QCH Kähler manifolds with \(\kappa =0\) (Q2875414)
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scientific article; zbMATH DE number 6330469
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | QCH Kähler manifolds with \(\kappa =0\) |
scientific article; zbMATH DE number 6330469 |
Statements
14 August 2014
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Kähler manifold
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holomorphic sectional curvature
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QCH Kähler manifold
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curvature tensor
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QCH Kähler manifolds with \(\kappa =0\) (English)
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Kählerian manifolds with quasi-constant holomorphic sectional curvature (QCH Kählerian manifolds) are considered. It is proved that if \((M,g,J)\) is a QCH Kählerian manifold of constant scalar curvature and \(\dim M\geq 6\) and its invariant \(k\) vanishes, then only two cases are possible, namely:NEWLINENEWLINE (I) \((M,g,J)\) has constant holomorphic sectional curvature;NEWLINENEWLINE (II) \((M,g,J)\) is locally a product \(M_a\times\Sigma\), where \(M_a\) is a Kählerian manifold of constant holomorphic sectional curvature \(a\) and \(\Sigma\) is a Riemannian surface of constant scalar curvature.
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0.853227972984314
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0.8507378101348877
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0.8424010276794434
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