On non-Riemannian geometry of twisted nematic liquid crystals

TL;DR

This paper introduces a teleparallel geometric framework for describing twisted nematic liquid crystals, linking their physical twist to a specific torsion form and analyzing particle trajectories within this geometry.

Contribution

It presents a novel teleparallel geometric model for nematic liquid crystals, emphasizing the role of Cartan torsion in twisted phases and deriving geodesics in this context.

Findings

Cartan torsion characterized by a spatial helical form

Geodesic equations for test particles in the teleparallel liquid crystal

Connection between twist angle and geometric torsion

Abstract

A teleparallel geometrical description of the nematic phases of liquid crystals is proposed.In the case of the twisted geometry of nematics Cartan torsion is given by a spatial helical form which depends on the twist angle. Geodesics of a test particle around the teleparallel liquid crystal are given.