  In liquid crystal elastomers, the orientational order of liquid crystals is
coupled with elastic distortions of crosslinked polymer networks. Previous
theoretical research has described these materials through two different
approaches: a neoclassical theory based on the liquid crystal director and the
deformation tensor, and a geometric elasticity theory based on the difference
between the actual metric tensor and a reference metric. Here, we connect those
two approaches using a formalism based on differential geometry. Through this
connection, we determine how both the director and the geometry respond to a
change of temperature.
