Hyperbolic 3-manifolds with totally geodesic boundary which are decomposed into hyperbolic truncated tetrahedra
type: Item
instance of: scholarly article
title: Hyperbolic 3-manifolds with totally geodesic boundary which are decomposed into hyperbolic truncated tetrahedra
zbMATH Open document ID: 0729.57005
author: Michihiko Fujii
published in: Tokyo Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Gluing the hexagonal faces of hyperbolic truncated tetrahedra by isometries, the author proves the following main result: Theorem 3.1. There are exactly eight mutually non-isometric compact oriented hyperbolic 3-manifolds with totally geodesic boundary such that they can be decomposed into two hyperbolic truncated tetrahedra and their boundaries are closed surfaces of genus 2. We remark that the hyperbolic volume of these manifolds (\(\approx 6.452)\) is the minimal one among all compact oriented hyperbolic 3-manifolds with totally geodesic closed boundary [\textit{S. Kojima} and \textit{Y. Miyamoto}, The smallest hyperbolic 3-manifolds with totally geodesic boundary, Preprint]. Uniqueness of these eight manifolds follows from \textit{E. M. Andreev}'s classification theorem on hyperbolic polyhedra [Mat. Sb., Nov. Ser. 81, 445-478 (1970; Zbl 0194.232); see also \textit{W. Thurston}, The geometry and topology of 3-manifolds, Princeton Lecture Notes, Ch.13].
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 4205407
zbMATH Keywords: hyperbolic 3-manifolds
zbMATH Keywords: totally geodesic boundary
zbMATH Keywords: closed surfaces of genus 2
zbMATH Keywords: hyperbolic volume
reviewed by: Boris N. Apanasov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270132267
OpenAlex ID: W2051747757
DOI: 10.3836/TJM/1270132267
description: scientific article; zbMATH DE number 4205407