Relieving Cholesteric Frustration: The Blue Phase in a Curved Space

The problem of minimizing the full cholesteric free energy in flat space is difficult since the bending and bulk energies favor different forms of the order parameter. It is shown, however, that the problem can be solved exactly on the surface of a sphere in four-space, where the curvature relieves the strains induced by the "double twist." The conventional Landau bulk free energy leads to a rigorously uniaxial structure. The model is also of interest as a simple and explicit example of the ideas underlying recent theories of glasses.