Abstract
Infinitely many new examples of compact Lorentzian surfaces without conjugate points are given. Further, we study the existence and the stability of this property among Lorentzian metrics with a Killing field. We obtain a new obstruction and prove that the Clifton–Pohl torus and some of our examples are as stable as possible. This shows that in constrast with the Riemannian Hopf theorem, the absence of conjugate points in the Lorentzian setting is neither "special" nor rigid.
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Acknowledgements
The author would like to warmly thank her thesis advisor Christophe Bavard for his support and encouragements, and the long hours of discussion he devoted to her, without which this article would not have been completed. She would also like to warmly thank the referee for their careful reading of the paper, and their comments and suggestions which helped to improve the writing and make it clearer.
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Mehidi, L. On the existence and stability of two-dimensional Lorentzian tori without conjugate points. Geom Dedicata 217, 90 (2023). https://doi.org/10.1007/s10711-023-00824-9
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DOI: https://doi.org/10.1007/s10711-023-00824-9