The gap of the eigenvalues for \(p\)-forms and harmonic \(p\)-forms of constant length
type: Item
instance of: scholarly article
title: The gap of the eigenvalues for \(p\)-forms and harmonic \(p\)-forms of constant length
zbMATH Open document ID: 1083.58029
author: Junya Takahashi
published in: Journal of Geometry and Physics
publication date: 2005-06-23T00:00:00Z
review text: Denote by \(\lambda_k^{(p)}(M,g)\) the \(k\)-th positive eigenvalue of the Laplacian acting on \(p\)-forms on an oriented closed Riemannian manifold \((M,g).\) The following estimate is the main result of the paper: If all non-trivial harmonic \(p\)-forms have constant length and if the \(p\)-th Betti number satisfies \(b_p(M)\geq1\) then \(\lambda_k^{(p)}(M,g)\leq \lambda_0^{(p)}(M,g).\) In the last section examples are studied.
reviewed by: Hans-Bert Rademacher
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 58J32
zbMATH DE Number: 2182202
zbMATH Keywords: eigenvalues
zbMATH Keywords: Laplace operator
zbMATH Keywords: harmonic forms
MaRDI profile type: Publication
full work available at URL: j.geomphys.2004.11.007
OpenAlex ID: W2028956420
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DOI: 10.1016/J.GEOMPHYS.2004.11.007
description: scientific article; zbMATH DE number 2182202