  In this work, we study the scattering of a spinless charged particle
constrained to move on a curved surface in the presence of the Aharonov-Bohm
potential. We begin with the equations of motion for the surface and transverse
dynamics previously obtained in the literature (Ferrari G. and Cuoghi G., Phys.
Rev. Lett. \textbf{100}, 230403 (2008)) and describe the surface with
non-trivial curvature in terms of linear defects such as dislocations and
disclinations. Expressions for the modified phase shift, S--matrix and
scattering amplitude are determined by applying a suitable boundary condition
at the origin, which comes from the self-adjoint extension theory. We also
discuss the presence of a bound state obtained from the pole of the S--matrix.
Finally, we claim that the bound state, the additional scattering and the
dependence of the scattering amplitude with energy are solely due to the
curvature effects.
