  We calculate electronic states on a closed cylindrical surface as a model of
a core-shell nanowire. The length of the cylinder can be infinite or finite. We
define cardinal points on the circumference of the cylinder and consider a
spatially uniform magnetic field perpendicular to the cylinder axis,in the
direction South-North. The orbital motion of the electrons depends on the
radial component of the field which is not uniform around the circumference: it
is equal to the total field at North and South, but vanishes at the West and
East sides. For a strong field, when the magnetic length is comparable to the
radius of the cylinder, the electronic states at North and South become
localized cyclotron orbits, whereas at East and West the states become long and
narrow snaking orbits propagating along the cylinder. The energy of the
cyclotron states increases with the magnetic field whereas the energy of the
snaking states is stable. Consequently, at high magnetic fields the electron
density vanishes at North and South and concentrates at East and West. We
include spin-orbit interaction with linear Rashba and Dresselhaus models. For a
cylinder of finite length the Dresselhaus interaction produces an axial twist
of the charge density relative to the center of the wire, which may be
amplified in the presence of the Rashba interaction.
