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Uniqueness theorems of Kähler metrics of semipositive bisectional curvature on compact Hermitian symmetric spaces. (English) Zbl 0612.53029

The following remarkable result is proved: Let (X,g) be an irreducible compact Hermitian symmetric space of rank \(\geq 2\). Suppose h is a twice differentiable Kaehler metric on X such that (X,h) carries semipositive holomorphic bisectional curvature. Then (X,h) is itself a Hermitian symmetric space. More precisely, there exists a biholomorphism \(\Phi\) of X and a positive constant c such that \(h=c\Phi^*g\).
Reviewer: T.Ochiai

MSC:

53C35 Differential geometry of symmetric spaces
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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References:

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