Almost complex submanifolds of quaternionic manifolds (Q2733939)
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scientific article; zbMATH DE number 1633261
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Almost complex submanifolds of quaternionic manifolds |
scientific article; zbMATH DE number 1633261 |
Statements
2 September 2001
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quaternionic Kähler manifold
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torsion
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hypercomplex manifolds
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almost complex submanifolds
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totally complex submanifolds
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parallel cubic line bundles
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quaternionic manifolds
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Obata connection
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Almost complex submanifolds of quaternionic manifolds (English)
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The authors first present some recent results concerning almost complex submanifolds of quaternionic manifolds and, in particular, quaternionic Kähler manifolds. Details have appeared in the paper [Osaka J. Math. 38, 869--904 (2001; Zbl 0998.53032)]. Then they prove the following result. Let \(M^{4n}\) be a smooth manifold equipped with a hypercomplex structure \(H\) and a complex structure \(J\). Then \(J\) is compatible with \(H\) if and only if \(J\) is parallel with respect to the Obata connection \(\nabla^H\).NEWLINENEWLINEFor the entire collection see [Zbl 0966.00031].
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