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TMF, 2014, Volume 181, Number 1, Pages 206–217 (Mi tmf8646)  

Real projective connections, V. I. Smirnov's approach, and black-hole-type solutions of the Liouville equation

L. A. Takhtadzhyanab

a Euler International Mathematical Institute, St. Petersburg, Russia
b Department of Mathematics, Stony Brook University, Stony Brook, NY, USA

Abstract: 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, monodromy group, Liouville equation, Liouville action, singular solution

DOI: https://doi.org/10.4213/tmf8646

Full text: PDF file (481 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 181:1, 1307–1316

Bibliographic databases:

Received: 21.01.2014

Citation: L. A. Takhtadzhyan, “Real projective connections, V. I. Smirnov's approach, and black-hole-type solutions of the Liouville equation”, TMF, 181:1 (2014), 206–217; Theoret. and Math. Phys., 181:1 (2014), 1307–1316

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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