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January, 2020 Generalization of Schläfli formula to the volume of a spherically faced simplex
Kazuhiko AOMOTO, Yoshinori MACHIDA
J. Math. Soc. Japan 72(1): 213-249 (January, 2020). DOI: 10.2969/jmsj/80238023


The purpose of this paper is to present a variational formula of Schläfli type for the volume of a spherically faced simplex in the Euclidean space. It is described in terms of Cayley–Menger determinants and their differentials involved with hypersphere arrangements. We derive it as a limit of fundamental identities for hypergeometric integrals associated with hypersphere arrangements obtained by the authors in the preceding article.


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Kazuhiko AOMOTO. Yoshinori MACHIDA. "Generalization of Schläfli formula to the volume of a spherically faced simplex." J. Math. Soc. Japan 72 (1) 213 - 249, January, 2020.


Received: 2 April 2018; Revised: 24 September 2018; Published: January, 2020
First available in Project Euclid: 2 November 2019

zbMATH: 07196504
MathSciNet: MR4055462
Digital Object Identifier: 10.2969/jmsj/80238023

Primary: 33C70
Secondary: 14F40 , 14H70

Keywords: Cayley–Menger determinant , contiguity relation , Gauss–Manin connection , hypergeometric integral , hypersphere arrangement , Schläfli formula , twisted rational de Rham cohomology

Rights: Copyright © 2020 Mathematical Society of Japan


Vol.72 • No. 1 • January, 2020
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