Generic special Lagrangian moduli spaces of a non-Kähler Calabi--Yau threefold

Given a (possibly non-Kähler) Calabi–Yau threefold $(X,\mathrm{\Omega })$, we introduce the notion of a (perturbed) special Lagrangian (SL) submanifold of $(X,\omega ,\mathrm{\Omega })$, where $\omega$ is a Hermitian metric on $X$. The equations defining this class of submanifolds reduce to the usual SL equations when $\omega$ is a Kähler metric. Using the Sard–Smale technique, we prove the existence of a comeagre set of Hermitian metrics $\omega$ on $X$ such that the moduli space of perturbed SL submanifolds in $(X,\omega ,\mathrm{\Omega })$ consists of isolated points.