On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group

@article{Batat2010OnTE,
  title={On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group},
  author={Wafaa Batat and Salima Rahmani},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2010},
  volume={6},
  pages={021}
}
  • W. Batat, S. Rahmani
  • Published 28 February 2010
  • Mathematics
  • Symmetry Integrability and Geometry-methods and Applications
In this note we prove that the Heisenberg group with a left-invariant pseudo- Riemannian metric admits a completely integrable totally geodesic distribution of codimen- sion 1. This is on the contrary to the Riemannian case, as it was proved by T. Hangan. 

References

SHOWING 1-10 OF 12 REFERENCES
Lorentzian Geometry of the Heisenberg Group
In this work we prove the existence of totally geodesic two-dimensional foliation on the Lorentzian Heisenberg group H3. We determine the Killing vector fields and the Lorentzian geodesics on H3.
Lorentz Geometry of 2-Step Nilpotent Lie Groups
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
PSEUDORIEMANNIAN 2-STEP NILPOTENT LIE GROUPS
We begin a systematic study of these spaces, initially following along the lines of Eberlein's comprehensive study of the Riemannian case. In particular, we integrate the geodesic equation, discuss
Au sujet des flots riemanniens sur le groupe nilpotent de Heisenberg
One proves that on the three dimensional nilpotent Lie group endowed with a left invariant riemannian metric, the only riemannian flows are the isometric ones.
Sur les groupes de Lie nilpotents
SummaryDémonstration élémentaire du résultat suivant: si le groupe de Lie N est nilpotent et simplement connexe, et si σ est un automorphisme de N tel que σ* n'ait pas de valeur propre égale à1,
Recent Advances in Riemannian and Lorentzian Geometries
Examples of conjugate loci of pseudoRiemannian 2-step nilpotent Lie groups with nondegenerate center
  • Recent Advances in Riemannian and Lorentzian Geometries
  • 2003
Sur les distributions totalement géodésiques du groupe nilpotent riemannien H 2 p + 1
  • Rend . Sem . Fac . Sci . Univ . Cagliari
  • 1985
Sur les distributions totalement géodésiques du groupe nilpotent riemannien H2p+1, Rend
  • Sem. Fac. Sci. Univ. Cagliari
  • 1985
...
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