  We study the influence of curvature on the exchange energy of skyrmions and
vortices on a paraboloidal surface. It is shown that such structures appear as
excitations of the Heisenberg model, presenting topological stability, unlike
what happens on other simply-connected geometries such as pseudospheres. We
also show that the skyrmion width depends on the geometrical parameters of the
paraboloid. The presence of a magnetic field leads to the appearance of
$2\pi$-skyrmions, introducing a new characteristic length into the system.
Regarding vortices, the geometrical parameters of the paraboloid play an
important role in the exchange energy of this excitation.
