  The interaction between an external action and the order parameter, via a
dependence described by a so-called Lifshitz invariant, is very important to
determine the final configuration of the liquid crystal cells. The external
action can be an electric field applied to the bulk or the confinement due to
free surfaces or cell walls. The Lifshitz invariant includes the order
parameter in the form of an elastic strain. This coupling between elastic
strains and fields, inserted in a Landau-Ginzburg formalism, is well known and
give rise to striction effects causing undulations in the director
configuration. We want to discuss here the role of Lifshitz coupling terms,
following an approach similar to that introduced by Dzyaloshinskii for magnetic
materials. Case studies on nematics in planar and cylindrical cells are also
proposed.
