  The quantization of a single particle without spin in an appropriate curved
space-time is considered. The Hamilton formalism on reduced space for a
particle in a curved space-time is constructed and the main aspects of
quantization scheme are developed. These investigations are applied to
quantization of the particle Hamiltonian in an appropriate curved space-time.
As an example the energy eigenvalues in Einstein universe are calculated. In
the last sections o the paper approximation for small values of momenta of the
results previously obtained is considered as well as quantization of polynomial
Hamiltonians of general type is discussed.
