  We have studied the collective motion of polar active particles confined to
ellipsoidal surfaces. The geometric constraints lead to the formation of
vortices that encircle surface points of constant curvature (umbilics). We have
found that collective motion patterns are particularly rich on ellipsoids, with
four umbilics where vortices tend to be located near pairs of umbilical points
to minimize their interaction energy. Our results provide a new perspective on
the migration of living cells, which most likely use the information provided
from the curved substrate geometry to guide their collective motion.
