  We study the stability and energetics associated to skyrmions appear- ing as
excitations on curved surfaces. Using a continuum model we show that the
presence of cylindrically radial and azimuthal fields destabilizes the
skyrmions that appear in the absence of an external field. Weak fields generate
fractional skyrmions while strong magnetic fields yield stable 2{$\pi$}-
skyrmions, which have their widths diminished by the magnetic field strength.
Under azimuthal fields vortex appear as stable states on the curved surface.
