Minimal real Kaehler submanifolds

Abstract

We show that generic rank conditions on the second fundamental form of an isometric immersion $f:M^{2n}\to {\mathbb{R}}^{2n+p}$ of a Kaehler manifold of complex dimension $n\ge 2$ 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.

11 Pages. Minor changes were done in v2

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• Kaehler submanifolds of the real hyperbolic space