  Soft and biological matter come in a variety of shapes and geometries. When
soft surfaces that do not fit into each other due to a mismatch in Gaussian
curvatures form an interface, beautiful geometry-induced patterns emerge. In
this paper, we study the effect of geometry on the dynamical response of soft
surfaces moving relative to each other. Using a novel experimental scheme, we
measure friction between a highly bendable thin polymer sheet and a hydrogel
substrate. At this soft and low-friction interface, we find a strong dependence
of friction on the relative geometry of the two surfaces - a flat sheet
experiences significantly larger friction on a spherical substrate than on
planar or cylindrical substrate. We show that the stress developed in the sheet
due to its geometrically incompatible confinement is responsible for the
enhanced friction. This mechanism also leads to a transition in the nature of
friction as the sheet radius is increased beyond a critical value. Our finding
reveals a hitherto unnoticed non-specific mechanism of purely geometrical
origin that may influence friction significantly in soft, biological, and
nano-scale systems. In particular, it provokes us to re-examine our
understanding of phenomena such as the curvature dependence of biological cell
mobility.
