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The influence of the geometrical curvature of chiral magnetic films on thestatic and dynamic properties of hosted skyrmions are studied theoretically. Wepredict the effects of the curvature-induced drift of skyrmions under theaction of the curvature gradients without any external stimuli. The strength ofthe curvature-induced driving force essentially depends on the skyrmion type,Neel or Bloch, while the trajectory of motion is determined by the type ofmagnetic ordering: ferro- or antiferromagnetic. When moving on the surface,skyrmions undergo deformations that depend on the type of skyrmion. In thesmall-curvature limit, using the collective-variable approach we show, that thedriving force acting on a Neel skyrmion is linear in the gradient of the meancurvature. The driving acting on a Bloch skyrmion is much smaller: it isproportional to the product of the mean curvature and its gradient. In contrastto the fast Neel skyrmions, the dynamics of the slow Bloch skyrmions isessentially affected by the skyrmion profile deformation. For the sake ofsimplicity, we restrict ourselves to the case of zero Gaussian curvature andconsider cylindrical surfaces of general type. Equations of motion forferromagnetic and antiferromagnetic skyrmions in curved magnetic films areobtained in terms of collective variables. All analytical predictions areconfirmed by numerical simulations.

Curvature induced drift and deformation of magnetic skyrmions: comparison of ferro- and antiferromagnetic cases