Strongly isospectral hyperbolic and elliptic manifolds
type: Item
instance of: scholarly article
title: Strongly isospectral hyperbolic and elliptic manifolds
zbMATH Open document ID: 0847.58077
author: Hubert Pesce
published in: Journal of Functional Analysis
publication date: 1996-10-14T00:00:00Z
review text: The author proves that if \(\Gamma_1\) and \(\Gamma_2\) are discrete fixed point free cocompact isometry groups of the hyperbolic space \(H^n\) (respectively, of elliptic space \(S^n\)), then the quotient manifolds are strongly isospectral if and only if the regular representations of the full group \(G\) of isometries of \(H^n\) (respectively \(S^n\)) into \(L^2 (\Gamma_1 \setminus G)\) and \(L^2 (\Gamma_2\setminus G)\) are equivalent. Here, strong isospectrality means isospectrality not only with respect to the Laplace operator but with respect to all natural elliptic autoadjoint operators (which include for instance the Hodge-de Rham and the Lichnerowicz operators). The result completes the work of Sunada who gave sufficient conditions for isospectrality.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 850626
zbMATH Keywords: Laplace-Beltrami operator
zbMATH Keywords: spectrum
zbMATH Keywords: hyperbolic manifold
zbMATH Keywords: elliptic manifold
zbMATH Keywords: regular representations
zbMATH Keywords: strong isospectrality
reviewed by: Athanase Papadopoulos
MaRDI profile type: Publication
full work available at URL: jfan.1995.1150
OpenAlex ID: W2064129079
DOI: 10.1006/JFAN.1995.1150
description: scientific article; zbMATH DE number 850626