Spherical geometry and integrable systems

Abstract

We prove that the cosine law for spherical triangles and spherical tetrahedra defines integrable systems, both in the sense of multidimensional consistency and in the sense of dynamical systems.

15 pages, 5 figures

References in corpus (2)

• On integrability of Hirota-Kimura type discretizations
• Volume formula for a ${\mathbb{Z}}_2$-symmetric spherical tetrahedron through its edge lengths

Cited by in corpus (3)

• Integrability properties of Kahan's method
• Discretization of polynomial vector fields by polarization
• On the classification of multidimensionally consistent 3D maps