We give the full classification of left-invariant metrics of an arbitrary signature on the Lie group corresponding to the real hyperbolic space. It is shown that all metrics have constant sectional curvature and that they are geodesically complete only in the Riemannian case.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 5, pp. 611–619, May, 2020.
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Vukmirović, S., Šukilović, T. Geodesic Completeness of the Left-Invariant Metrics on ℝHn. Ukr Math J 72, 702–711 (2020). https://doi.org/10.1007/s11253-020-01810-0
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DOI: https://doi.org/10.1007/s11253-020-01810-0