Topological magnetic solitons on a paraboloidal shell
  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. 
P. S. C. Vilas-Boas, R. G. Elias, D. Altbir, J. M. fonseca, V. L.   Carvalho-Santos
cond-mat.mes-hall cond-mat.other