On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups

This paper has manifold purposes. We first introduce a description of the Gauss map for submanifolds (both spacelike and timelike) of a Lorentzian ambient space and relate the conformality of the Gauss map of a surface to total umbilicity and minimality. We then focus on surfaces of the three-dimens...

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Detalles Bibliográficos
Autores: Calvaruso, Giovanni, Castrillón López, Marco, Pellegrino, Lorenzo
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:20.500.14352/120716
Acceso en línea:https://hdl.handle.net/20.500.14352/120716
Access Level:acceso abierto
Palabra clave:CMC surfaces
Gauss map
Heisenberg group
Minimal surfaces
Totally umbilic surfaces
Geometría diferencial
1204.04 Geometría Diferencial
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spelling On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groupsCalvaruso, GiovanniCastrillón López, MarcoPellegrino, LorenzoCMC surfacesGauss mapHeisenberg groupMinimal surfacesTotally umbilic surfacesGeometría diferencial1204.04 Geometría DiferencialThis paper has manifold purposes. We first introduce a description of the Gauss map for submanifolds (both spacelike and timelike) of a Lorentzian ambient space and relate the conformality of the Gauss map of a surface to total umbilicity and minimality. We then focus on surfaces of the three-dimensional Heisenberg group, equipped with any of its left-invariant Lorentzian metrics. We prove that with the obvious exception of the flat case, no totally umbilical surfaces occur. On the other hand, we determine and explicitly describe several examples of minimal and constant mean curvature (CMC) surfaces.WileyUniversidad Complutense de Madrid20252025-01-0120252025-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/120716reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/1207162026-06-02T12:44:21Z
dc.title.none.fl_str_mv On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups
title On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups
spellingShingle On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups
Calvaruso, Giovanni
CMC surfaces
Gauss map
Heisenberg group
Minimal surfaces
Totally umbilic surfaces
Geometría diferencial
1204.04 Geometría Diferencial
title_short On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups
title_full On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups
title_fullStr On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups
title_full_unstemmed On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups
title_sort On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups
dc.creator.none.fl_str_mv Calvaruso, Giovanni
Castrillón López, Marco
Pellegrino, Lorenzo
author Calvaruso, Giovanni
author_facet Calvaruso, Giovanni
Castrillón López, Marco
Pellegrino, Lorenzo
author_role author
author2 Castrillón López, Marco
Pellegrino, Lorenzo
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv CMC surfaces
Gauss map
Heisenberg group
Minimal surfaces
Totally umbilic surfaces
Geometría diferencial
1204.04 Geometría Diferencial
topic CMC surfaces
Gauss map
Heisenberg group
Minimal surfaces
Totally umbilic surfaces
Geometría diferencial
1204.04 Geometría Diferencial
description This paper has manifold purposes. We first introduce a description of the Gauss map for submanifolds (both spacelike and timelike) of a Lorentzian ambient space and relate the conformality of the Gauss map of a surface to total umbilicity and minimality. We then focus on surfaces of the three-dimensional Heisenberg group, equipped with any of its left-invariant Lorentzian metrics. We prove that with the obvious exception of the flat case, no totally umbilical surfaces occur. On the other hand, we determine and explicitly describe several examples of minimal and constant mean curvature (CMC) surfaces.
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/20.500.14352/120716
url https://hdl.handle.net/20.500.14352/120716
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 4.0 International
http://creativecommons.org/licenses/by/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 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Wiley
publisher.none.fl_str_mv Wiley
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
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