  The multicellular organization of diverse systems, such as embryos,
intestines and tumours, relies on the coordinated migration of cells in 3D
curved environments. In these settings, cells establish supracellular patterns
of motion, including collective rotation and invasion. While such collective
modes are increasingly well understood in 2D flat systems, the consequences of
geometrical and topological constraints on collective cell migration in 3D
curved tissues are largely unknown. Here, we study 3D collective migration in
mammary cell spheroids, which represent a common and conceptually simple curved
geometry. We discover that these rotating spheroids exhibit a collective mode
of cell migration in the form of a velocity wave propagating along the equator
with a wavelength equal to the spheroid perimeter. This wave is accompanied by
a pattern of incompressible cellular flow across the spheroid surface featuring
topological defects, as dictated by the closed spherical topology. Using a
minimal active particle model, we reveal that this collective mode originates
from the active flocking behaviour of a cell layer confined to a curved
surface. Our results thus identify curvature-induced velocity waves as a
generic mode of collective cell migration, which could impact the dynamical
organization of 3D curved tissues.
