The Tanaka-Webster connection and real hypersurfaces in a complex space form (Q655539)

The first author defined in [Publ. Math. 54, No. 3--4, 473--487 (1999; Zbl 0929.53029)] the notion of a generalized Tanaka-Webster connection, \(\widehat{\nabla }^{(k)}\), \(k\neq 0\), for real hypersurfaces \(M\) in a Kähler manifold. Then \(M\) is called a \(g\)-Tanaka-Webster parallel space if its \(g\)-Tanaka-Webster torsion tensor \(\widehat{T}\) and its curvature tensor \(\widehat{R}\) satisfy \[ \widehat{\nabla }^{(k)}\widehat{T}=0\quad\text{and}\quad\widehat{\nabla }^{(k)}\widehat{R}=0. \] The present paper gives a classification of \(g\)-Tanaka-Webster parallel spaces.