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

Abstract

Given a (possibly non-Kähler) Calabi--Yau threefold $(X,\Omega )$, we introduce the notion of a (perturbed) special Lagrangian (SL) submanifold of $(X,\omega ,\Omega )$, 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 $(X,\omega ,\Omega )$ consists of isolated points.

23 pages, 2 figures, comments welcome!