A uniqueness theorem in Kähler geometry (Q842308)

Let \((M, g)\) be a compact Kähler manifold with Kähler metric \(g\) of quasi-positive bisectional curvature tensor such that its Ricci tensor Ric satisfies a relation \(F(\text{Ric}) =\) constant for some elliptic function \(F\). In this paper, the authors prove that such a metric \(g\) is Kähler-Einstein if \(F\) is a function defined on a convex subset of all positive \(n \times n\) Hermitian matrices such that \(F\) is monotone and invariant under the unitary transformation.