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The effect of the curvature of a cylindrical surface on the energy spectrumfor a curved two-dimensional electron gas in a homogeneous magnetic field isconsidered. The corrections to the energy spectrum are obtained for the firsttime perturbatively, in contrast to previous works where it was obtainednumerically. The dispersion relationship is obtained as a function of curvatureradius and the results for curved surface have been compared with the flatsurface.

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