  The influence of the curvature on the dynamical properties of transversal
domain walls in a thin antiferromagnetic wire is studied theoretically.
Equations of motion for antiferromagnetic domain wall are obtained within the
collective variable approach ($q-\Phi$ model). It is shown that (i) for the
case of localized bend, curvature results in a pinning potential for domain
wall. (ii) The gradient of the curvature results in a driving force on the
domain wall and it effectively moves without any external stimuli. Although we
showcase our approach on the specific parabola and Euler spiral geometries, the
approach is general and valid for a wide class of geometries. All analytical
predictions are confirmed by numerical simulations.
