Notes on a connection of the pseudo-Hermitian structure (Q2755649)

Let \(M\) be a \((2n+2)\)-dimensional manifold endowed with a CR-structure \((\Delta,J)\), where \(\Delta\) is a 1-codimensional subbundle of \(TM\) and \(J\) is an integrable complex structure on \(\Delta\) [\textit{N. Tanaka}, A differential geometric study on strongly pseudo-convex manifolds, Kyoto Univ. (1975; Zbl 0331.53025), \textit{S. M. Webster}, J. Differ. Geom. 13, 25-41 (1978; Zbl 0379.53016), \textit{K. Sakamoto} and \textit{Y. Takemura}, Kodai Math. J. 3, 144-161 (1980; Zbl 0449.53034)]. A canonical connection \(D\) associated to the CR-structure, unique with respect to certain properties, is constructed here. If \(Dg=0\) (where \(g\) is the adapted metric on \(TM\)), then \(D\) is the Webster connection.