  The locomotion of flexible membrane-like organisms on top of curved surfaces
appears in different contexts and scales. Still, such dynamics have not yet
been quantitatively modeled and no realization of such motion in manmade
systems has been achieved. We present an experimental and theoretical study of
active gel ribbons surfing on a curved fluid-fluid interface via periodic
modulation of their reference curvature. We derive a theoretical model, in
which forces and torques emerge from curvature mismatch between the ribbon and
the substrate. Analytic and numerical solutions of the equations of motion
successfully predict the experimentally measured velocity profiles. We conclude
by highlighting the relevance of this new, curvature-driven, mode of locomotion
for a broad range of mechanical, as well as biological systems.
