The index of symmetry of compact naturally reductive spaces
Fil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.
| Main Authors: | , , |
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| Format: | submittedVersion |
| Language: | eng |
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2021
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| Subjects: | |
| Online Access: | http://hdl.handle.net/11086/19594 https://doi.org/10.1007/s00209-013-1268-0 |
| _version_ | 1801211389271867392 |
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| author | Olmos, Carlos Enrique Reggiani, Silvio Nicolás Tamaru, Hiroshi |
| author_facet | Olmos, Carlos Enrique Reggiani, Silvio Nicolás Tamaru, Hiroshi |
| author_sort | Olmos, Carlos Enrique |
| collection | Repositorio Digital Universitario |
| description | Fil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. |
| format | submittedVersion |
| id | rdu-unc.19594 |
| institution | Universidad Nacional de Cordoba |
| language | eng |
| publishDate | 2021 |
| record_format | dspace |
| spelling | rdu-unc.195942022-10-13T11:07:17Z The index of symmetry of compact naturally reductive spaces Olmos, Carlos Enrique Reggiani, Silvio Nicolás Tamaru, Hiroshi Index of symmetry Distribution of symmetry Naturally reductive space Symmetric space submittedVersion Fil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Tamuru, Hiroshi. Universidad de Hiroshima. Escuela de Ciencias. Departamento de Matemática; Japón. 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. submittedVersion Fil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Tamuru, Hiroshi. Universidad de Hiroshima. Escuela de Ciencias. Departamento de Matemática; Japón. Matemática Pura 2021-08-17T17:09:28Z 2021-08-17T17:09:28Z 2014 article Olmos, C. E., Reggiani, S. N. y Tamaru, H. (2014). The index of symmetry of compact naturally reductive spaces. Mathematische Zeitschrift, 277 (3-4), 611-628. https://doi.org/10.1007/s00209-013-1268-0 http://hdl.handle.net/11086/19594 https://doi.org/10.1007/s00209-013-1268-0 eng Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ Impreso; Electrónico y/o Digital ISSN 1432-1823 |
| spellingShingle | Index of symmetry Distribution of symmetry Naturally reductive space Symmetric space Olmos, Carlos Enrique Reggiani, Silvio Nicolás Tamaru, Hiroshi The index of symmetry of compact naturally reductive spaces |
| title | 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_short | The index of symmetry of compact naturally reductive spaces |
| title_sort | index of symmetry of compact naturally reductive spaces |
| topic | Index of symmetry Distribution of symmetry Naturally reductive space Symmetric space |
| url | http://hdl.handle.net/11086/19594 https://doi.org/10.1007/s00209-013-1268-0 |
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