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

L. A. Takhtajan

doi:10.1007/s11232-014-0214-6

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

L. A. Takhtajan

Mathematics

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5 Scopus citations

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.

Original language	English
Pages (from-to)	1307-1316
Number of pages	10
Journal	Theoretical and Mathematical Physics(Russian Federation)
Volume	181
Issue number	1
DOIs	https://doi.org/10.1007/s11232-014-0214-6
State	Published - Oct 2014

Keywords

Fuchsian projective connection
Liouville action
Liouville equation
monodromy group
projective connection
Riemann surface
singular solution
uniformization

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10.1007/s11232-014-0214-6

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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{\textquoteright}s thesis (Petrograd, 1918) in detail.",

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N2 - 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.

AB - 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.

KW - Fuchsian projective connection

KW - Liouville action

KW - Liouville equation

KW - monodromy group

KW - projective connection

KW - Riemann surface

KW - singular solution

KW - uniformization

UR - https://www.scopus.com/pages/publications/84920172683

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DO - 10.1007/s11232-014-0214-6

M3 - Article

AN - SCOPUS:84920172683

SN - 0040-5779

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SP - 1307

EP - 1316

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

IS - 1

ER -

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

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Keywords

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