  Curvature effects are important for a proper description of the properties of
magnetic systems. In this paper the exchange and dipolar energy of vortices on
a paraboloidal shell is studied. Using analytical calculations it is shown that
the in-plane component of vortices has larger energy on a paraboloidal shell
than in a planar disk with same thickness. On the other hand, the dipolar
energy associated to the vortex core diminishes if the vortex core is on a
paraboloidal surface. This reduction in the dipolar energy may cause a vortex
pinning mechanism by a paraboloidal shaped defect in a planar nanomagnet.
Regarding skyrmions, by using an in-plane anisotropy approximation to the
dipolar energy, it is shown that the skyrmion must have its width shrunk in
order to diminishes the magnetostatic energy and satisfy geometrical
constraints of the system.
