  We study the Heisenberg Model on cylindrically symmetric curved surfaces. Two
kinds of excitations are considered. The first is given by the isotropic
regime, yielding the sine-Gordon equation and $\pi$-solitons are predicted. The
second one is given by the XY model, leading to a vortex turning around the
surface. Helical states are also considered, however, topological arguments can
not be used to ensure its stability. The energy and the anisotropy parameter
which stabilizes the vortex state are explicitly calculated for two surfaces:
catenoid and hyperboloid. The results show that the anisotropy and the vortex
energy depends on the underlying geometry.
