Uniqueness theorems of Kähler metrics of semipositive bisectional curvature on compact Hermitian symmetric spaces (Q1088163)

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 \(h=c\Phi^*g\).