  Considerable recent attention has been given to the study of shape formation
using modern responsive materials that can be preprogrammed to undergo
spatially inhomogeneous local deformations. In particular, nematic liquid
crystal polymer networks offer exciting possibilities in this context. In this
paper, we discuss the generation of Gaussian curvature in thin nematic sheets
using smooth in-plane director fields patterned across the surface. We
highlight specific patterns which encode constant Gaussian curvature of
prescribed sign and magnitude and present experimental results which appear to
support the theoretical predictions. Specifically, we provide experimental
evidence for the realization of positive and negative Gaussian curvature in
glassy and elastomeric liquid crystal polymer networks through the stimulation
of smoothly varying in-plane director fields.
