Chiral nematic liquid crystals in cylindrical cavities. A classification of planar structures and models of non-singular disclination lines

A part of homotopy theory is applied to classify planar structures in chiral nematic liquid crystals confined to cylindrical cavities. The resulting classification is exact in the approximation of undeformed chiral nematic surfaces. Within this approach the relative stability of possible planar structures with surface and bulk disclination lines is discussed. The number and the shape of these disclinations, which in some cases form spiral structures, are predicted. Further approximate analytical expressions for non-singular director fields close to disclination lines with integral strength are introduced. Our predictions, which are also in agreement with some previously suggested pictures of such director fields, are used to improve stability considerations of the confined planar chiral nematic structures in tubes and droplets.