Abstract
We consider Lie groups equipped with a left-invariant cyclic Lorentzian metric. As in the Riemannian case, in terms of homogeneous structures, such metrics can be considered as different as possible from bi-invariant metrics. We show that several results concerning cyclic Riemannian metrics do not extend to their Lorentzian analogues, and obtain a full classification of three- and four-dimensional cyclic Lorentzian metrics.
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Giovanni Calvaruso has been partially supported by funds of the University of Salento and MURST (PRIN). Both authors have been partially supported by MINECO (Spain) under grant MTM2014-53201-P.
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Calvaruso, G., López, M.C. Cyclic Lorentzian Lie groups. Geom Dedicata 181, 119–136 (2016). https://doi.org/10.1007/s10711-015-0116-2
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DOI: https://doi.org/10.1007/s10711-015-0116-2