  Heisenberg-like spins lying on the pseudosphere (a 2-dimensional infinite
space with constant negative curvature) cannot give rise to stable soliton
solutions. Only fractional solutions can be stabilized on this surface provided
that at least a hole is incorporated. We also address the issue of `in-plane'
vortices, in the XY regime. Interestingly, the energy of a single vortex no
longer blows up as the excitation spreads to infinity. This yields a
non-confining potential between a vortex and a antivortex at large distances so
that the pair may dissociate at arbitrarily low temperature.
