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arXiv · 2112.13061

Minimal real Kaehler submanifolds

S. Chion·M. Dajczer
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Abstract

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

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S. Chion, M. Dajczer. 2021-12-24. Minimal real Kaehler submanifolds. https://doi.org/10.21711/231766362022%2Frmc499

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