The type number of real hypersurfaces in \(P_n(\mathbb{C})\)
It is proved that on a complete real hypersurface in complex projective \(n\)-space \(P_n (\mathbb{C})\) there exists a point \(p\) where the type number \(t(p)\) is greater than or equal to \(n\). The theorem generalizes former results in this direction, for instance, the result due to \textit{Y. J. Suh} [ibid. 15, 99-104 (1991; Zbl 0736.32016)], saying that under the assumptions of the above theorem and with \(n\geq 3\), there exists a point \(p\) such that \(t(p)\geq 3\).
scientific article; zbMATH DE number 1102947