Abstract
We study the geometry of 2-step nilpotent Lie groups endowed with left-invariant Lorentz metrics. After integrating explicitly the geodesic equations, we discuss the problem of the existence of translated geodesics in those groups. A good part of the paper focuses on the existence of closed timelike geodesics in compact Lorentz 2-step nilmanifolds. Other related results, corollaries, and examples are also presented.
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Guediri, M. Lorentz Geometry of 2-Step Nilpotent Lie Groups. Geometriae Dedicata 100, 11–51 (2003). https://doi.org/10.1023/A:1025832108196
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DOI: https://doi.org/10.1023/A:1025832108196