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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 021, 4 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.021 (Mi sigma478) 		 
On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group

Wafaa Batata, Salima Rahmanibc

a Ecole Normale Supérieure de L'Enseignement Technologique d'Oran, Département de Mathématiques et Informatique, B.P. 1523 El M'Naouar Oran, Algeria
b Laboratoire de Mathématiques-Informatique et Applications, Universitée de Haute Alsace, 68093 Mulhouse Cedex, France
c Ecole Doctorale de Systèmes Dynamiques et Géométrie, Département de Mathématiques, Faculté des Sciences, Université des Sciences et de la Technologie d'Oran, B.P. 1505 Oran El M'Naouer, Algeria
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DOI: https://doi.org/10.3842/SIGMA.2010.021
Abstract: In this note we prove that the Heisenberg group with a left-invariant pseudo-Riemannian metric admits a completely integrable totally geodesic distribution of codimension 1. This is on the contrary to the Riemannian case, as it was proved by T. Hangan.
Keywords: Heisenberg group; pseudo-Riemannian metrics; geodesics; codimension 1 distributions.
Received: December 23, 2009; in final form February 23, 2010; Published online February 28, 2010
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Document Type: Article
MSC: 58A30; 53C15; 53C30
Language: English
Citation: Wafaa Batat, Salima Rahmani, “On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group”, SIGMA, 6 (2010), 021, 4 pp.
Citation in format AMSBIB
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\by Wafaa Batat, Salima Rahmani
\paper On the Existence of a~Codimension~1 Completely Integrable Totally Geodesic Distribution on a~Pseudo-Riemannian Heisenberg Group
\jour SIGMA
\yr 2010
\vol 6
\papernumber 021
\totalpages 4
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