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