  The domain wall motion along a helix-shaped nanowire is studied for the case
of spin-current driving via Bazaliy-Zhang-Li mechanism. The analysis is based
on collective variable approach. Two new effects are ascertained: (i) the
curvature results in appearance of the Walker limit for a uniaxial wire, (ii)
the torsion results in effective shift of the nonadiabatic spin torque
parameter $\beta$. The latter effect changes considerably the domain wall
velocity and can result in negative domain wall mobility. This effect can be
also used for an experimental determination of the nonadiabatic parameter
$\beta$ and damping coefficient $\alpha$.
