  The quantum dynamics of carriers bound to helical tube surfaces is
investigated in a thin-layer quantization scheme. By numerically solving the
open-boundary Schr$\ddot{\rm o}$dinger equation in curvilinear coordinates,
geometric effect on the coherent transmission spectra is analysed in the case
of single propagating mode as well as multimode. It is shown that, the coiling
endows the helical nanotube with different transport properties from a bent
cylindrical surface. Fano resonance appears as a purely geometric effect in the
conductance, the corresponding energy of quasibound state is obviously
influenced by the torsion and length of the nanotube. We also find new plateaus
in the conductance. The transport of double-degenerate mode in this geometry is
reminiscent of the Zeeman coupling between the magnetic field and spin angular
momentum in quasi-one-dimensional structure.
