Bismut constant holomorphic sectional curvature conjecture

Let $(M^n,g)$ be a compact Hermitian manifold, and let the Bismut connection be the canonical Hermitian connection with totally skew-symmetric torsion. Denote its holomorphic sectional curvature by $c$.

Bismut space-form conjecture. If a compact Hermitian manifold $(M^n,g)$ has constant Bismut holomorphic sectional curvature $c$ and $c\neq 0$, then $g$ must be Kähler.

This is the nonzero-curvature part of the analogue of the constant holomorphic sectional curvature conjecture for the Bismut connection. The source presents it as an analogous conjectural statement; no general resolution is supplied.