Geodesic
On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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Wafaa Batat; Salima Rahmani. On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a20/

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