Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds
In this work it is shown that a necessary condition for the completeness of the geodesics of left invariant pseudo-Riemannian metrics on Lie groups is also sufficient in the case of 3-dimensional unimodular Lie groups, and not sufficient for 3-dimensional non unimodular Lie groups. As a consequence...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148001 |
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| Zitieren: | Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds / S. Bromberg, A. Medina // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862749629568778240 |
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| author | Bromberg, S. Medina, A. |
| author_facet | Bromberg, S. Medina, A. |
| citation_txt | Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds / S. Bromberg, A. Medina // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this work it is shown that a necessary condition for the completeness of the geodesics of left invariant pseudo-Riemannian metrics on Lie groups is also sufficient in the case of 3-dimensional unimodular Lie groups, and not sufficient for 3-dimensional non unimodular Lie groups. As a consequence it is possible to identify, amongst the compact locally homogeneous Lorentzian 3-manifolds with non compact (local) isotropy group, those that are geodesically complete.
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| first_indexed | 2025-12-07T21:01:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148001 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:01:47Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bromberg, S. Medina, A. 2019-02-16T16:24:54Z 2019-02-16T16:24:54Z 2008 Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds / S. Bromberg, A. Medina // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 8 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 53C22; 53C50; 57M50; 22E30 https://nasplib.isofts.kiev.ua/handle/123456789/148001 In this work it is shown that a necessary condition for the completeness of the geodesics of left invariant pseudo-Riemannian metrics on Lie groups is also sufficient in the case of 3-dimensional unimodular Lie groups, and not sufficient for 3-dimensional non unimodular Lie groups. As a consequence it is possible to identify, amongst the compact locally homogeneous Lorentzian 3-manifolds with non compact (local) isotropy group, those that are geodesically complete. The authors wish to thank the anonymous referee for the careful reading and the pertinent observations that led, in particular, to a revision of the proof of Lemma 4 and to reformulate accordingly Proposition 5. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds Article published earlier |
| spellingShingle | Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds Bromberg, S. Medina, A. |
| title | Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds |
| title_full | Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds |
| title_fullStr | Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds |
| title_full_unstemmed | Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds |
| title_short | Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds |
| title_sort | geodesically complete lorentzian metrics on some homogeneous 3 manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148001 |
| work_keys_str_mv | AT brombergs geodesicallycompletelorentzianmetricsonsomehomogeneous3manifolds AT medinaa geodesicallycompletelorentzianmetricsonsomehomogeneous3manifolds |