The space of Schwarz-Klein triangles

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 ${\mathbf{R}}^3$. The angles and sides are real analytic functions on this manifold which embed it to ${\mathbf{R}}^6$.

25 pages, 8 figures

References in corpus (2)

• Moduli of spherical tori with one conical point
• Moduli spaces for Lamé functions and Abelian integrals of the second kind

Cited by in corpus (1)

• Moduli of spherical tori with one conical point