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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Structure of Lorentzian tori with
a killing vector field


Author: Miguel Sánchez
Journal: Trans. Amer. Math. Soc. 349 (1997), 1063-1080
MSC (1991): Primary 53C50, 53C22
MathSciNet review: 1376554
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Abstract: All Lorentzian tori with a non-discrete group of isometries are characterized and explicitly obtained. They can lie into three cases: (a) flat, (b) conformally flat but non-flat, and (c) geodesically incomplete. A detailed study of many of their properties (including results on the logical dependence of the three kinds of causal completeness, on geodesic connectedness and on prescribed curvature) is carried out. The incomplete case is specially analyzed, and several known examples and results in the literature are generalized from a unified point of view.


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Additional Information

Miguel Sánchez
Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
Email: sanchezm@goliat.ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01745-5
PII: S 0002-9947(97)01745-5
Keywords: Killing vector field, conformally flat torus, isometry group, incomplete geodesic, geodesic connectedness, prescribed curvature Lorentzian torus
Received by editor(s): July 6, 1995
Additional Notes: This research has been partially supported by a DGICYT Grant No. PB94-0796
Article copyright: © Copyright 1997 American Mathematical Society