Minimal real Kaehler submanifolds

Abstract

We show that generic rank conditions on the second fundamental form of an isometric immersion f : M 2n → R 2n+p of a Kaehler manifold of complex dimension n ≥ 2 into Euclidean space with low codimension p implies that the submanifold has to be minimal. If M 2n if simply connected, this amounts to the existence of a one-parameter associated family of isometric minimal immersions unless f is holomorphic.