Global smooth geodesic foliations of the hyperbolic space

Autores
Godoy, Yamile Alejandra; Salvai, Marcos Luis
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider foliations of the whole three dimensional hyperbolic space H3 by oriented geodesics. Let L be the space of all the oriented geodesics of H3, which is a four dimensional manifold carrying two canonical pseudo-Riemannian metrics of signature (2,2). We characterize, in terms of these geometries of L, the subsets M in L that determine foliations of H3. We describe in a similar way some distinguished types of geodesic foliations of H3, regarding to which extent they are in some sense trivial in some directions: On the one hand, foliations whose leaves do not lie in a totally geodesic surface, not even at the infinitesimal level. On the other hand, those for which the forward and backward Gauss maps (Formula presented.) are local diffeomorphisms. Besides, we prove that for this kind of foliations, φ± are global diffeomorphisms onto their images. The subject of this article is within the framework of foliations by congruent submanifolds, and follows the spirit of the paper by Gluck and Warner where they understand the infinite dimensional manifold of all the great circle foliations of the three sphere.
Fil: Godoy, Yamile Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Salvai, Marcos Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
Geodesic Foliation
Hyperbolic Space
Space of Oriented Lines
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/51723
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Global smooth geodesic foliations of the hyperbolic spaceGodoy, Yamile AlejandraSalvai, Marcos LuisGeodesic FoliationHyperbolic SpaceSpace of Oriented Lineshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider foliations of the whole three dimensional hyperbolic space H3 by oriented geodesics. Let L be the space of all the oriented geodesics of H3, which is a four dimensional manifold carrying two canonical pseudo-Riemannian metrics of signature (2,2). We characterize, in terms of these geometries of L, the subsets M in L that determine foliations of H3. We describe in a similar way some distinguished types of geodesic foliations of H3, regarding to which extent they are in some sense trivial in some directions: On the one hand, foliations whose leaves do not lie in a totally geodesic surface, not even at the infinitesimal level. On the other hand, those for which the forward and backward Gauss maps (Formula presented.) are local diffeomorphisms. Besides, we prove that for this kind of foliations, φ± are global diffeomorphisms onto their images. The subject of this article is within the framework of foliations by congruent submanifolds, and follows the spirit of the paper by Gluck and Warner where they understand the infinite dimensional manifold of all the great circle foliations of the three sphere.Fil: Godoy, Yamile Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Salvai, Marcos Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaSpringer2015-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/51723Godoy, Yamile Alejandra; Salvai, Marcos Luis; Global smooth geodesic foliations of the hyperbolic space; Springer; Mathematische Zeitschrift; 281; 1-2; 10-2015; 43-540025-58741432-1823CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00209-015-1474-zinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00209-015-1474-zinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:50:11Zoai:ri.conicet.gov.ar:11336/51723instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:50:11.436CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Global smooth geodesic foliations of the hyperbolic space
title Global smooth geodesic foliations of the hyperbolic space
spellingShingle Global smooth geodesic foliations of the hyperbolic space
Godoy, Yamile Alejandra
Geodesic Foliation
Hyperbolic Space
Space of Oriented Lines
title_short Global smooth geodesic foliations of the hyperbolic space
title_full Global smooth geodesic foliations of the hyperbolic space
title_fullStr Global smooth geodesic foliations of the hyperbolic space
title_full_unstemmed Global smooth geodesic foliations of the hyperbolic space
title_sort Global smooth geodesic foliations of the hyperbolic space
dc.creator.none.fl_str_mv Godoy, Yamile Alejandra
Salvai, Marcos Luis
author Godoy, Yamile Alejandra
author_facet Godoy, Yamile Alejandra
Salvai, Marcos Luis
author_role author
author2 Salvai, Marcos Luis
author2_role author
dc.subject.none.fl_str_mv Geodesic Foliation
Hyperbolic Space
Space of Oriented Lines
topic Geodesic Foliation
Hyperbolic Space
Space of Oriented Lines
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider foliations of the whole three dimensional hyperbolic space H3 by oriented geodesics. Let L be the space of all the oriented geodesics of H3, which is a four dimensional manifold carrying two canonical pseudo-Riemannian metrics of signature (2,2). We characterize, in terms of these geometries of L, the subsets M in L that determine foliations of H3. We describe in a similar way some distinguished types of geodesic foliations of H3, regarding to which extent they are in some sense trivial in some directions: On the one hand, foliations whose leaves do not lie in a totally geodesic surface, not even at the infinitesimal level. On the other hand, those for which the forward and backward Gauss maps (Formula presented.) are local diffeomorphisms. Besides, we prove that for this kind of foliations, φ± are global diffeomorphisms onto their images. The subject of this article is within the framework of foliations by congruent submanifolds, and follows the spirit of the paper by Gluck and Warner where they understand the infinite dimensional manifold of all the great circle foliations of the three sphere.
Fil: Godoy, Yamile Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Salvai, Marcos Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description We consider foliations of the whole three dimensional hyperbolic space H3 by oriented geodesics. Let L be the space of all the oriented geodesics of H3, which is a four dimensional manifold carrying two canonical pseudo-Riemannian metrics of signature (2,2). We characterize, in terms of these geometries of L, the subsets M in L that determine foliations of H3. We describe in a similar way some distinguished types of geodesic foliations of H3, regarding to which extent they are in some sense trivial in some directions: On the one hand, foliations whose leaves do not lie in a totally geodesic surface, not even at the infinitesimal level. On the other hand, those for which the forward and backward Gauss maps (Formula presented.) are local diffeomorphisms. Besides, we prove that for this kind of foliations, φ± are global diffeomorphisms onto their images. The subject of this article is within the framework of foliations by congruent submanifolds, and follows the spirit of the paper by Gluck and Warner where they understand the infinite dimensional manifold of all the great circle foliations of the three sphere.
publishDate 2015
dc.date.none.fl_str_mv 2015-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/51723
Godoy, Yamile Alejandra; Salvai, Marcos Luis; Global smooth geodesic foliations of the hyperbolic space; Springer; Mathematische Zeitschrift; 281; 1-2; 10-2015; 43-54
0025-5874
1432-1823
CONICET Digital
CONICET
url http://hdl.handle.net/11336/51723
identifier_str_mv Godoy, Yamile Alejandra; Salvai, Marcos Luis; Global smooth geodesic foliations of the hyperbolic space; Springer; Mathematische Zeitschrift; 281; 1-2; 10-2015; 43-54
0025-5874
1432-1823
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00209-015-1474-z
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00209-015-1474-z
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/zip
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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