Submanifolds in complex projective and hyperbolic planes

In this PhD thesis we study submanifolds in complex projective and hyperbolic spaces. More specifically, we classify isoparametric and Terng-isoparametric submanifolds. The former correspond to principal orbits of polar actions, whereas the latter are homogeneous but not necessarily arising from pol...

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Detalles Bibliográficos
Autor: Vidal Castiñeira, Cristina
Tipo de recurso: tesis doctoral
Fecha de publicación:2016
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/14866
Acceso en línea:http://hdl.handle.net/10347/14866
Access Level:acceso abierto
Palabra clave:Materias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencial
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spelling Submanifolds in complex projective and hyperbolic planesVidal Castiñeira, CristinaMaterias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencialIn this PhD thesis we study submanifolds in complex projective and hyperbolic spaces. More specifically, we classify isoparametric and Terng-isoparametric submanifolds. The former correspond to principal orbits of polar actions, whereas the latter are homogeneous but not necessarily arising from polar actions. We also study real hypersurfaces with two distinct principal curvatures, show that there are non-Hopf inhomogeneous examples, and characterize them. Using the method of equivariant geometry, we investigate strongly 2-Hopf hypersurfaces and give some applications for Levi-flat and constant mean curvature hypersurfaces. Finally, we classify austere hypersurfaces such that the number of nontrivial projections of the Hopf vector field onto the principal curvature spaces is less or equal than two; all the examples are ruled in this case.Díez Ramos, José CarlosDomínguez Vázquez, MiguelUniversidade de Santiago de Compostela. Facultade de Matemáticas. Departamento de Matemáticas20162016-08-2520162016-08-25doctoral thesishttp://purl.org/coar/resource_type/c_db06info:eu-repo/semantics/doctoralThesisapplication/pdfhttp://hdl.handle.net/10347/14866reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Esta obra atópase baixo unha licenza internacional Creative Commons BY-NC-ND 4.0. Calquera forma de reprodución, distribución, comunicación pública ou transformación desta obra non incluída na licenza Creative Commons BY-NC-ND 4.0 só pode ser realizada coa autorización expresa dos titulares, salvo excepción prevista pola lei. Pode acceder Vde. ao texto completo da licenza nesta ligazón: https://creativecommons.org/licenses/by-nc-nd/4.0/deed.glhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.glinfo:eu-repo/semantics/openAccessoai:minerva.usc.gal:10347/148662026-06-15T12:47:27Z
dc.title.none.fl_str_mv Submanifolds in complex projective and hyperbolic planes
title Submanifolds in complex projective and hyperbolic planes
spellingShingle Submanifolds in complex projective and hyperbolic planes
Vidal Castiñeira, Cristina
Materias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencial
title_short Submanifolds in complex projective and hyperbolic planes
title_full Submanifolds in complex projective and hyperbolic planes
title_fullStr Submanifolds in complex projective and hyperbolic planes
title_full_unstemmed Submanifolds in complex projective and hyperbolic planes
title_sort Submanifolds in complex projective and hyperbolic planes
dc.creator.none.fl_str_mv Vidal Castiñeira, Cristina
author Vidal Castiñeira, Cristina
author_facet Vidal Castiñeira, Cristina
author_role author
dc.contributor.none.fl_str_mv Díez Ramos, José Carlos
Domínguez Vázquez, Miguel
Universidade de Santiago de Compostela. Facultade de Matemáticas. Departamento de Matemáticas
dc.subject.none.fl_str_mv Materias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencial
topic Materias::Investigación::12 Matemáticas::1204 Geometría::120404 Geometría diferencial
description In this PhD thesis we study submanifolds in complex projective and hyperbolic spaces. More specifically, we classify isoparametric and Terng-isoparametric submanifolds. The former correspond to principal orbits of polar actions, whereas the latter are homogeneous but not necessarily arising from polar actions. We also study real hypersurfaces with two distinct principal curvatures, show that there are non-Hopf inhomogeneous examples, and characterize them. Using the method of equivariant geometry, we investigate strongly 2-Hopf hypersurfaces and give some applications for Levi-flat and constant mean curvature hypersurfaces. Finally, we classify austere hypersurfaces such that the number of nontrivial projections of the Hopf vector field onto the principal curvature spaces is less or equal than two; all the examples are ruled in this case.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-08-25
2016
2016-08-25
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/10347/14866
url http://hdl.handle.net/10347/14866
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
https://creativecommons.org/licenses/by-nc-nd/4.0/deed.gl
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
https://creativecommons.org/licenses/by-nc-nd/4.0/deed.gl
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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