  We investigate wave propagation in curved, thin elastic waveguides, where
curvature is shown to be equivalent to a spatially modulated refractive index.
We establish this relationship within a theoretical framework that leverages
non-Euclidean transformations. Theoretical predictions illustrate how curved
profiles can be designed to manipulate wave trajectories in analogy with
geometrical optics principles. Experiments on 3D printed curved membranes
confirm the theoretical predictions, and suggest curvature as a viable approach
for guiding, focusing and steering of elastic waves.
