Liouville conjecture for compact generalized Calabi–Yau manifolds

Let $(Z,\mathcal{J})$ be a compact generalized Calabi–Yau manifold of real dimension $2n$, and let $\phi$ be a global, closed, nowhere-vanishing differential form representing $\mathcal{J}$. Suppose that $f$ is a nowhere-zero smooth complex-valued function such that

$$d(f\phi)=0.$$

Liouville conjecture. The function $f$ is constant. Equivalently, a compact generalized Calabi–Yau manifold has no nonconstant nowhere-zero smooth rescaling of a global closed generator of its generalized Calabi–Yau spinor line that remains closed.

The conjecture would give uniqueness, up to multiplication by constants, of the projective cohomology class associated with a generalized Calabi–Yau structure. The source notes that symplectic manifolds, compact Calabi–Yau manifolds, products, and $B$-field transformations of Liouville generalized Calabi–Yau manifolds satisfy the condition, but gives no resolution of the conjecture.