The canonical contact structure on the space of oriented null geodesics of pseudospheres and products

Autores
Godoy, Yamile Alejandra; Salvai, Marcos Luis
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let Sk,m be the pseudosphere of signature (k,m). We show that the space ℒ0(Sk,m) of all oriented null geodesics in Sk,m is a manifold, and we describe geometrically its canonical contact distribution in terms of the space of oriented geodesics of certain totally geodesic degenerate hypersurfaces in Sk;m. Further, we find a contactomorphism with some standard contact manifold, namely, the unit tangent bundle of some pseudo-Riemannian manifold. Also, we express the null billiard operator on ℒ0(Sk,m) associated with some simple regions in Sk;m in terms of the geodesic flows of spheres. For the pseudo-Riemannian product N of two complete Riemannian manifolds, we give geometrical conditions on the factors for ℒ0(N) to be manifolds and exhibit a contactomorphism with some standard contact manifold.
Fil: Godoy, Yamile Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentina
Fil: Salvai, Marcos Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentina
Materia
CONTACT MANIFOLD
NULL GEODESIC
SPACE OF GEODESICS
BILLIARDS
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:11336/8933
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The canonical contact structure on the space of oriented null geodesics of pseudospheres and productsGodoy, Yamile AlejandraSalvai, Marcos LuisCONTACT MANIFOLDNULL GEODESICSPACE OF GEODESICSBILLIARDShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let Sk,m be the pseudosphere of signature (k,m). We show that the space ℒ0(Sk,m) of all oriented null geodesics in Sk,m is a manifold, and we describe geometrically its canonical contact distribution in terms of the space of oriented geodesics of certain totally geodesic degenerate hypersurfaces in Sk;m. Further, we find a contactomorphism with some standard contact manifold, namely, the unit tangent bundle of some pseudo-Riemannian manifold. Also, we express the null billiard operator on ℒ0(Sk,m) associated with some simple regions in Sk;m in terms of the geodesic flows of spheres. For the pseudo-Riemannian product N of two complete Riemannian manifolds, we give geometrical conditions on the factors for ℒ0(N) to be manifolds and exhibit a contactomorphism with some standard contact manifold.Fil: Godoy, Yamile Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; ArgentinaFil: Salvai, Marcos Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentinade Gruyter2013-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/8933Godoy, Yamile Alejandra; Salvai, Marcos Luis; The canonical contact structure on the space of oriented null geodesics of pseudospheres and products; de Gruyter; Advances In Geometry; 13; 4; 10-2013; 713-7221615-715Xenginfo:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/advg.2013.13.issue-4/advgeom-2013-0019/advgeom-2013-0019.xmlinfo:eu-repo/semantics/altIdentifier/doi/10.1515/advgeom-2013-0019info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:40:55Zoai:ri.conicet.gov.ar:11336/8933instacron: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:34982025-09-29 10:40:55.967CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
title The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
spellingShingle The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
Godoy, Yamile Alejandra
CONTACT MANIFOLD
NULL GEODESIC
SPACE OF GEODESICS
BILLIARDS
title_short The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
title_full The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
title_fullStr The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
title_full_unstemmed The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
title_sort The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
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 CONTACT MANIFOLD
NULL GEODESIC
SPACE OF GEODESICS
BILLIARDS
topic CONTACT MANIFOLD
NULL GEODESIC
SPACE OF GEODESICS
BILLIARDS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let Sk,m be the pseudosphere of signature (k,m). We show that the space ℒ0(Sk,m) of all oriented null geodesics in Sk,m is a manifold, and we describe geometrically its canonical contact distribution in terms of the space of oriented geodesics of certain totally geodesic degenerate hypersurfaces in Sk;m. Further, we find a contactomorphism with some standard contact manifold, namely, the unit tangent bundle of some pseudo-Riemannian manifold. Also, we express the null billiard operator on ℒ0(Sk,m) associated with some simple regions in Sk;m in terms of the geodesic flows of spheres. For the pseudo-Riemannian product N of two complete Riemannian manifolds, we give geometrical conditions on the factors for ℒ0(N) to be manifolds and exhibit a contactomorphism with some standard contact manifold.
Fil: Godoy, Yamile Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentina
Fil: Salvai, Marcos Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentina
description Let Sk,m be the pseudosphere of signature (k,m). We show that the space ℒ0(Sk,m) of all oriented null geodesics in Sk,m is a manifold, and we describe geometrically its canonical contact distribution in terms of the space of oriented geodesics of certain totally geodesic degenerate hypersurfaces in Sk;m. Further, we find a contactomorphism with some standard contact manifold, namely, the unit tangent bundle of some pseudo-Riemannian manifold. Also, we express the null billiard operator on ℒ0(Sk,m) associated with some simple regions in Sk;m in terms of the geodesic flows of spheres. For the pseudo-Riemannian product N of two complete Riemannian manifolds, we give geometrical conditions on the factors for ℒ0(N) to be manifolds and exhibit a contactomorphism with some standard contact manifold.
publishDate 2013
dc.date.none.fl_str_mv 2013-10
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/11336/8933
Godoy, Yamile Alejandra; Salvai, Marcos Luis; The canonical contact structure on the space of oriented null geodesics of pseudospheres and products; de Gruyter; Advances In Geometry; 13; 4; 10-2013; 713-722
1615-715X
url http://hdl.handle.net/11336/8933
identifier_str_mv Godoy, Yamile Alejandra; Salvai, Marcos Luis; The canonical contact structure on the space of oriented null geodesics of pseudospheres and products; de Gruyter; Advances In Geometry; 13; 4; 10-2013; 713-722
1615-715X
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/advg.2013.13.issue-4/advgeom-2013-0019/advgeom-2013-0019.xml
info:eu-repo/semantics/altIdentifier/doi/10.1515/advgeom-2013-0019
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/pdf
dc.publisher.none.fl_str_mv de Gruyter
publisher.none.fl_str_mv de Gruyter
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 13.070432

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