  Manipulation of the domain wall propagation in magnetic wires is a key
practical task for a number of devices including racetrack memory and magnetic
logic. Recently, curvilinear effects emerged as an efficient mean to impact
substantially the statics and dynamics of magnetic textures. Here, we
demonstrate that the curvilinear form of the exchange interaction of a magnetic
helix results in an effective anisotropy term and Dzyaloshinskii--Moriya
interaction with a complete set of Lifshitz invariants for a one-dimensional
system. In contrast to their planar counterparts, the geometrically induced
modifications of the static magnetic texture of the domain walls in magnetic
helices offer unconventional means to control the wall dynamics relying on
spin-orbit Rashba torque. The chiral symmetry breaking due to the
Dzyaloshinskii-Moriya interaction leads to the opposite directions of the
domain wall motion in left- or right-handed helices. Furthermore, for the
magnetic helices, the emergent effective anisotropy term and
Dzyaloshinskii-Moriya interaction can be attributed to the clear geometrical
parameters like curvature and torsion offering intuitive understanding of the
complex curvilinear effects in magnetism.
