Reducibility of complex submanifolds of the complex Euclidean space (Q1591403)
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scientific article; zbMATH DE number 1546902
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Reducibility of complex submanifolds of the complex Euclidean space |
scientific article; zbMATH DE number 1546902 |
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Reducibility of complex submanifolds of the complex Euclidean space (English)
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19 March 2001
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The author proves the following extrinsic analogue of the de Rham decomposition theorem for Kähler manifolds: A complex isometric full immersion of a simply connected complete Kähler manifold into \(\mathbb{C}^n\) is irreducible (up to a totally geodesic factor) if and only if the normal holonomy group acts irreducibly.
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irreducibility of immersions
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Kähler submanifold
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normal holonomy group
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