Journal of Mathematical Physics, Analysis, Geometry 2020, vol. 16, No 3, pp. 263-282   https://doi.org/10.15407/mag16.03.263     ( to contents , go back )

The space of Schwarz-Klein spherical triangles

Alexandre Eremenko

Department of Mathematics, Purdue University, West Lafayette, IN 47907 USA
E-mail: eremenko@purdue.edu

Andrei Gabrielov

Department of Mathematics, Purdue University, West Lafayette, IN 47907 USA
E-mail: gabrielov@purdue.edu

Received June 14, 2020.

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 $\mathbb{R}^6$.

Mathematics Subject Classification 2010: 51F99
Key words: spherical geometry, triangles