  We present the first experimental observation of accelerating beams in curved
space. More specifically, we demonstrate, experimentally and theoretically,
shape-preserving accelerating beams propagating on spherical surfaces:
closed-form solutions of the wave equation manifesting nongeodesic self-similar
evolution. Unlike accelerating beams in flat space, these wave packets change
their acceleration trajectory due to the interplay between interference effects
and the space curvature, and they focus and defocus periodically due to the
spatial curvature of the medium in which they propagate.
