Two-dimensional electron gas under the effect of constrained potential and magnetic field in curved space

The effect of the curvature of a cylindrical surface on the energy spectrum for a curved two-dimensional electron gas in a homogeneous magnetic field is considered. The corrections to the energy spectrum are obtained for the first time perturbatively, in contrast to previous works where it was obtained numerically. The dispersion relationship is obtained as a function of curvature radius and the results for curved surface have been compared with the flat surface.