Vortex interaction on curved surfaces

The vortex-excitation energy on a sphere can be obtained by using the stereographic projection. By applying this method, we calculate the energy needed to create a vortex on a surface with a constant negative curvature. It is found that the energy is a linear function of the radius of the vortex. In accordance with this result, the interaction energy between a pair of vortices is also found to change linearly with the vortex separation distance. Explicit vortex configurations are obtained numerically with this interaction.