TY - JOUR

T1 - An elementary proof of sforza-santaló relation for spherical and hyperbolic polyhedra

AU - Cho, Yunhi

PY - 2013/10/1

Y1 - 2013/10/1

N2 - We defined and studied a naturally extended hyperbolic space (see [1] and [2]). In this study, we describe Sforza's formula [7] and San- taló's formula [6], which were rediscovered and later discussed by many mathematicians (Milnor [4], Suárez-Peiró [8], J. Murakami and Ushijima [5], and Mednykh [3]) in the spherical space in an elementary way. There- after, using the extended hyperbolic space, we apply the same method to prove their results in the hyperbolic space.

AB - We defined and studied a naturally extended hyperbolic space (see [1] and [2]). In this study, we describe Sforza's formula [7] and San- taló's formula [6], which were rediscovered and later discussed by many mathematicians (Milnor [4], Suárez-Peiró [8], J. Murakami and Ushijima [5], and Mednykh [3]) in the spherical space in an elementary way. There- after, using the extended hyperbolic space, we apply the same method to prove their results in the hyperbolic space.

KW - Polyhedron

KW - Spherical space

KW - Volume

KW - hyperbolic space

UR - http://www.scopus.com/inward/record.url?scp=84887506770&partnerID=8YFLogxK

U2 - 10.4134/CKMS.2013.28.4.799

DO - 10.4134/CKMS.2013.28.4.799

M3 - Article

AN - SCOPUS:84887506770

SN - 1225-1763

VL - 28

SP - 799

EP - 807

JO - Communications of the Korean Mathematical Society

JF - Communications of the Korean Mathematical Society

IS - 4

ER -