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 -