English

Generalization of Schlafli formula to the volume of a spherically faced simplex

Differential Geometry 2017-10-31 v1 Algebraic Geometry Complex Variables Metric Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.1710.10735,
  title  = {Generalization of Schlafli formula to the volume of a spherically faced simplex},
  author = {Kazuhiko Aomoto and Yoshinori Machida},
  journal= {arXiv preprint arXiv:1710.10735},
  year   = {2017}
}

Comments

37 pages, 2 figures