Liquid crystals defects: geometric aspects

Lamellar liquid crystals (they have one-dimensional positional order) and
columnar liquid crystals (two-dimensional positional order) present specific
defect textures, with remarkable geometric properties. In fact, elastically
deformed 1D and 2D liquid crystals can show isometric distortions, in the
sense that the positional order is locally conserved, whereas pure curvature
deformations extend over macroscopic scales! The singularities that attend
such specific deformations are confocal conics in lamellar phases and
developable surfaces in columnar phases. Perfect confocal conics of
millimetric size are easily observed in lamellar phases.
Some newly discovered phases, which are simultaneously lamellar, columnar, and
chiral also show astonishing isometric textures, with the shape of helical
ribbons.