Cylindrical, spherical and toroidal layering of smectic C liquid crystals

This article examines static solutions to the smectic C continuum equations of Leslie et al.(1) for a variety of layer geometries. In particular it is shown that valid molecular configurations exist for cylindrical, spherical and toroidal layers. Suitable parameterizations are introduced for each surface and the Euler-Lagrange balance equations are solved in a suitable coordinate system. Plots of the surfaces are presented, and their relationship to singularities in the solutions are discussed.