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This article is cited in 9 scientific papers (total in 9 papers)
Spherical quadrilaterals with three non-integer angles
A. Eremenkoa, A. Gabrielova, V. Tarasovbc a Department of Mathematics, Purdue University, West Lafayette, IN 47907-2067 USA
b St. Petersburg Department of V.A. Steklov Institute of Mathematics
of the Russian Academy of Sciences,
27 Fontanka, St. Petersburg, 191023, Russia
c Department of Mathematical Sciences, IUPUI, Indianapolis, IN 46202-3216 USA
Abstract:
A spherical quadrilateral is a bordered surface homeomorphic to a closed disk, with four distinguished boundary points called corners, equipped with a Riemannian metric of constant curvature $1$, except at the corners, and such that the boundary arcs between the corners are geodesic. We discuss the problem of classification of these quadrilaterals and perform the classification up to isometry in the case that one corner of a quadrilateral is integer (i.e., its angle is a multiple of $\pi$) while the angles at its other three corners are not multiples of $\pi$. The problem is equivalent to classification of Heun's equations with real parameters and unitary monodromy, with the trivial monodromy at one of its four singular point.
Key words and phrases:
surfaces of positive curvature, conic singularities, Heun equation, Schwarz equation, accessory parameter, conformal mapping, circular polygon.
Received: 07.07.2015
Citation:
A. Eremenko, A. Gabrielov, V. Tarasov, “Spherical quadrilaterals with three non-integer angles”, Zh. Mat. Fiz. Anal. Geom., 12:2 (2016), 134–167
Linking options:
https://www.mathnet.ru/eng/jmag649 https://www.mathnet.ru/eng/jmag/v12/i2/p134
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