An elementary proof of Sforza-Santal\'o relation for spherical and hyperbolic polyhedra
Commun. Korean Math. Soc. 2013 Vol. 28, No. 4, 799-807
https://doi.org/10.4134/CKMS.2013.28.4.799
Printed October 1, 2013
Yunhi Cho
University of Seoul
Abstract : We defined and studied a naturally extended hyperbolic space (see \cite{C} and \cite{CK}). In this study, we describe Sforza's formula \cite{sf} and Santal\'o's formula \cite{S}, which were rediscovered and later discussed by many mathematicians (Milnor \cite{M}, Su\'arez-Peir\'o \cite{E}, J. Murakami and Ushijima \cite{J}, and Mednykh \cite{Me}) 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
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