  In this article, we prove a Kahler extension theorem for real Kahler
submanifolds of codimension 4 and rank at least 5. Our main theorem states that
such a manifold is a holomorphic hypersurface in another real Kahler
submanifold of codimension 2. This generalizes a result of Dajczer and Gromoll
in 1997 which states that any real Kahler submanifolds of codimension 3 and
rank at least 4 admits a Kahler extension.
