Einstein Kähler submanifolds with codimension 2 in a complex space form
Einstein-Kähler hypersurfaces in complex space forms are completely classified by \textit{B. Smyth} [Ann. Math., II. Ser. 85, 246-266 (1967; Zbl 0168.196)] and \textit{S. S. Chern} [J. Differ. Geom. 1, 21-31 (1967; Zbl 0168.195)]. The author proves that the same classification holds for Einstein-Kähler submanifolds of codimension 2 in complex space forms, that is, he proves the following: Let M be an n-dimensional Einstein- Kähler submanifold immersed in \(P_{n+2}(C)\), \(C^{n+2}\) or \(D^{n+2}\). Then M is either totally geodesic or locally a complex hyperquadric in some \(P_{n+1}(C)\) in \(P_{n+2}(C)\).
scientific article; zbMATH DE number 3951494