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Article

Classification of compact Lorentzian 2-orbifolds with noncompact full isometry groups

Siberian Mathematical Journal. 2012. Vol. 53. No. 6. P. 1037-1050.
N. I. Zhukova, E. A. Rogozhina ..

Among closed Lorentzian surfaces, only flat tori admit non-compact full isometry groups. Moreover, for every n > 2 the standard n-dimensional flat torus equipped with canonical metric has a non-compact full isometry Lie group. We show that this fails for n= 2 and classify the flat Lorentzian metrics on the torus with a non-compact 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 non-compact full isometry Lie group. We classify the metrics of this type and construct some examples.