Some totally geodesic submanifolds of the nonlinear Grassmannian of a compact symmetric space
Fil: Salvai, Marcos Luis. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.
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| Format: | submittedVersion |
| Language: | eng |
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2021
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| Online Access: | http://hdl.handle.net/11086/20321 http://dx.doi.org/10.1007/s00605-014-0642-2 |
| _version_ | 1801213460319567872 |
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| author | Salvai, Marcos Luis |
| author_facet | Salvai, Marcos Luis |
| author_sort | Salvai, Marcos Luis |
| collection | Repositorio Digital Universitario |
| description | Fil: Salvai, Marcos Luis. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. |
| format | submittedVersion |
| id | rdu-unc.20321 |
| institution | Universidad Nacional de Cordoba |
| language | eng |
| publishDate | 2021 |
| record_format | dspace |
| spelling | rdu-unc.203212022-10-13T11:06:59Z Some totally geodesic submanifolds of the nonlinear Grassmannian of a compact symmetric space Salvai, Marcos Luis Manifold of embeddings Geodesic Symmetric space Reflective submanifold submittedVersion Fil: Salvai, Marcos Luis. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Let M and N be two connected smooth manifolds, where M is compact and oriented and N is Riemannian. Let E be the Fréchet manifold of all embeddings of M in N, endowed with the canonical weak Riemannian metric. Let ∼ be the equivalence relation on E defined by f ∼ g if and only if f = g ◦ φ for some orientation preserving diffeomorphism φ of M. The Fréchet manifold S = E/∼ of equivalence classes, which may be thought of as the set of submanifolds of N diffeomorphic to M and is called the nonlinear Grassmannian (or Chow manifold) of N of type M, inherits from E a weak Riemannian structure. Its geodesics, although they are not good from the metric point of view, are distinguished curves and have proved to be useful in various situations. We consider the following particular case: N is a compact irreducible symmetric space and M is a reflective submanifold of N (that is, a connected component of the set of fixed points of an involutive isometry of N). Let C be the set of submanifolds of N which are congruent to M. We prove that the natural inclusion of C in S is totally geodesic. submittedVersion Fil: Salvai, Marcos Luis. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Matemática Pura 2021-09-15T15:48:17Z 2021-09-15T15:48:17Z 2014 article Salvai, M. L. (2014). Some totally geodesic submanifolds of the nonlinear Grassmannian of a compact symmetric space. Monatshefte für Mathematik, 175 (4), 613-619. http://dx.doi.org/10.1007/s00605-014-0642-2 http://hdl.handle.net/11086/20321 http://dx.doi.org/10.1007/s00605-014-0642-2 eng Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ ISSN 0026-9255 |
| spellingShingle | Manifold of embeddings Geodesic Symmetric space Reflective submanifold Salvai, Marcos Luis Some totally geodesic submanifolds of the nonlinear Grassmannian of a compact symmetric space |
| title | Some totally geodesic submanifolds of the nonlinear Grassmannian of a compact symmetric space |
| title_full | Some totally geodesic submanifolds of the nonlinear Grassmannian of a compact symmetric space |
| title_fullStr | Some totally geodesic submanifolds of the nonlinear Grassmannian of a compact symmetric space |
| title_full_unstemmed | Some totally geodesic submanifolds of the nonlinear Grassmannian of a compact symmetric space |
| title_short | Some totally geodesic submanifolds of the nonlinear Grassmannian of a compact symmetric space |
| title_sort | some totally geodesic submanifolds of the nonlinear grassmannian of a compact symmetric space |
| topic | Manifold of embeddings Geodesic Symmetric space Reflective submanifold |
| url | http://hdl.handle.net/11086/20321 http://dx.doi.org/10.1007/s00605-014-0642-2 |
| work_keys_str_mv | AT salvaimarcosluis sometotallygeodesicsubmanifoldsofthenonlineargrassmannianofacompactsymmetricspace |