Curvature surfaces of Hopf hypersurfaces in complex space forms
Let \(N\) be the \(n\)-dimensional complex projective or complex hyperbolic space of constant holomorphic curvature \(\pm 4\) and denote its complex structure by \(J\). Furthermore, let \(M\) be a Hopf hypersurface of \(N\), i.e., \(M\) is a real hypersurface with a global unit normal field \(\eta\) whose structure field \(U := -J\eta\) is principal. In the present article the author thoroughly investigates the behaviour of the other principal curvatures of \(M\). In particular, he examines the integrability of the principal distributions and the geometry of their integral foliations. Often they turn out to be totally real; then they have the properties known from hypersurfaces of real space forms. The results are used to classify Hopf hypersurfaces with three principal curvatures.
scientific article; zbMATH DE number 824171
scientific article