Skip to main content
SpringerLink
Log in

Lorentzian Geometry of the Heisenberg Group

Dedicated to Prof. Jacek Gancarzewicz

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hangan, Th.: Au sujet des flots riemanniens sur le groupe nilpotent de Heisenberg, Rend. Circ. Mat. Palermo. (3) 35 (1986), 291–305.

    Article  MATH  MathSciNet  Google Scholar 

  2. Rahmani, S.: Métriques de Lorentz sur les groupes de Lie unimodulaires de dimension 3, J. Geom. Phys. 9 (1992), 295–302.

    Article  MATH  MathSciNet  Google Scholar 

  3. Sanini, A.: Gauss map of a surface of the Heisenberg group, Boll. Un. Mat. Ital. B (7),11 (1997), suppl.fasc.2, 79–93.

  4. Wilson, E. N.: Isometry groups on homogeneous nilmanifolds, Geom. Dedicata 12(1982), 337–346.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Author notes

  1. S. Rahmani

    Present address: Laboratoire de Mathématiques et Informatique, 4 Rue des Frères Lumière, 68093, Mulhouse-Cedex, France

  2. N. Rahmani

    Present address: Département de Mathématiques, Faculté des Sciences, Université des Sciences et de la Technologie, 16 rue Alexandre Nobel, 31025, Oran, Algeria

Authors and Affiliations

  1. Laboratoire de Mathématiques et Informatique, 4 Rue des Frères Lumière, 68093, Mulhouse-Cedex, France

    N. Rahmani

Authors
  1. N. Rahmani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Rahmani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Rahmani.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rahmani, N., Rahmani, S. Lorentzian Geometry of the Heisenberg Group. Geom Dedicata 118, 133–140 (2006). https://doi.org/10.1007/s10711-005-9030-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10711-005-9030-3

Mathematics Subject Classifications (2000)

Keywords

Search

Navigation