# Riemannian flows and adiabatic limits

## TL;DR

This paper investigates how the eigenvalues of the Dirac operator behave when a spin manifold with a Riemannian flow is subjected to metric collapse along the flow, revealing convergence properties.

## Contribution

It provides new insights into the spectral behavior of the Dirac operator under collapsing Riemannian flows on spin manifolds.

## Key findings

- Eigenvalues of the Dirac operator converge under metric collapse
- Characterization of spectral limits in collapsing scenarios
- Extension of spectral convergence results to Riemannian flows

## Abstract

We show the convergence properties of the eigenvalues of the Dirac operator on a spin manifold with a Riemannian flow when the metric is collapsed along the flow.