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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Structure of Lorentzian tori with a killing vector field
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by Miguel Sánchez PDF
Trans. Amer. Math. Soc. 349 (1997), 1063-1080 Request permission

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
  • Received by editor(s): July 6, 1995
  • Additional Notes: This research has been partially supported by a DGICYT Grant No. PB94-0796
  • © Copyright 1997 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 349 (1997), 1063-1080
  • MSC (1991): Primary 53C50, 53C22
  • DOI: https://doi.org/10.1090/S0002-9947-97-01745-5
  • MathSciNet review: 1376554