A Schläfli differential formula for simplices in semi-Riemannian hyperquadrics, Gauss-Bonnet formulas for simplices in the de Sitter sphere and the dual volume of a hyperbolic simplex
type: Item
instance of: scholarly article
title: A Schläfli differential formula for simplices in semi-Riemannian hyperquadrics, Gauss-Bonnet formulas for simplices in the de Sitter sphere and the dual volume of a hyperbolic simplex
zbMATH Open document ID: 1023.53039
author: Eva Suárez-Peiró
published in: Pacific Journal of Mathematics
publication date: 2000-12-03T00:00:00Z
review text: We refer to the paper \textit{The Schläfli differential equality} by \textit{J. Milnor} [In: Collected papers, Vol. I, Publish Perish (1994; Zbl 0857.01015)] as a reference introducing to this problem, and the paper under review for its recent history. In the present paper, the author proves the Schläfli differential formula for the volume of simplices in central unit hyperquadrics of \(\mathbb R^{n+1}_q\) (\(=\) the semi-Euclidean space of index \(q\)). Next she applies this result to obtain the Gauss-Bonnet formula for simplices with Riemannian faces in the de Sitter sphere. And she also generalizes the formula of L. Santalò relating the volume of a hyperbolic simplex with the measure of the set of hyperbolic hyperplanes intersecting it.
reviewed by: Zbigniew Olszak
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1537817
zbMATH Keywords: Schläfli formula
zbMATH Keywords: Gauss-Bonnet formula
zbMATH Keywords: de Sitter sphere
zbMATH Keywords: simplex
Wikidata QID: Q115230675
MaRDI profile type: Publication
full work available at URL: pjm.2000.194.229
OpenAlex ID: W1977997247
DOI: 10.2140/PJM.2000.194.229
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description: scientific article; zbMATH DE number 1537817