Extensions maximales et classification des tores lorentziens munis d'un champ de Killing

BAVARD, Christophe; MOUNOUD, Pierre

doi:10.5802/aif.3309

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BAVARD, Christophe
Institut de Mathématiques de Bordeaux [IMB]

MOUNOUD, Pierre
Institut de Mathématiques de Bordeaux [IMB]

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Annales de l'Institut Fourier. 2020, vol. 70, n° 1, p. 67-168

Association des Annales de l'Institut Fourier

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We define a family of model spaces for 2-dimensional Lorentzian geometry, consisting of simply connected inextendable Lorentzian surfaces admitting a Killing field. These spaces, called " universal extensions " , are constructed by an extension process and characterized by symmetry and completeness conditions. In general, these surfaces have a rich combinatorics and admit many quotient spaces and many divisible open sets. As applications, we show the existence of plenty (both topologically and geometrically) of Lorentzian surfaces with a Killing field. We also prove uniformisation results for the compact case and for the analytic case, which in particular allows us to give a classification of Lorentzian tori and Klein bottles with a Killing field.< Leer menos

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