Comptes Rendus
no. 1
Géométrie différentielle
Sur les variétés sous-riemanniennes de contact isotropes
[On isotropic sub-Riemannian contact manifolds]
Presented by: Étienne Ghys
Abdol-Reza Mansouri1
1 Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, États-Unis
Comptes Rendus. Mathématique, Volume 339 (2004) no. 1, pp. 39-42

Dans cette Note, nous montrons que contrairement au cas de la dimension 3, il n'existe guère de variété sous-riemannienne de contact isotrope en dimension supérieure à 3.

In this Note, we show that contrary to the dimension 3 case, isotropic contact sub-Riemannian manifolds of dimension greater than 3 do not exist.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.04.009

Abdol-Reza Mansouri 1

1 Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, États-Unis 
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Abdol-Reza Mansouri. Sur les variétés sous-riemanniennes de contact isotropes. Comptes Rendus. Mathématique, Volume 339 (2004) no. 1, pp. 39-42. doi: 10.1016/j.crma.2004.04.009

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[2] E. Falbel, personal communication, March 2004

[3] E. Falbel; C. Gorodski On contact sub-Riemannian symmetric spaces, Ann. Sci. École Norm. Sup. (4), Volume 28 (1995) no. 5, pp. 571-589

[4] E. Falbel; J.M. Veloso; J.A. Verderesi Constant curvature models in sub-Riemannian geometry, Campinas, 1992 (Mat. Contemp.), Volume 4 (1993), pp. 119-125

[5] R.B. Gardner The Method of Equivalence and its Applications, SIAM, Philadelphia, 1989

[6] K. Hughen, The geometry of subriemannian three-manifolds, Ph.D. Thesis, Duke University, 1995

[7] R. Montgomery A Tour of Subriemannian Geometries, Their Geodesics and Applications, Math. Surveys Monographs, vol. 91, American Mathematical Society, 2002

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