Geodesic
An analog of the Fefferman construction
Archivum mathematicum, Tome 42 (2006) no. 5, pp. 349-356 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The Fefferman construction associates to a manifold carrying a CR–structure a conformal structure on a sphere bundle over the manifold. There are some analogs to this construction, with one giving a Lie contact structure, a refinement of the contact bundle on the bundle of rays in the cotangent bundle of a manifold with a conformal metric. Since these structures are parabolic geometries, these constructions can be dealt with in this setting.
The Fefferman construction associates to a manifold carrying a CR–structure a conformal structure on a sphere bundle over the manifold. There are some analogs to this construction, with one giving a Lie contact structure, a refinement of the contact bundle on the bundle of rays in the cotangent bundle of a manifold with a conformal metric. Since these structures are parabolic geometries, these constructions can be dealt with in this setting.
Classification : 32Vxx 
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Wisser, Florian. An analog of the Fefferman construction. Archivum mathematicum, Tome 42 (2006) no. 5, pp. 349-356. http://geodesic.mathdoc.fr/item/ARM_2006_42_5_a21/

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[3] Sato H., Yamaguchi K.: Lie contact manifolds II. Math. Ann. 297, No. 1 (1993), 33–57. | MR | Zbl