We identify the two-dimensional surfaces corresponding to certain solutions of the Liouville equation of importance for mathematical physics, the non-topological Chern-Simons (or Jackiw-Pi) vortex solutions, characterized by an integer $N \ge 1$. Such surfaces, that we call $S^2 (N)$, have positive constant Gaussian curvature, $K$, but are spheres only when $N=1$... (read more)

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