GEOMETRIC AND ANALYTIC INTERPRETATION OF ORTHOSCHEME AND LAMBERT CUBE IN EXTENDED HYPERBOLIC SPACE

Title & Authors
GEOMETRIC AND ANALYTIC INTERPRETATION OF ORTHOSCHEME AND LAMBERT CUBE IN EXTENDED HYPERBOLIC SPACE
Cho, Yunhi; Kim, Hyuk;

Abstract
We give a geometric proof of the analyticity of the volume of a tetrahedron in extended hyperbolic space, when vertices of the tetrahedron move continuously from inside to outside of a hyperbolic space keeping every face of the tetrahedron intersecting the hyperbolic space. Then we find a geometric and analytic interpretation of a truncated orthoscheme and Lambert cube in the hyperbolic space from the viewpoint of a tetrahedron in the extended hyperbolic space.
Keywords
hyperbolic space;volume;analytic continuation;
Language
English
Cited by
1.
Combinatorial Decompositions, Kirillov–Reshetikhin Invariants, and the Volume Conjecture for Hyperbolic Polyhedra, Experimental Mathematics, 2016, 1
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