  We study the Heisenberg model in an external magnetic field on curved
surfaces with rotational symmetry. The Euler-Lagrange static equations, derived
from the Hamiltonian lead to the inhomogeneous double sine-Gordon equation
(DSG). However, if the magnetic field is coupled with the metric elements of
the surface, and consequently, its curvature, the homogeneous DSG appears and a
$2\pi$-soliton is obtained as a solution for this model. In order to obey the
self-dual equations, surface deformations are predicted at the sector where the
spins point in the opposite direction to the magnetic field. The model was used
to particularize the characteristic lenght of the 2$\pi$-soliton for three
specific rotationally symmetric surfaces: the cylinder, the catenoid and the
hyperboloid. Fractional 2$\pi$-solitons must appear on finite surfaces, as the
sphere, torus and barrels, for example.
