Spherical geometry and integrable systems

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.

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Bibliographic Details
Published inGeometriae dedicata Vol. 169; no. 1; pp. 83 - 98
Main Authors Petrera, Matteo, Suris, Yuri B.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2014
Subjects
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
37J35
37K25
Discrete Darboux system
Sine law
37K10
Multidimensional consistency
Euler top
Hirota–Kimura discretization
51M10
Cosine law
Spherical triangle
Spherical simplex
Integrable systems
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Summary: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.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-013-9843-4