Geodesic
The Tanaka-Webster connection for almost $\mathcal{S}$-manifolds and Cartan geometry
Archivum mathematicum, Tome 40 (2004) no. 1, pp. 47-61.

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We prove that a CR-integrable almost $\mathcal S$-manifold admits a canonical linear connection, which is a natural generalization of the Tanaka–Webster connection of a pseudo-hermitian structure on a strongly pseudoconvex CR manifold of hypersurface type. Hence a CR-integrable almost $\mathcal S$-structure on a manifold is canonically interpreted as a reductive Cartan geometry, which is torsion free if and only if the almost $\mathcal S$-structure is normal. Contrary to the CR-codimension one case, we exhibit examples of non normal almost $\mathcal S$-manifolds with higher CR-codimension, whose Tanaka–Webster curvature vanishes.
Classification : 32V05, 53B05, 53C10, 53C15, 53C25
Keywords: almost $\mathcal S$-structure; Tanaka–Webster connection; Cartan connection; CR manifold 
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Lotta, Antonio; Pastore, Anna Maria. The Tanaka-Webster connection for almost $\mathcal{S}$-manifolds and Cartan geometry. Archivum mathematicum, Tome 40 (2004) no. 1, pp. 47-61. http://geodesic.mathdoc.fr/item/ARM_2004__40_1_a5/