On pseudo-Einstein hypersurfaces of \({\mathcal H}^{2n+s}\) (Q1917721)

The concept of \(S\)-manifold was introduced by \textit{D. E. Blair} [J. Differ. Geom. 4, 155-167 (1970; Zbl 0202.20903)] as a generalization of Sasakian manifold to an arbitrary dimension. D. E. Blair also introduced a generalization of the Hopf fibration \(\pi:S^{2n+1}\to P\mathbb{C}^n\). This is an \(S\)-manifold which is denoted by the symbol \({\mathcal H}^{2n+s}\). The purpose of the present paper is to study a special kind of submanifolds of \({\mathcal H}^{2n+s}\), namely the pseudo-Einstein hypersurfaces. These submanifolds correspond to pseudo-Einstein real hypersurfaces of \(P\mathbb{C}^n\) [see \textit{M. Kon}, J. Differ. Geom. 14, 339-354 (1979; Zbl 0461.53031)] and, in the case \(s=1\), to pseudo-Einstein hypersurfaces of \(S^{2n+1}\) [see \textit{K. Yano} and \textit{M. Kon}, Kodai Math. J. 3, 163-196 (1980; Zbl 0452.53034)].