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Summary:
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.
References:
[1] Cecil T. E.: Lie Sphere Geometry. Springer–Verlag, New York, 1992. MR 1219311 | Zbl 0752.53003
[2] Čap A.: Two constructions with parabolic geometries. Proceedings of the 25th Winter School on Geometry and Physics, Srní 2005, Rend. Circ. Mat. Palermo (2) Suppl. 79 (2006), 11–38, preprint math.DG/0504389. MR 2287124 | Zbl 1120.53013
[3] Sato H., Yamaguchi K.: Lie contact manifolds II. Math. Ann. 297, No. 1 (1993), 33–57. MR 1238406 | Zbl 0789.53021
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