Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type

Symmetry lies at the very core of science. Indeed, geometry was defined by Felix Klein as the study of those properties in a space that are invariant under a given transformation symmetry group. In this thesis, we study certain kind of geometrical objects from the viewpoint of their symmetries in th...

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Detalhes bibliográficos
Autor: Sanmartín López, Víctor
Tipo de documento: tese
Data de publicação:2019
País:España
Recursos:Universidad de Santiago de Compostela (USC)
Repositório:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglês
OAI Identifier:oai:minerva.usc.gal:10347/19772
Acesso em linha:http://hdl.handle.net/10347/19772
Access Level:Acceso aberto
Palavra-chave:Materias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencial
Materias::Investigación::12 Matemáticas::1204 Geometría::120411 Geometría de Riemann
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spelling Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact typeSanmartín López, VíctorMaterias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencialMaterias::Investigación::12 Matemáticas::1204 Geometría::120411 Geometría de RiemannSymmetry lies at the very core of science. Indeed, geometry was defined by Felix Klein as the study of those properties in a space that are invariant under a given transformation symmetry group. In this thesis, we study certain kind of geometrical objects from the viewpoint of their symmetries in the context of symmetric spaces of non-compact type. More precisely, we have classified isoparametric hypersurfaces in complex hyperbolic spaces and spacelike isoparametric hypersurfaces in anti-De Sitter spaces, produced a large family of non-totally geodesic CPC submanifolds (submanifolds whose principal curvatures do not depend on the normal directions) that are not orbits of cohomogeneity one actions and classified certain austere orbits arising from the theory of parabolic subgroups.Díaz Ramos, José CarlosDomínguez Vázquez, MiguelUniversidade de Santiago de Compostela. Centro Internacional de Estudos de Doutoramento e Avanzados (CIEDUS)Universidade de Santiago de Compostela. Escola de Doutoramento Internacional en Ciencias e Tecnoloxía20192019-01-0120192019-01-01doctoral thesishttp://purl.org/coar/resource_type/c_db06info:eu-repo/semantics/doctoralThesisapplication/pdfhttp://hdl.handle.net/10347/19772reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:minerva.usc.gal:10347/197722026-06-15T12:47:27Z
dc.title.none.fl_str_mv Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type
title Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type
spellingShingle Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type
Sanmartín López, Víctor
Materias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencial
Materias::Investigación::12 Matemáticas::1204 Geometría::120411 Geometría de Riemann
title_short Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type
title_full Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type
title_fullStr Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type
title_full_unstemmed Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type
title_sort Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type
dc.creator.none.fl_str_mv Sanmartín López, Víctor
author Sanmartín López, Víctor
author_facet Sanmartín López, Víctor
author_role author
dc.contributor.none.fl_str_mv Díaz Ramos, José Carlos
Domínguez Vázquez, Miguel
Universidade de Santiago de Compostela. Centro Internacional de Estudos de Doutoramento e Avanzados (CIEDUS)
Universidade de Santiago de Compostela. Escola de Doutoramento Internacional en Ciencias e Tecnoloxía
dc.subject.none.fl_str_mv Materias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencial
Materias::Investigación::12 Matemáticas::1204 Geometría::120411 Geometría de Riemann
topic Materias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencial
Materias::Investigación::12 Matemáticas::1204 Geometría::120411 Geometría de Riemann
description Symmetry lies at the very core of science. Indeed, geometry was defined by Felix Klein as the study of those properties in a space that are invariant under a given transformation symmetry group. In this thesis, we study certain kind of geometrical objects from the viewpoint of their symmetries in the context of symmetric spaces of non-compact type. More precisely, we have classified isoparametric hypersurfaces in complex hyperbolic spaces and spacelike isoparametric hypersurfaces in anti-De Sitter spaces, produced a large family of non-totally geodesic CPC submanifolds (submanifolds whose principal curvatures do not depend on the normal directions) that are not orbits of cohomogeneity one actions and classified certain austere orbits arising from the theory of parabolic subgroups.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01
2019
2019-01-01
dc.type.none.fl_str_mv doctoral thesis
http://purl.org/coar/resource_type/c_db06
dc.type.openaire.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
dc.identifier.none.fl_str_mv http://hdl.handle.net/10347/19772
url http://hdl.handle.net/10347/19772
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname:Universidad de Santiago de Compostela (USC)
instname_str Universidad de Santiago de Compostela (USC)
reponame_str Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
collection Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
repository.name.fl_str_mv
repository.mail.fl_str_mv
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