On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group Wafaa Batat a ,
Salima Rahmani bc 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 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.
MSC: 58A30 ;
53C15 ;
53C30 Received: December 23, 2009 ; in final form
February 23, 2010 ; Published online
February 28, 2010
Language: English
DOI:
10.3842/SIGMA.2010.021
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