  In this paper the Dirac-Weyl equation on a hyperbolic surface of graphene
under magnetic fields is considered. In order to solve this equation
analytically for some cases, we will deal with vector potentials symmetric
under rotations around the z axis. Instead of using tetrads we will get this
equation from a more intuitive point of view by restriction from the Dirac-Weyl
equation of an ambient space. The eigenvalues and corresponding eigenfunctions
for some magnetic fields are found by means of the factorization method. The
existence of a zero energy ground level and its degeneracy is also analysed in
relation to the Aharonov-Casher theorem valid for flat graphene.
