Geometric influences of a particle confined to curved surface

In the spirit of the thin-layer quantization approach, we give the formula of the geometric influences of a particle confined to curved surface. The geometric contributions are defined by the reduced commutation relations of normal directive and its post functions of normal variable. According to the formula, we obtain 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 investigated. We find interesting results that the geometric orbital angular momentum can provide an azimuthal polarization for spin, the sign of the geometric Dresselhaus spin-orbit coupling can be controlled by the inclination angle of generatrix.