In the case of Kähler manifolds (or Calabi–Yau manifolds) we can make a choice \Omega=\Omega_1+\mathrm{i}\Omega_2 on M as a holomorphic n-form, where \Omega_1 is the real part and \Omega_2 imaginary. A Lagrangian submanifold L is called special if in addition to the above Lagrangian condition the restriction \Omega_2 to L is vanishing. In other words, the real part \Omega_1 restricted on L leads the volume form on L. The following examples are known as special Lagrangian submanifolds,
