  In this paper we study the quantum dynamics of an electron/hole in a
two-dimensional quantum ring within a spherical space. For this geometry, we
consider a harmonic confining potential. Suggesting that the quantum ring is
affected by the presence of an Aharonov-Bohm flux and an uniform magnetic
field, we solve the Schr\"odinger equation for this problem and obtain exactly
the eigenvalues of energy and corresponding eigenfunctions for this nanometric
quantum system. Afterwards, we calculate the magnetization and persistent
current are calculated, and discuss influence of curvature of space on these
values.
