Codimension of immersions with parallel pluri-mean curvature (Q1038512)

An isometric immersion of a Kähler manifold in Euclidean space is said to have parallel pluri-mean curvature (`ppmc') if the \((1,1)\) part of its second fundamental form \(\alpha\) is parallel. Among the examples, there are the Hermitian symmetric spaces. In this paper, the authors show that these ones have the smallest codimension among all ppmc immersions, with the exception of the reducible Kähler manifolds.