  The Schrodinger equation for an electron near an azimuthally symmetric curved
surface $\Sigma$ in the presence of an arbitrary uniform magnetic field
$\mathbf B$ is developed. A thin layer quantization procedure is implemented to
bring the electron onto $\Sigma$, leading to the well known geometric potential
$V_C \propto h^2-k$ and a second potential that couples $A_N$, the component of
$\mathbf A$ normal to $\Sigma$ to mean surface curvature, as well as a term
dependent on the normal derivative of
  $A_N$ evaluated on $\Sigma$. Numerical results in the form of ground state
energies as a function of the applied field in several orientations are
presented for a toroidal model.
