On some real hypersurfaces of a complex hyperbolic space (Q1072121)

The authors classify real hypersurfaces of a complex hyperbolic space \({\mathbb{C}}H^ n\) whose second fundamental form and induced almost contact structure commute. The Hopf fibration from Okumura's theory [see \textit{M. Okumura}, Trans. Am. Math. Soc. 212, 355-364 (1975; Zbl 0288.53043)] is replaced here by the \(S^ 1\)-fibration \(\pi\) : \(H_ 1^{2n+1}\to {\mathbb{C}}H^ n\) of the anti-de Sitter space \(H_ 1^{2n+1}\) over \({\mathbb{C}}H^ n\).