  Noninteracting electrons confined to a corrugated surface are investigated in
magnetic field, and the associated effective Pauli equation is given
analytically by the thin-layer quantization scheme. Interestingly, the Zeeman
splitting gaps can be adjusted by curvature, and there is a geometric potential
induced by curvature. Further, we discuss the spin-dependent transport
properties for confined electrons by numerical calculation. More interestingly,
we find that the spin polarization induced by curvature becomes substantial
when the incident energy has small value. The results are considerable for a
spin transistor with small spin current.
