, Volume 100, Issue 1, pp 11-51

Lorentz Geometry of 2-Step Nilpotent Lie Groups

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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.