Abstract:
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.
Keywords:
Lorentzian orbifold, Lorentzian surface, isometry group, Anosov automorphism of the torus.
Citation:
N. I. Zhukova, E. A. Rogozhkina, “Classification of compact Lorentzian 2-orbifolds with noncompact full isometry groups”, Sibirsk. Mat. Zh., 53:6 (2012), 1292–1309; Siberian Math. J., 53:6 (2012), 1037–1050
\Bibitem{ZhuRog12}
\by N.~I.~Zhukova, E.~A.~Rogozhkina
\paper Classification of compact Lorentzian $2$-orbifolds with noncompact full isometry groups
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 6
\pages 1292--1309
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\transl
\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 6
\pages 1037--1050
\crossref{https://doi.org/10.1134/S0037446612060080}
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Linking options:
https://www.mathnet.ru/eng/smj2383
https://www.mathnet.ru/eng/smj/v53/i6/p1292
This publication is cited in the following 8 articles:
N. I. Zhukova, G. S. Levin, N. S. Tonysheva, “Chaos in Topological Foliations”, J Math Sci, 282:3 (2024), 337
N. I. Zhukova, A. G. Korotkov, “Chaotic behaviour of countable products of homeomorphism groups”, Journal of Difference Equations and Applications, 29:9-12 (2023), 1287
N. I. Zhukova, G. S. Levin, N. S. Tonysheva, “Khaos v topologicheskikh sloeniyakh”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 68, no. 3, Rossiiskii universitet druzhby narodov, M., 2022, 424–450
E. V. Bogolepova, N. I. Zhukova, “Suschestvennye gruppy izometrii nekompaktnykh dvumernykh ploskikh lorentsevykh orbifoldov”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2019, no. 1, 14–28
N. I. Zhukova, “Influence of stratification on the groups of conformal transformations of pseudo-Riemannian orbifolds”, Ufa Math. J., 10:2 (2018), 44–57
Sheina K.I., Zhukova N.I., “The Groups of Basic Automorphisms of Complete Cartan Foliations”, Lobachevskii J. Math., 39:2, 3, SI (2018), 271–280
Dolgonosova A.Yu., Zhukova N.I., “Pseudo-Riemannian Foliations and Their Graphs”, Lobachevskii J. Math., 39:1, SI (2018), 54–64
A. V. Bagaev, N. I. Zhukova, “Transversalno analiticheskie lorentsevy sloeniya korazmernosti dva”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2017, no. 4, 33–45
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