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

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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’s thesis (Petrograd, 1918) in detail.

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Authors and Affiliations

  1. Department of Mathematics, Stony Brook University, Stony Brook, New York, USA

    L. A. Takhtajan

  2. Euler International Mathematical Institute, St. Petersburg, Russia

    L. A. Takhtajan

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  1. L. A. Takhtajan
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Correspondence to L. A. Takhtajan.

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Dedicated to my teacher Ludvig Dmitrievich Faddeev on the occasion of his 80th birthday

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Takhtajan, L.A. Real projective connections, V. I. Smirnov’s approach, and black-hole-type solutions of the Liouville equation. Theor Math Phys 181, 1307–1316 (2014). https://doi.org/10.1007/s11232-014-0214-6

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  • DOI: https://doi.org/10.1007/s11232-014-0214-6

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