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J. Korean Math. Soc. 2013; 50(6): 1223-1256
Printed November 1, 2013
https://doi.org/10.4134/JKMS.2013.50.6.1223
Copyright © The Korean Mathematical Society.
Geometric and analytic interpretation of orthoscheme and Lambert cube in extended hyperbolic space
Yunhi Cho and Hyuk Kim
University of Seoul, Seoul National University
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
MSC numbers: 51M10, 51M25, 53B30
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