THE MAGNETIC FLOW ON THE MANIFOLD OF ORIENTED GEODESICS OF A THREE DIMENSIONAL SPACE FORM

Godoy, Yamile; Salvai, Marcos

doi:info:doi/10.18910/26012

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タイトル	THE MAGNETIC FLOW ON THE MANIFOLD OF ORIENTED GEODESICS OF A THREE DIMENSIONAL SPACE FORM
著者	Godoy, Yamile Godoy, Yamile
著者	Salvai, Marcos Salvai, Marcos
抄録	Let M be the three dimensional complete simply connected manifold of constant sectional curvature 0, 1 or -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) and Kähler structure J. A smooth curve in L determines a ruled surface in M. We characterize the ruled surfaces of M associated with the magnetic geodesics of L, that is, those curves σ in L satisfying ∇_σ σ = Jσ. More precisely: a timelike (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.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	50
号	3
開始ページ	749
終了ページ	763
刊行年月	2013-09
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/26012
言語	英語
DOI	info:doi/10.18910/26012
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 50, Number 3　(2013-9）

著者版フラグ	publisher
NII資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
dcmi資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics.50(3) P.749-P.763
DC.title	THE MAGNETIC FLOW ON THE MANIFOLD OF ORIENTED GEODESICS OF A THREE DIMENSIONAL SPACE FORM
DC.creator	Godoy, Yamile
DC.creator	Salvai, Marcos
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2013-09
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/26012
DCTERMS.abstract	Let M be the three dimensional complete simply connected manifold of constant sectional curvature 0, 1 or -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) and Kähler structure J. A smooth curve in L determines a ruled surface in M. We characterize the ruled surfaces of M associated with the magnetic geodesics of L, that is, those curves σ in L satisfying ∇_σ σ = Jσ. More precisely: a timelike (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.
DC.identifier	info:doi/10.18910/26012
citation_title	THE MAGNETIC FLOW ON THE MANIFOLD OF ORIENTED GEODESICS OF A THREE DIMENSIONAL SPACE FORM
citation_author	Godoy, Yamile
citation_author	Salvai, Marcos
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2013-09
citation_journal_title	Osaka Journal of Mathematics
citation_volume	50
citation_issue	3
citation_firstpage	749
citation_lastpage	763
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/26012
citation_doi	info:doi/10.18910/26012

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