The stationary deformations of nematic layers with a twisted structure
are analysed by means of the Taylor expansion method based on catastr
ophe theory. The role of weak anchoring is investigated. Variations of
the polar and azimuthal angles describing the surface director orient
ation are allowed. The stability of two equilibrium states, the twiste
d and the homeotropic, is studied. Several types of continuous and dis
continuous transitions between them are revealed. The threshold voltag
es are calculated.