  In this study, firstly it is reviewed how the solutions of the Dirac-Weyl
equation for a massless charge on the hyperboloid under perpendicular magnetic
fields are obtained by using supersymmetric (SUSY) quantum mechanics methods.
Then, the solutions of the Dirac equation for a massive charge under magnetic
fields have been computed in terms of the solutions which were found before for
the Dirac-Weyl equation. As an example, the case of a constant magnetic field
on the hyperbolic surface for massless and massive charges has been worked out.
