Complex Hopf conjecture for compact Kähler manifolds

Let $(M,\omega)$ be an $n$-dimensional compact Kähler manifold with nonpositive holomorphic bisectional curvature, and suppose its Ricci curvature is quasi-negative, meaning nonpositive everywhere and negative somewhere. Complex Hopf conjecture. The signed Euler number satisfies

$$(-1)^n c_n[M]>0.$$

This is proposed as a complex analogue of the Hopf conjecture. The source gives no general proof and notes that suitable structure theorems for compact Kähler manifolds with nonpositive holomorphic bisectional curvature are unavailable.