Classification of compact lorentzian 2-orbifolds with noncompact full isometry groups
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Among closed Lorentzian surfaces, only flat tori can admit noncompact full isometry groups. Moreover, for every n ≥ 3 the standard n-dimensional flat torus equipped with canonical metric has a noncompact full isometry Lie group. We show that this fails for n = 2 and classify the flat Lorentzian metrics on the torus with a noncompact full isometry Lie group. We also prove that every two-dimensional Lorentzian orbifold is very good. This implies the existence of a unique smooth compact 2-orbifold, called the pillow, admitting Lorentzian metrics with a noncompact full isometry group. We classify the metrics of this type and make some examples.
KeywordsLorentzian orbifold Lorentzian surface isometry group Anosov automorphism of the torus
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