The magnetic flow on the manifold of oriented geodesics of a three dimensional space form

Autores
Godoy, Yamile Alejandra; Salvai, Marcos Luis
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let M be the three dimensional complete simply connected manifold of constant sectional curvature 0,10,1 or −1−1. Let L be the manifold of all (unparametrized) complete oriented geodesics of M, endowed with its canonical pseudo-Riemannian metric of signature (2,2)(2,2) and Kähler structure J. A smooth curve in L determines a ruled surface in M. We characterize the ruled surfaces of MM associated with the magnetic geodesics of LL, that is, those curves σσ in LL satisfying ∇σ˙σ˙=Jσ˙∇σ˙σ˙=Jσ˙. More precisely: a time-like (space-like) magnetic geodesic determines the ruled surface in M given by the binormal vector field along a helix with positive (negative) torsion. Null magnetic geodesics describe cones, cylinders or, in the hyperbolic case, also cones with vertices at infinity. This provides a relationship between the geometries of L and M.
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
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
Materia
MANIFOLD OF ORIENTED GEODESICS
HERMITIAN SYMMETRIC SPACE
MAGNETIC FLOW
RULED SURFACE
HOROSPHERICAL DISTRIBUTION
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:11336/8984
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/8984
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The magnetic flow on the manifold of oriented geodesics of a three dimensional space formGodoy, Yamile AlejandraSalvai, Marcos LuisMANIFOLD OF ORIENTED GEODESICSHERMITIAN SYMMETRIC SPACEMAGNETIC FLOWRULED SURFACEHOROSPHERICAL DISTRIBUTIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let M be the three dimensional complete simply connected manifold of constant sectional curvature 0,10,1 or −1−1. Let L be the manifold of all (unparametrized) complete oriented geodesics of M, endowed with its canonical pseudo-Riemannian metric of signature (2,2)(2,2) and Kähler structure J. A smooth curve in L determines a ruled surface in M. We characterize the ruled surfaces of MM associated with the magnetic geodesics of LL, that is, those curves σσ in LL satisfying ∇σ˙σ˙=Jσ˙∇σ˙σ˙=Jσ˙. More precisely: a time-like (space-like) magnetic geodesic determines the ruled surface in M given by the binormal vector field along a helix with positive (negative) torsion. Null magnetic geodesics describe cones, cylinders or, in the hyperbolic case, also cones with vertices at infinity. This provides a relationship between the geometries of L and M.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); 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); ArgentinaOsaka University. Departments of Mathematics2013-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/8984Godoy, Yamile Alejandra; Salvai, Marcos Luis; The magnetic flow on the manifold of oriented geodesics of a three dimensional space form; Osaka University. Departments of Mathematics; Osaka Journal of Mathematics; 50; 3; 9-2013; 749-7630030-6126enginfo:eu-repo/semantics/altIdentifier/url/http://projecteuclid.org/euclid.ojm/1380287431info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:47:01Zoai:ri.conicet.gov.ar:11336/8984instacron: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 10:47:02.173CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The magnetic flow on the manifold of oriented geodesics of a three dimensional space form
title The magnetic flow on the manifold of oriented geodesics of a three dimensional space form
spellingShingle The magnetic flow on the manifold of oriented geodesics of a three dimensional space form
Godoy, Yamile Alejandra
MANIFOLD OF ORIENTED GEODESICS
HERMITIAN SYMMETRIC SPACE
MAGNETIC FLOW
RULED SURFACE
HOROSPHERICAL DISTRIBUTION
title_short The magnetic flow on the manifold of oriented geodesics of a three dimensional space form
title_full The magnetic flow on the manifold of oriented geodesics of a three dimensional space form
title_fullStr The magnetic flow on the manifold of oriented geodesics of a three dimensional space form
title_full_unstemmed The magnetic flow on the manifold of oriented geodesics of a three dimensional space form
title_sort The magnetic flow on the manifold of oriented geodesics of a three dimensional space form
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 MANIFOLD OF ORIENTED GEODESICS
HERMITIAN SYMMETRIC SPACE
MAGNETIC FLOW
RULED SURFACE
HOROSPHERICAL DISTRIBUTION
topic MANIFOLD OF ORIENTED GEODESICS
HERMITIAN SYMMETRIC SPACE
MAGNETIC FLOW
RULED SURFACE
HOROSPHERICAL DISTRIBUTION
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 M be the three dimensional complete simply connected manifold of constant sectional curvature 0,10,1 or −1−1. Let L be the manifold of all (unparametrized) complete oriented geodesics of M, endowed with its canonical pseudo-Riemannian metric of signature (2,2)(2,2) and Kähler structure J. A smooth curve in L determines a ruled surface in M. We characterize the ruled surfaces of MM associated with the magnetic geodesics of LL, that is, those curves σσ in LL satisfying ∇σ˙σ˙=Jσ˙∇σ˙σ˙=Jσ˙. More precisely: a time-like (space-like) magnetic geodesic determines the ruled surface in M given by the binormal vector field along a helix with positive (negative) torsion. Null magnetic geodesics describe cones, cylinders or, in the hyperbolic case, also cones with vertices at infinity. This provides a relationship between the geometries of L and M.
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
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
description Let M be the three dimensional complete simply connected manifold of constant sectional curvature 0,10,1 or −1−1. Let L be the manifold of all (unparametrized) complete oriented geodesics of M, endowed with its canonical pseudo-Riemannian metric of signature (2,2)(2,2) and Kähler structure J. A smooth curve in L determines a ruled surface in M. We characterize the ruled surfaces of MM associated with the magnetic geodesics of LL, that is, those curves σσ in LL satisfying ∇σ˙σ˙=Jσ˙∇σ˙σ˙=Jσ˙. More precisely: a time-like (space-like) magnetic geodesic determines the ruled surface in M given by the binormal vector field along a helix with positive (negative) torsion. Null magnetic geodesics describe cones, cylinders or, in the hyperbolic case, also cones with vertices at infinity. This provides a relationship between the geometries of L and M.
publishDate 2013
dc.date.none.fl_str_mv 2013-09
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/11336/8984
Godoy, Yamile Alejandra; Salvai, Marcos Luis; The magnetic flow on the manifold of oriented geodesics of a three dimensional space form; Osaka University. Departments of Mathematics; Osaka Journal of Mathematics; 50; 3; 9-2013; 749-763
0030-6126
url http://hdl.handle.net/11336/8984
identifier_str_mv Godoy, Yamile Alejandra; Salvai, Marcos Luis; The magnetic flow on the manifold of oriented geodesics of a three dimensional space form; Osaka University. Departments of Mathematics; Osaka Journal of Mathematics; 50; 3; 9-2013; 749-763
0030-6126
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://projecteuclid.org/euclid.ojm/1380287431
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 Osaka University. Departments of Mathematics
publisher.none.fl_str_mv Osaka University. Departments of Mathematics
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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