完整的实卡勒子漫游

Pub Date : 2024-03-12 DOI:10.1002/mana.202300369

A. de Carvalho

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引用次数: 0

摘要

让 f:M2n→R2n+p$f：M^{2n}\rightarrow \mathbb {R}^{2n+p}$ 表示复维度 n≥2$n\ge 2$ 的凯勒流形等距浸入标度 p$p$ 的欧几里得空间。我们证明，关于非最小完整实凯勒子流形 f$f$ 的第二基本形式的一般秩条件意味着 f$f$ 是实凯勒子流形 g:N2p→R2p+p$g 上的圆柱体：N^{2p}\rightarrow \mathbb {R}^{2p+p}$.

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Complete real Kähler submanifolds

Let $f : M^{2 n} \to R^{2 n + p}$ denote an isometric immersion of a Kähler manifold with complex dimension $n \geq 2$ into Euclidean space with codimension $p$ . We show that generic rank conditions on the second fundamental form of a non-minimal complete real Kähler submanifold $f$ imply that $f$ is a cylinder over a real Kähler submanifold $g : N^{2 p} \to R^{2 p + p}$ .

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