Explicit metrics for a class of two-dimensional superintegrable systems
  We obtain, in local coordinates, the explicit form of the two-dimensional, super-integrable systems of Matveev and Shevchishin involving cubic integrals. This enables us to determine for which values of the parameters these systems are indeed globally defined on the two-sphere. 
Galliano Valent, Christian Duval and Vsevolod Shevchishin
math-ph math.MP nlin.SI