The Ambrose-Singer Theorem for Cohomogeneity One Riemannian Manifolds

We characterize regular isometric actions whose principal orbits are hypersurfaces through the existence of a linear connection satisfying a set of covariant equations in the same spirit as the Ambrose-Singer Theorem for homogeneous spaces. These results are then used to describe isometric cohomogen...

Descripción completa

Detalles Bibliográficos
Autores: Carmona Jiménez, José Luis, Castrillón López, Marco, Díaz Ramos, José Carlos
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/132710
Acceso en línea:https://hdl.handle.net/20.500.14352/132710
Access Level:acceso abierto
Palabra clave:Ambrose-Singer theorem
Canonical connection
Cohomogeneity one actions
Geometría diferencial
1204.04 Geometría Diferencial
id ES_02b520c0df6aa786d712d86c574f573a
oai_identifier_str oai:docta.ucm.es:20.500.14352/132710
network_acronym_str ES
network_name_str España
repository_id_str
spelling The Ambrose-Singer Theorem for Cohomogeneity One Riemannian ManifoldsCarmona Jiménez, José LuisCastrillón López, MarcoDíaz Ramos, José CarlosAmbrose-Singer theoremCanonical connectionCohomogeneity one actionsGeometría diferencial1204.04 Geometría DiferencialWe characterize regular isometric actions whose principal orbits are hypersurfaces through the existence of a linear connection satisfying a set of covariant equations in the same spirit as the Ambrose-Singer Theorem for homogeneous spaces. These results are then used to describe isometric cohomogeneity one foliations in terms of such connections. Finally, we provide explicit examples of these objects in Euclidean spaces and real hyperbolic spaces.SpringerUniversidad Complutense de Madrid20252025-01-0120252025-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/132710reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/1327102026-06-02T12:44:21Z
dc.title.none.fl_str_mv The Ambrose-Singer Theorem for Cohomogeneity One Riemannian Manifolds
title The Ambrose-Singer Theorem for Cohomogeneity One Riemannian Manifolds
spellingShingle The Ambrose-Singer Theorem for Cohomogeneity One Riemannian Manifolds
Carmona Jiménez, José Luis
Ambrose-Singer theorem
Canonical connection
Cohomogeneity one actions
Geometría diferencial
1204.04 Geometría Diferencial
title_short The Ambrose-Singer Theorem for Cohomogeneity One Riemannian Manifolds
title_full The Ambrose-Singer Theorem for Cohomogeneity One Riemannian Manifolds
title_fullStr The Ambrose-Singer Theorem for Cohomogeneity One Riemannian Manifolds
title_full_unstemmed The Ambrose-Singer Theorem for Cohomogeneity One Riemannian Manifolds
title_sort The Ambrose-Singer Theorem for Cohomogeneity One Riemannian Manifolds
dc.creator.none.fl_str_mv Carmona Jiménez, José Luis
Castrillón López, Marco
Díaz Ramos, José Carlos
author Carmona Jiménez, José Luis
author_facet Carmona Jiménez, José Luis
Castrillón López, Marco
Díaz Ramos, José Carlos
author_role author
author2 Castrillón López, Marco
Díaz Ramos, José Carlos
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv Ambrose-Singer theorem
Canonical connection
Cohomogeneity one actions
Geometría diferencial
1204.04 Geometría Diferencial
topic Ambrose-Singer theorem
Canonical connection
Cohomogeneity one actions
Geometría diferencial
1204.04 Geometría Diferencial
description We characterize regular isometric actions whose principal orbits are hypersurfaces through the existence of a linear connection satisfying a set of covariant equations in the same spirit as the Ambrose-Singer Theorem for homogeneous spaces. These results are then used to describe isometric cohomogeneity one foliations in terms of such connections. Finally, we provide explicit examples of these objects in Euclidean spaces and real hyperbolic spaces.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-01-01
2025
2025-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/132710
url https://hdl.handle.net/20.500.14352/132710
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 International
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 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869402673245061120
score 15,812429

Similares en LA Referencia