This article is cited in 3 papers

The space of Schwarz–Klein spherical triangles

Alexandre Eremenko, Andrei Gabrielov

Department of Mathematics, Purdue University, West Lafayette, IN 47907 USA

Abstract: We describe the space of spherical triangles (in the sense of Schwarz and Klein). It is a smooth connected orientable $3$ manifold, homotopy equivalent to the $1$-skeleton of the cubic partition of the closed first octant in $\mathbb{R}^3$. The angles and sides are real analytic functions on this manifold which embed it to $\mathbb{R}^6$.

Key words and phrases: spherical geometry, triangles.

MSC: 51F99

Received: 14.06.2020

Language: English

DOI: 10.15407/mag16.03.263

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