  It is shown, that oscillators on the sphere and the pseudosphere are related,
by the so-called Bohlin transformation, with the Coulomb systems on the
pseudosphere. The even states of an oscillator yield the conventional Coulomb
system on the pseudosphere, while the odd states yield the Coulomb system on
the pseudosphere in the presence of magnetic flux tube generating spin 1/2. A
similar relation is established for the oscillator on the (pseudo)sphere
specified by the presence of constant uniform magnetic field $B_0$ and the
Coulomb-like system on pseudosphere specified by the presence of the magnetic
field $\frac{B}{2r_0}(|\frac{x_3}{{\bf x}}|-\epsilon)$. The correspondence
between the oscillator and the Coulomb systems the higher dimensions is also
discussed.
