Nematic bend ($K_3|\mathbf{n}\times \nabla \times \mathbf{n}{|}^2/2$)

Nematic bend curves the integral lines of the nematic director. For a unit field, $(\mathbf{n}\cdot \nabla )\mathbf{n}=-\mathbf{n}\times (\nabla \times \mathbf{n})$, so the bend energy measures curvature along those lines.