On real projective connections, V.I. Smirnov's approach, and black hole   type solutions of the Liouville equation
  We consider real projective connections on Riemann surfaces and corresponding solutions of the Liouville equation. It is shown that these solutions have singularities of special type (of a black hole type) on a finite number of simple analytical contours. The case of the Riemann sphere with four real punctures, considered in V.I. Smirnov's thesis (Petrograd, 1918), is analyzed in detail. 
Leon A Takhtajan
math.CV hep-th