Abstract
The Lorentzian oscillator group \((G_{\mu },g_a)\), that is, the four-dimensional oscillator group \(G_\mu \), together with the family \(g_a\) of left-invariant metrics obtained generalizing its bi-invariant metric, ‘is probably the most relevant naturally reductive Lorentzian example in the literature’ Batat et al. (Differ Geometry Appl 41: 48–64, [1]) . We describe an explicit system of global coordinates for the Lorentzian oscillator group, and use it to compute its symmetries and solutions to the Ricci soliton equation.
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Author partially supported by funds of the University of Salento and MIUR (PRIN).
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Calvaruso, G. (2017). Recent Results on Oscillator Spacetimes. In: Cañadas-Pinedo, M., Flores, J., Palomo, F. (eds) Lorentzian Geometry and Related Topics. GELOMA 2016. Springer Proceedings in Mathematics & Statistics, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-319-66290-9_3
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DOI: https://doi.org/10.1007/978-3-319-66290-9_3
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