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Geometriae Dedicata

, Volume 118, Issue 1, pp 133–140 | Cite as

Lorentzian Geometry of the Heisenberg Group

Dedicated to Prof. Jacek Gancarzewicz
  • N. Rahmani
  • S. Rahmani
Article

Abstract

In this work we prove the existence of totally geodesic two-dimensional foliation on the Lorentzian Heisenberg group H 3. We determine the Killing vector fields and the Lorentzian geodesics on H 3.

Mathematics Subject Classifications (2000)

53Cxx 53C50 22E35 

Keywords

Heisenberg group totally geodesic distribution Lorentzian flow 

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References

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    Sanini, A.: Gauss map of a surface of the Heisenberg group, Boll. Un. Mat. Ital. B (7),11 (1997), suppl.fasc.2, 79–93.Google Scholar
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    Wilson, E. N.: Isometry groups on homogeneous nilmanifolds, Geom. Dedicata 12(1982), 337–346.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et InformatiqueMulhouse-CedexFrance
  2. 2.Département de Mathématiques, Faculté des SciencesUniversité des Sciences et de la TechnologieOranAlgeria

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