  Rigidity transitions in simple models of confluent cells have been a powerful
organizing principle in understanding the dynamics and mechanics of dense
biological tissue. In this work we explore the interplay between geometry and
rigidity in two-dimensional vertex models confined to the surface of a sphere.
By considering shapes of cells defined by perimeters whose magnitude depends on
geodesic distances and areas determined by spherical polygons, the critical
shape index in such models is affected by the size of the cell relative to the
radius of the sphere on which it is embedded. This implies that cells can
collectively rigidify by growing the size of the sphere, i.e. by tuning the
curvature of their domain. Finite-temperature studies indicate that cell
motility is affected well away from the zero-temperature transition point.
