Abstract : Cell monolayers are a central model system to tissue biophysics. In vivo, epithelial tissues are curved on the scale of microns, and curvature’s role in the onset of spontaneous tissue flows is still not well-understood. Here, we present a hydrodynamic theory for an apical-basal asymmetric active nematic gel on a curved strip. We show that surface curvature qualitatively changes monolayer motion compared to flat space : the resulting flows can be thresholdless, and the transition to motion may change from continuous to discontinuous. Surface curvature, friction and active tractions are all shown to control the flow pattern selected : from simple shear to vortex chains.