Isospectral Submersion Metrics

TL;DR

This paper develops a general method to construct continuous families of isospectral metrics on various Riemannian manifolds, including quotients, using the torus method and submersion metrics.

Contribution

It introduces a unifying principle for applying the torus method to produce isospectral metrics on manifolds and their quotients, with conditions for submersion metrics.

Findings

Constructed new families of isospectral metrics on Lie groups and projective spaces.

Provided a sufficient condition for these metrics to be submersion metrics.

Extended the applicability of the torus method to quotient manifolds.

Abstract

We construct continuous families of pairwise isospectral metrics on various Riemannian manifolds (e.g., Lie groups, projective spaces and products of these with tori) which arise as quotients of other manifolds. This is done by developing a general principle which guarantees that the torus method can be used to simultaneously construct isospectral metrics on a manifold and a quotient of it. Furthermore, a suffient condition will be given such that the constructed metrics are submersion metrics.