoFil: Olmos, Carlos Enrique. 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; ArgentinaInternational Press Boston2016-10info: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/11336/58456Berndt, Jürgen; Olmos, Carlos Enrique; Maximal totally geodesic submanifolds and index of symmetric spaces; International Press Boston; Journal of Differential Geometry; 104; 2; 10-2016; 187-2170022-040XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.jdg/1476367055info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1405.0598info:eu-repo/semantics/altIdentifier/doi/10.4310/jdg/1476367055info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:36:58Zoai:ri.conicet.gov.ar:11336/58456instacron: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 14:36:59.144CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Maximal totally geodesic submanifolds and index of symmetric spaces
title Maximal totally geodesic submanifolds and index of symmetric spaces
spellingShingle Maximal totally geodesic submanifolds and index of symmetric spaces
Berndt, Jürgen
totally geodesic submanifolds
symmetric spaces
title_short Maximal totally geodesic submanifolds and index of symmetric spaces
title_full Maximal totally geodesic submanifolds and index of symmetric spaces
title_fullStr Maximal totally geodesic submanifolds and index of symmetric spaces
title_full_unstemmed Maximal totally geodesic submanifolds and index of symmetric spaces
title_sort Maximal totally geodesic submanifolds and index of symmetric spaces
dc.creator.none.fl_str_mv Berndt, Jürgen
Olmos, Carlos Enrique
author Berndt, Jürgen
author_facet Berndt, Jürgen
Olmos, Carlos Enrique
author_role author
author2 Olmos, Carlos Enrique
author2_role author
dc.subject.none.fl_str_mv totally geodesic submanifolds
symmetric spaces
topic totally geodesic submanifolds
symmetric 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 Let M be an irreducible Riemannian symmetric space. The index i(M) of M is the minimal codimension of a totally geodesic submanifold of M. In [1] we proved that i(M) is bounded from below by the rank rk(M) of M, that is, rk(M) ≤ i(M). In this paper we classify all irreducible Riemannian symmetric spaces M for which the equality holds, that is, rk(M) = i(M). In this context we also obtain an explicit classification of all non-semisimple maximal totally geodesic submanifolds in irreducible Riemannian symmetric spaces of noncompact type and show that they are closely related to irreducible symmetric R-spaces. We also determine the index of some symmetric spaces and classify the irreducible Riemannian symmetric spaces of noncompact type with i(M) ∈ {4, 5, 6}.
Fil: Berndt, Jürgen. King's College London; Reino Unido
Fil: Olmos, Carlos Enrique. 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 Let M be an irreducible Riemannian symmetric space. The index i(M) of M is the minimal codimension of a totally geodesic submanifold of M. In [1] we proved that i(M) is bounded from below by the rank rk(M) of M, that is, rk(M) ≤ i(M). In this paper we classify all irreducible Riemannian symmetric spaces M for which the equality holds, that is, rk(M) = i(M). In this context we also obtain an explicit classification of all non-semisimple maximal totally geodesic submanifolds in irreducible Riemannian symmetric spaces of noncompact type and show that they are closely related to irreducible symmetric R-spaces. We also determine the index of some symmetric spaces and classify the irreducible Riemannian symmetric spaces of noncompact type with i(M) ∈ {4, 5, 6}.
publishDate 2016
dc.date.none.fl_str_mv 2016-10
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/11336/58456
Berndt, Jürgen; Olmos, Carlos Enrique; Maximal totally geodesic submanifolds and index of symmetric spaces; International Press Boston; Journal of Differential Geometry; 104; 2; 10-2016; 187-217
0022-040X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/58456
identifier_str_mv Berndt, Jürgen; Olmos, Carlos Enrique; Maximal totally geodesic submanifolds and index of symmetric spaces; International Press Boston; Journal of Differential Geometry; 104; 2; 10-2016; 187-217
0022-040X
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://projecteuclid.org/euclid.jdg/1476367055
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1405.0598
info:eu-repo/semantics/altIdentifier/doi/10.4310/jdg/1476367055
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 International Press Boston
publisher.none.fl_str_mv International Press Boston
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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