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