A Dajczer-Rodriguez type cylinder theorem for real Kähler submanifolds (Q2438005)

The authors extend the classification theorem obtained by \textit{M. Dajczer} and \textit{L. Rodríguez} [J. Reine Angew. Math. 419, 1--8 (1991; Zbl 0726.53041)] for real Kähler submanifolds of real codimension 2 in an Euclidean space, to codimensions 3 and 4. Under suitable conditions on the complex dimension and on the relative nullity index of real Kähler submanifolds, it is proved that they must be partially holomorphic, or a cylinder, or a twisted cylinder. Also, the authors find sufficient conditions for real Kähler submanifolds to be complex ruled.