Characterizations of some product manifolds by their spectrum
type: Item
instance of: scholarly article
title: Characterizations of some product manifolds by their spectrum
zbMATH Open document ID: 1088.53028
published in: Monatshefte für Mathematik
publication date: 2006-02-07T00:00:00Z
review text: It is proved that \(S^2(c)\times S^2(c'), S^4(c)\times S^4(c')\) and \(\mathbb CP^2(c)\times \mathbb CP^2(c')\) are well identified by their spectra, respectively. Here, \(S^n(c)\) is the \(n\)-dimensional sphere with constant sectional curvature \(c>0\), and \(\mathbb CP^2(c)\) is the complex projective space of complex dimension \(2\) with constant holomorphic sectional curvature \(c>0.\) These results provide new positive examples for the old problem: does the spectrum of a manifold determine its metric?
reviewed by: Feng-Yu Wang
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 5004423
zbMATH Keywords: metric
zbMATH Keywords: spectrum
zbMATH Keywords: manifold
author: Changyu Xia
MaRDI profile type: Publication
full work available at URL: s00605-005-0315-2
OpenAlex ID: W2046525801
cites work: Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
cites work: EIGENVALUES OF THE LAPLACE OPERATOR ON CERTAIN MANIFOLDS
cites work: Eigenvalues of the Laplacian of Riemannian manifolds
cites work: A characterization of the product of two 3-spheres by the spectrum
DOI: 10.1007/S00605-005-0315-2
description: scientific article; zbMATH DE number 5004423