Holomorphicity of real Kaehler submanifolds

22 Sep 2019  ·  de Carvalho A., Chion S., Dajczer M. ·

Let $f\colon M^{2n}\to\mathbb{R}^{2n+p}$ denote an isometric immersion of a Kaehler manifold of complex dimension $n\geq 2$ into Euclidean space with codimension $p$. If $2p\leq 2n-1$, we show that generic rank conditions on the second fundamental form of the submanifold imply that $f$ has to be a minimal submanifold... In fact, for codimension $p\leq 11$ we prove that $f$ must be holomorphic with respect to some complex structure in the ambient space. read more

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Differential Geometry