  In this work, we use the thin-layer quantization procedure to study the
physical implications due to curvature effects on a quantum dot in the presence
of an external magnetic field. Among the various physical implications due to
the curvature of the system, we can mention the absence of the $m=0$ state is
the most relevant one. The absence of it affects the Fermi energy and
consequently the thermodynamic properties of the system. In the absence of
magnetic fields, we verify that the rotational symmetry in the lateral
confinement is preserved in the electronic states of the system and its
degeneracy with respect to the harmonicity of the confining potential is
broken. In the presence of a magnetic field, however, the energies of the
electronic states in a quantum dot with a curvature are greater than those
obtained for a quantum dot in a flat space, and the profile of degeneracy
changes when the field is varied. We show that the curvature of the surface
modifies the number of subbands occupied in the Fermi energy. In the study of
both magnetization and persistent currents, we observe that Aharonov-Bohm-type
(AB-type) oscillations are present, whereas de Haas-van Alphen-type (dHvA)
oscillations are not well defined.
