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In this work, we investigate the electronic transport properties of curvedtwo-dimensional quantum systems with a position-dependent mass (PDM). We foundthe Schr\"odinger equation for a general surface following the da Costaapproach, obtaining the geometrical potential for systems with PDM. We obtainedexpressions for the transmittance and reflectance for a general surface ofrevolution. As a first application of the general results obtained here, weinvestigate the transport properties of deformed nanotubes, since the variationof the effective mass with the radius of the nanotubes has been dis-consideredin previous studies of this system and experimentally a change of the effectivemass is observed for different radii. We found that the inclusion of theposition-dependent mass, particularly a radial change in the mass distribution,can induce a significant change in the transport properties of the system,which reveals that the transport properties of two dimensional quantum systemsare sensitive to the PDM and when modeling electronic transport in surfacesthis effects should be considered.

Position-dependent mass effects in the electronic transport of two-dimensional quantum systems