Einstein \(H\)-umbilical submanifolds with parallel mean curvatures in complex space forms (Q1433480)

The author classifies complete \(n\)-dimensional (\(n\geq 3\)) Einstein \(H\)-umbilical submanifolds with parallel mean curvature vector \(H\) in complex space forms \(\tilde{M}\) of (real) dimension \(2n\) and constant holomorphic curvature \(c\geq 0\). He shows that any such submanifold \(M\) is congruent either to a totally geodesic Lagrangian submanifold of \(\tilde{M}\) or to the product of a circle and the Euclidean space \(\mathbb{R}^{n-1}\).