Real cohomology characterization under n-positive Kähler curvature

Prove that if a closed Kähler manifold of complex dimension n has n-positive Kähler curvature operator, then it has the real cohomology ring of complex projective n-space.

Background

The paper combines vanishing theorems for holomorphic forms and primitive harmonic (n−1,1)-forms with earlier curvature estimates to characterize closed Kähler manifolds whose cohomology ring agrees with that of complex projective space. Theorem MainTheoremCPn establishes this characterization under a dimension-dependent positivity threshold k_n, and the paper notes that the case n=3 is covered by the main results.

A positive resolution of the preceding conjecture on primitive (p,q)-forms would imply the stronger uniform statement that n-positive Kähler curvature operator suffices in every complex dimension. Thus, this conjecture is presented as a consequence of the broader unresolved curvature-vanishing problem.