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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/58456
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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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13.22299 |