  In the da Costa's thin-layer approach, a quantum particle moving in a 3D
sample is confined on a curved thin interface. At the end, the interface
effects are ignored and such quantum particle is localized on a curved surface.
A geometric potential arises and, since it manifests due to this confinement
procedure, it depends on the transverse to the surface mass component. This
inspired us to consider, in this paper, the effects due to an anisotropic
effective mass on a non-interacting two dimensional electron gas confined on a
curved surface, a fact not explored before in this context. By tailoring the
mass, many investigations carried out in the literature can be improved which
in turns can be useful to better designing electronic systems without modifying
the geometry of a given system. Some examples are examined here, as a particle
on helicoidal surface, on a cylinder, on a catenoid and on a cone, with some
possible applications briefly discussed.
