  In the spirit of the thin-layer quantization approach, we give the formula of
the geometric influences of a particle confined to a curved surface embedded in
three-dimensional Euclidean space. The geometric contributions can result from
the reduced commutation relation between the acted function depending on normal
variable and the normal derivative. According to the formula, we obtain the
geometric potential, geometric momentum, geometric orbital angular momentum,
geometric linear Rashba and cubic Dresselhaus spin-orbit couplings. As an
example, a truncated cone surface is considered. We find that the geometric
orbital angular momentum can provide an azimuthal polarization for spin, and
the sign of the geometric Dresselhaus spin-orbit coupling can be flipped
through the inclination angle of generatrix.
