Special Lagrangian submanifold
= Special Lagrangian submanifold
{title2=$\omega|_\Sigma=0,\quad\operatorname{Im}(e^{-i\theta}\Omega)|_\Sigma=0$}
A Lagrangian submanifold in a Calabi–Yau geometry is special when the phase of its holomorphic volume form is constant. With orientation chosen so that the real part is positive, it is a <calibrated submanifold> for $\operatorname{Re}(e^{-i\theta}\Omega)$. In $\mathbb C^3$, its spatial three-fold can describe a supersymmetric curved <D3-brane>.