Maximal totally geodesic submanifolds and index of symmetric spaces

Artículo finalmente publicado en: Berndt, J. y Olmos, C. (2016). Maximal totally geodesic submanifolds and index of symmetric spaces. Journal of Differential Geometry, 104 (2), 187-217. https://doi.org/10.4310/jdg/1476367055

Detalles Bibliográficos
Autores principales: Berndt, Jürgen, Olmos, Carlos Enrique
Otros Autores: https://orcid.org/0000-0002-8632-0560
Formato: submittedVersion article
Lenguaje:Inglés
Publicado: 2024
Materias:
Totally geodesic submanifolds
Symmetric spaces
Acceso en línea:http://hdl.handle.net/11086/550693
https://doi.org/10.48550/arXiv.1405.0598
Aporte de:
Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba
id I10-R141-11086-550693
record_format dspace
spelling I10-R141-11086-5506932024-02-29T06:38:27Z Maximal totally geodesic submanifolds and index of symmetric spaces Berndt, Jürgen Olmos, Carlos Enrique https://orcid.org/0000-0002-8632-0560 Totally geodesic submanifolds Symmetric spaces Artículo finalmente publicado en: Berndt, J. y Olmos, C. (2016). Maximal totally geodesic submanifolds and index of symmetric spaces. Journal of Differential Geometry, 104 (2), 187-217. https://doi.org/10.4310/jdg/1476367055 info:eu-repo/semantics/submittedVersion Fil: Berndt, Jürgen. King’s College London. Department of Mathematics; United Kingdom. Fil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. 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}. This research was supported by Famaf-UNC and CIEM-Conicet. info:eu-repo/semantics/submittedVersion Fil: Berndt, Jürgen. King’s College London. Department of Mathematics; United Kingdom. Fil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. Matemática Pura 2024-02-28T12:23:13Z 2024-02-28T12:23:13Z 2016 article http://hdl.handle.net/11086/550693 https://doi.org/10.48550/arXiv.1405.0598 eng De la versión publicada: https://doi.org/10.4310/jdg/1476367055 Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ Impreso; Electrónico y/o Digital ISSN: 0022-040X e-ISSN: 1945-743X
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-141
collection Repositorio Digital Universitario (UNC)
language Inglés
topic Totally geodesic submanifolds
Symmetric spaces
spellingShingle Totally geodesic submanifolds
Symmetric spaces
Berndt, Jürgen
Olmos, Carlos Enrique
Maximal totally geodesic submanifolds and index of symmetric spaces
topic_facet Totally geodesic submanifolds
Symmetric spaces
description Artículo finalmente publicado en: Berndt, J. y Olmos, C. (2016). Maximal totally geodesic submanifolds and index of symmetric spaces. Journal of Differential Geometry, 104 (2), 187-217. https://doi.org/10.4310/jdg/1476367055
author2 https://orcid.org/0000-0002-8632-0560
author_facet https://orcid.org/0000-0002-8632-0560
Berndt, Jürgen
Olmos, Carlos Enrique
format submittedVersion
article
author Berndt, Jürgen
Olmos, Carlos Enrique
author_sort Berndt, Jürgen
title Maximal totally geodesic submanifolds and index of 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
publishDate 2024
url http://hdl.handle.net/11086/550693
https://doi.org/10.48550/arXiv.1405.0598
work_keys_str_mv AT berndtjurgen maximaltotallygeodesicsubmanifoldsandindexofsymmetricspaces
AT olmoscarlosenrique maximaltotallygeodesicsubmanifoldsandindexofsymmetricspaces
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