Vanishing real bisectional curvature conjecture for compact Hermitian manifolds

Let $M^n$ be a compact Hermitian manifold with $n$. Its real bisectional curvature is the curvature notion denoted by $B_g$ in the source, and let $R$ be the Chern curvature tensor.

Vanishing real bisectional curvature conjecture. If the real bisectional curvature is constantly equal to $c$, then $c=0$ and

$$R=0.$$

The preceding theorem shows that constant real bisectional curvature satisfies $c 0$ and, when $c=0$, imposes balancedness, vanishing first, second, and third Ricci tensors, and a skew-symmetry of the Chern curvature. The conjecture asks for the stronger conclusion that the full Chern curvature vanishes; the source does not give a resolution.