The projective-space conjecture for compact Kähler manifolds with positive orthogonal bisectional curvature

Let $M$ be an irreducible compact Kähler manifold with positive orthogonal bisectional curvature. Projective-space conjecture. Is $M$ necessarily biholomorphic to $\mathbb{C}\mathbb{P}^n$? The question asks whether positive orthogonal bisectional curvature forces an irreducible compact Kähler manifold to be complex projective space; the source presents it as a natural question after discussing curvature improvement under the Kähler–Ricci flow, and does not provide a resolution.