Isospectral hypersurfaces in Euclidean spheres
type: Item
instance of: scholarly article
title: Isospectral hypersurfaces in Euclidean spheres
zbMATH Open document ID: 1085.53046
author: José N. B. Barbosa
published in: Kodai Mathematical Journal
publication date: 2005-04-18T00:00:00Z
review text: Let \(M\) be a compact Riemannian manifold without boundary of dimension \(n\) and \(\text{Spec}^{p}(M):=\{0\leq \lambda_{0}^{p}\leq \lambda_{1}^{p},\dots\uparrow +\infty\}\), \(p=0,1,\dots,n,\) be the spectrum of the Laplacian p-forms in \(M\). If \(\text{Spec}^{p}(M)=\text{Spec}^{p}(M_{0})\) for a given hypersurface \(M_{0}\) then classification results for \(M\) are given. Denote by \(H, H_{0}\) the mean curvature of \(M\), \(M_{0}\) respectively. The case \(H=H_{0}=0,\) is studied and he showed that the assumption \(H=H_{0}\) in [\textit{J. Wang}, J. Math. Res. Expo. 17, No. 4, 496--500 (1997; Zbl 0915.53027)] is not necessary,
reviewed by: M. Belkhelfa
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 58J53
zbMATH DE Number: 2157856
zbMATH Keywords: closed hypersurface
zbMATH Keywords: spectrum
zbMATH Keywords: minimal hypersurface
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1104247347
OpenAlex ID: W1973631337
DOI: 10.2996/KMJ/1104247347
description: scientific article; zbMATH DE number 2157856