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On class A Lorentzian 2-tori with poles I: closed geodesics pass through poles

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Abstract

In this paper, by studying certain isometries on globally hyperbolic planes, we prove that if p is a timelike pole on a class A Lorentzian 2-torus, then there exists a closed timelike geodesic passing through p with any pre-assigned free homotopy class in the interior of the stable time cone.

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Acknowledgements

The authors wish to thank the anonymous referee for very careful reading of the preliminary version of this paper and many useful suggestions, which led to significant improvements of the exposition and clarity of the proof.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Lu Peng & Xiaojun Cui

  2. Department of Mathematics, Nanjing University of Science and Technology, Nanjing, 210094, China

    Liang Jin

Authors
  1. Lu Peng
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  2. Liang Jin
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  3. Xiaojun Cui
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Corresponding author

Correspondence to Xiaojun Cui.

Additional information

X. Cui is supported by the National Natural Science Foundation of China (Grants 11571166, 11631006, 11790272), the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and the Fundamental Research Funds for the Central Universities.

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Peng, L., Jin, L. & Cui, X. On class A Lorentzian 2-tori with poles I: closed geodesics pass through poles. manuscripta math. 160, 543–559 (2019). https://doi.org/10.1007/s00229-018-1067-3

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  • DOI: https://doi.org/10.1007/s00229-018-1067-3

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