AN ELEMENTARY PROOF OF SFORZA-SANTALÓ RELATION FOR SPHERICAL AND HYPERBOLIC POLYHEDRA

Title & Authors
AN ELEMENTARY PROOF OF SFORZA-SANTALÓ RELATION FOR SPHERICAL AND HYPERBOLIC POLYHEDRA
Cho, Yunhi;

Abstract
We defined and studied a naturally extended hyperbolic space (see [1] and [2]). In this study, we describe Sforza's formula [7] and Santal$\small{\acute{o}}$'s formula [6], which were rediscovered and later discussed by many mathematicians (Milnor [4], Su$\small{\acute{a}}$rez-Peir$\small{\acute{o}}$ [8], J. Murakami and Ushijima [5], and Mednykh [3]) in the spherical space in an elementary way. Thereafter, using the extended hyperbolic space, we apply the same method to prove their results in the hyperbolic space.
Keywords
hyperbolic space;spherical space;polyhedron;volume;
Language
English
Cited by
References
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