Calculus of generalized hyperbolic tetrahedron
Ren Guo
TL;DR
This paper derives the Jacobian matrix relating dihedral angles to edge lengths in generalized hyperbolic tetrahedra and identifies its symmetries, advancing understanding of hyperbolic polyhedral geometry.
Contribution
It provides explicit calculations of the Jacobian matrix and uncovers its symmetry properties, which were not previously known in hyperbolic geometry.
Findings
Jacobian matrix of dihedral angles explicitly calculated
Complete set of symmetries of the Jacobian matrix identified
Enhanced understanding of hyperbolic tetrahedral geometry
Abstract
We calculate the Jacobian matrix of the dihedral angles of a generalized hyperbolic tetrahedron as functions of edge lengths and find the complete set of symmetries of this matrix.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematics and Applications · Advanced Combinatorial Mathematics