  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.
