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Structure of Lorentzian tori with a killing vector field

Author(s): Miguel Sánchez
Journal: Trans. Amer. Math. Soc. 349 (1997), 1063-1080.
MSC (1991): Primary 53C50, 53C22
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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: 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
Copyright of article: Copyright 1997, American Mathematical Society

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M. Sánchez, Geodesic connectedness in generalized Reissner-Norsdström type Lorentzian manifolds, Gen. Relativity Gravitation 29 (1997), 1023-1037. MR 98h:53106

M. Sánchez, Lorentzian manifolds admitting a Killing vector field, Nonlinear Anal. 30 (1997), 643-654. MR 99h:53092

A. Romero and M. Sánchez, Bochner's technique on Lorentzian manifolds and infintesimal conformal symmetries, Pac. J. Math. 186 (1998), 141-148.

M. Sánchez, On the geometry of Generalized Robertson Walker spacetimes: geodesics, Gen. Relativity Gravitation 30 (1998), 915-932. MR 98h:53106

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M. Sánchez, Timelike periodic trajectories in spatially compact Lorentz manifolds, Proc. Amer. Math. Soc. 127 (1999), 3057-3066.

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