 Special Lagrangian submanifold

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 $\mathrm{Re}(e^{-i\theta }\Omega )$. In ${\mathbb{C}}^3$, its spatial three-fold can describe a supersymmetric curved D3-brane.