Geometriae Dedicata

, Volume 100, Issue 1, pp 11–51

Lorentz Geometry of 2-Step Nilpotent Lie Groups

  • Mohammed Guediri

DOI: 10.1023/A:1025832108196

Cite this article as:
Guediri, M. Geometriae Dedicata (2003) 100: 11. doi:10.1023/A:1025832108196


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.

2-step nilpotent Lie groupsleft-invariant Lorentz metricsclosed timelike geodesics

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Mohammed Guediri
    • 1
  1. 1.Department of Mathematics, College of SciencesKing Saud UniversitySaudi Arabia