Isospectral metrics on weighted projective spaces

TL;DR

This paper constructs the first known examples of weighted projective spaces that are isospectral but not isometric, using a generalized torus method to produce families of bad Riemannian orbifolds with identical Laplacian spectra.

Contribution

It introduces the first examples of isospectral non-isometric weighted projective spaces, expanding understanding of spectral geometry on orbifolds.

Findings

First examples of isospectral non-isometric weighted projective spaces.

Use of a generalized Sch"uth's torus method for construction.

Identification of families of bad Riemannian orbifolds with identical spectra.

Abstract

We construct the first examples of families of bad Riemannian orbifolds which are isospectral with respect to the Laplacian but not isometric. In our case these are particular fixed weighted projective spaces equipped with isospectral metrics obtained by a generalization of Sch\"uth's version of the torus method.