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
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| Format: | info:eu-repo/semantics/submittedVersion |
| Language: | eng |
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2024
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| Online Access: | http://hdl.handle.net/11086/550693 https://doi.org/10.48550/arXiv.1405.0598 |
| _version_ | 1801216173212172288 |
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| author | Berndt, Jürgen Olmos, Carlos Enrique |
| author2 | https://orcid.org/0000-0002-8632-0560 |
| author_facet | https://orcid.org/0000-0002-8632-0560 Berndt, Jürgen Olmos, Carlos Enrique |
| author_sort | Berndt, Jürgen |
| collection | Repositorio Digital Universitario |
| 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 |
| format | info:eu-repo/semantics/submittedVersion |
| id | rdu-unc.550693 |
| institution | Universidad Nacional de Cordoba |
| language | eng |
| publishDate | 2024 |
| record_format | dspace |
| spelling | rdu-unc.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 |
| spellingShingle | Totally geodesic submanifolds Symmetric spaces Berndt, Jürgen Olmos, Carlos Enrique Maximal totally geodesic submanifolds and index of symmetric spaces |
| title | 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_short | Maximal totally geodesic submanifolds and index of symmetric spaces |
| title_sort | maximal totally geodesic submanifolds and index of symmetric spaces |
| topic | Totally geodesic submanifolds Symmetric spaces |
| 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 |