Isospectral connections on line bundles
type: Item
instance of: scholarly article
title: Isospectral connections on line bundles
zbMATH Open document ID: 0728.53025
DOI: 10.1007/BF02570886
author: Ruishi Kuwabara
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183783
review text: The author constructs line bundles on some compact Riemannian manifold without boundary admitting non-equivalent (with respect to gauge transformations) connections but isospectral Bochner-Laplacians. The essential ingredients in the proofs are the elementary trace formula of \textit{T. Sunada} [Ann. Math., II. Ser. 121, 169-186 (1985; Zbl 0585.58047)] and results of \textit{R. Brooks} [Topology 26, 63-66 (1987; Zbl 0617.53048)] in the framework of Riemannian coverings. Unfortunately, the arguments in the present paper are not complete at some points and there are several linguistic mistakes. For instance, isospectrality is proven by comparing (heat) spectral functions but no additional argument is given to prove that (in the present situation) the spectra coincide in fact. Nevertheless, it is possible to fill all the gaps.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 4203196
zbMATH Keywords: line bundles
zbMATH Keywords: connections
zbMATH Keywords: Bochner-Laplacians
zbMATH Keywords: isospectrality
MaRDI profile type: Publication
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OpenAlex ID: W2010126320
description: scientific article; zbMATH DE number 4203196