The smallest hyperbolic 3-manifolds with totally geodesic boundary
type: Item
instance of: scholarly article
title: The smallest hyperbolic 3-manifolds with totally geodesic boundary
zbMATH Open document ID: 0729.53042
author: Sadayoshi Kojima
author: Yosuke Miyamoto
published in: Journal of Differential Geometry
publication date: 1991-01-01T00:00:00Z
review text: The authors prove that, among compact hyperbolic 3-manifolds with non- empty totally geodesic boundary, each one having the minimum volume admits a polyhedral decomposition by two regular truncated tetrahedra of dihedral angle \(\pi\) /6. Moreover, using a definite integral of some elementary functions, they show that this minimal volume (it is twice the volume of a regular truncated tetrahedron of dihedral angle \(\pi\) /6) is 6.452.... For a classification of such manifolds with the minimal volume, see \textit{M. Fujii} [Hyperbolic 3-manifolds with totally geodesic boundary which are decomposed into hyperbolic truncated tetrahedra, Tokyo J. Math. 13, No.2, 353-373 (1990; Zbl 0729.57005)].
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 53A35
zbMATH DE Number: 4205314
zbMATH Keywords: compact hyperbolic 3-manifolds
zbMATH Keywords: totally geodesic boundary
zbMATH Keywords: minimum volume
zbMATH Keywords: polyhedral decomposition
zbMATH Keywords: truncated tetrahedra
reviewed by: Boris N. Apanasov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214446997
OpenAlex ID: W1538177203
Wikidata QID: Q115181540
DOI: 10.4310/JDG/1214446997
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description: scientific article; zbMATH DE number 4205314