Geodesic
Real projective connections, V.\,I.~Smirnov's approach, and black-hole-type solutions of the~Liouville equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 1, pp. 206-217

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We consider real projective connections on Riemann surfaces and their corresponding solutions of the Liouville equation. We show that these solutions have singularities of a special type (a black-hole type) on a finite number of simple analytic contours. We analyze the case of the Riemann sphere with four real punctures, considered in V. I. Smirnov's thesis (Petrograd, 1918) in detail.
Keywords: uniformization, Riemann surface, projective connection, Fuchsian projective connection
Mots-clés : monodromy group, Liouville equation, Liouville action, singular solution. 
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     author = {L. A. Takhtadzhyan},
     title = {Real projective connections, {V.\,I.~Smirnov's} approach, and black-hole-type solutions of {the~Liouville} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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L. A. Takhtadzhyan. Real projective connections, V.\,I.~Smirnov's approach, and black-hole-type solutions of the~Liouville equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 1, pp. 206-217. http://geodesic.mathdoc.fr/item/TMF_2014_181_1_a10/