An isospectral deformation on an orbifold quotient of a nilmanifold

TL;DR

This paper constructs a family of metrics on an orbifold quotient of a nilmanifold that are isospectral, meaning they have identical Laplace spectra, despite differences in their geometric structure.

Contribution

It introduces a novel isospectral deformation on orbifold quotients of nilmanifolds using a generalized Sunada's Theorem, including singular points.

Findings

Successfully constructed isospectral metrics on orbifold quotients

Demonstrated the presence of singular points with order two isotropy

Extended Sunada's Theorem to orbifold settings

Abstract

We construct a Laplace isospectral deformation of metrics on an orbifold quotient of a nilmanifold. Each orbifold in the deformation contains singular points with order two isotropy. Isospectrality is obtained by modifying a generalization of Sunada's Theorem due to DeTurck and Gordon.