  In this work, we explore the strain and curvature effects on the electronic
properties of a curved graphene structure, called the graphene wormhole. The
electron dynamics is described by a massless Dirac fermion containing
position--dependent Fermi velocity. In addition, the strain produces a
pseudo--magnetic vector potential to the geometric coupling. For an isotropic
strain tensor, the decoupled components of the spinor field exhibit a
supersymmetric (SUSY) potential, depending on the centrifugal term and the
external magnetic field only. In the absence of a external magnetic field, the
strain yields to an exponential damped amplitude, whereas the curvature leads
to a power--law damping of the wave function. The spin--curvature coupling
breaks the chiral symmetry between the upper and the lower spinor component,
which leads to the increasing of the wave function on either upper or lower
region of the wormhole, i.e., depending on the spin number. By adding an
uniform magnetic field, the effective potential exhibits an asymptotic
quadratic profile and a spin--curvature barrier near the throat. As a result,
the bound states (Landau levels) are confined around the wormhole throat
showing an asymmetric and spin--dependent profile.
