Smectic Liquid Crystals: Materials with One-Dimensional, Periodic Order

Details Smectic Liquid Crystals: Materials with One-Dimensional, Periodic Order Smectic Liquid Crystals: Materials with One-Dimensional, Periodic Order

2006-01-20

arxiv.org/abs/math/0601494v1

Geometriae Dedicata 120 (2006) 229

Mathematics

Differential Geometry

16 pages

Scientific paper

10.1007/s10711-006-9075-y

Smectic liquid crystals are materials formed by stacking deformable, fluid layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary conditions can impose curvature on the layers. Since the layer spacing and curvature are intertwined, the problem of finding minimal configurations for the layers becomes highly nontrivial. We discuss various topological and geometrical aspects of these materials and present recent progress on finding some exact layer configurations. We also exhibit connections to the study of certain embedded minimal surfaces and briefly summarize some important open problems.

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