Thus far we have only considered large-scale deformations of continuous director fields. We have shown that, in the absence of applied fields, the equilibrium director configuration must satisfy in the bulk the condition of zero elastic torque Ε, while at the surfaces it must be compatible with the boundary conditions. In the case of strong anchoring on the walls limiting the sample, these conditions are geometric in nature and cannot be modified. As such, they can be topologically incompatible with the existence of a continuous director field.