Cartan connections for CR manifolds (Q996063)

For a strictly pseudoconvex CR manifold \(M\) of hypersurface type, \textit{S. S. Chern} and \textit{J. K. Moser} [Acta Math. 133, 219--271 (1975; Zbl 0302.32015)] and \textit{N. Tanaka} [Jap. J. Math., New Ser. 2, 131--190 (1976; Zbl 0346.32010)] gave two equivalent constructions of a normal Cartan connection \(\Omega\), with values in a principal bundle over \(M\). In the paper under review a very explicit description and proof of this equivalence is given in the case where \(M\) has dimension three. The author also proves that a compact, connected and simply connected strictly pseudoconvex CR manifold of dimension \(3\) that is spherical (i.e. the curvature of \(\Omega\) vanishes everywhere) is CR-diffeomorphic to the sphere \(S^3\) with the standard CR structure.