Isospectral connections on line bundles
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.
scientific article; zbMATH DE number 4203196