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  • Title: Gnomonious projections for bend-free textures: thoughts on the splay-twist phase.
    Author: Chaturvedi N, Kamien RD.
    Journal: Proc Math Phys Eng Sci; 2020 Feb; 476(2234):20190824. PubMed ID: 32201482.
    Abstract:
    The Hopf fibration has inspired any number of geometric structures in physical systems, in particular, in chiral liquid crystalline materials. Because the Hopf fibration lives on the three sphere, S 3 , some method of projection or distortion must be employed to realize textures in flat space. Here, we explore the geodesic-preserving gnomonic projection of the Hopf fibration, and show that this could be the basis for a new liquid crystalline texture with only splay and twist. We outline the structure and show that it is defined by the tangent vectors along the straight line rulings on a series of hyperboloids. The phase is defined by a lack of bend deformations in the texture, and is reminiscent of the splay-bend and twist-bend nematic phases. We show that domains of this phase may be stabilized through anchoring and saddle-splay.
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