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It is shown that there exist several ways to treat the quantum-mechanicalCoulomb problem for a Dirac particle in flat Minkowski space with the help ofthe Heun differential equation, Fuchs's equation with four singular points.When extending the problem to curved spaces of constant curvature, LobachevskyH_{3} and Rimann S_{3}, there arise 2-nd order differential equations of theFuchs type with 6 singular points, a method to get relevant equations with fivesingular points has been elaborated.

Coulomb problem for a Dirac particle in flat Minkowski space and the Heun functions, extension to curved models