2017/10/30 by Kazuhiko Aomoto, Aomoto, Kazuhiko, Yoshinori Machida +1
Mathematics · #33C70 #Advanced Mathematical Theories #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #Primary 14F40 #Secondary 14H70
paper · pdf · doi:10.48550/arxiv.1710.10735
openalex publication_date 2017/10/30 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28
We present two identities (contiguity relation and variation formula) concerning the volume of a spherically faced simplex in the Euclidean space. These identities are described in terms of Cayley-Menger determinants and their differentials involved with hypersphere arrangements. They are derived as a limit of fundamental identities for hypergeometric integrals.