Geodesic completeness of the left-invariant metrics on ${{\mathbb{R}} H^n} $

Srdjan Vukmirović; Tijana Šukilović

doi:10.37863/umzh.v72i5.645

Srdjan Vukmirović University of Belgrade, Faculty of Mathematics, Serbia
Tijana Šukilović University of Belgrade, Faculty of Mathematics, Serbia

DOI: https://doi.org/10.37863/umzh.v72i5.645

Abstract

UDC 514

We give the full classification of left-invariant metrics of an arbitrary signature on the Lie group corresponding to the real hyperbolic space. We show that all metrics have constant sectional curvature and that they are geodesically complete only in the Riemannian case.

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