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 suf ficient for 3-dimensional non unimodular Lie groups. As a consequence...
- Autores:
-
Medina Perea, Alirio Alberto
Bromberg, Shirley
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2008
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/45969
- Acceso en línea:
- https://hdl.handle.net/10495/45969
- Palabra clave:
- Lagrange equations
Lorentzian metrics
Complete geodesics
3-dimensional Lie groups
http://id.loc.gov/authorities/subjects/sh85073964
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-sa/4.0/
| Summary: | 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 suf ficient 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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