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We study the spatiotemporal patterns that emerge when an active nematic filmis topologically constraint. These topological constraints allow to control thenon-equilibrium dynamics of the active system. We consider ellipsoidal shapesfor which the resulting defects are 1/2 disclinations and analyze the relationbetween their location and dynamics and local geometric properties of theellipsoid. We highlight two dynamic modes: a tunable periodic state thatoscillates between two defect configurations on a spherical shape and a tunablerotating state for oblate spheroids. We further demonstrate the relationbetween defects and high Gaussian curvature and umbilical points and point outlimits for a coarse-grained description of defects as self-propelled particles.

Curvature controlled defect dynamics in topological active nematics