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Riemannian flows and adiabatic limits

Georges Habib, Ken Richardson

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.

Riemannian flows and adiabatic limits

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.

Paper Structure

This paper contains 5 sections, 11 theorems, 77 equations.

Table of Contents

  1. Introduction
  2. Dirac operators on Riemannian flows
  3. Adiabatic limits
  4. Examples
  5. Appendix

Key Result

Lemma \oldthetheorem

(in HabThesis) If $K\left( X,Y\right) =X\cdot Y\cdot \left( \nabla _{X}^{\Sigma Q}\nabla _{Y}^{\Sigma Q}-\nabla _{Y}^{\Sigma Q}\nabla _{X}^{\Sigma Q}+\nabla _{\left[ X_{i},Y\right] }^{\Sigma Q}\right)$ is the Clifford curvature of $\Sigma Q$, then $K\left( X,Y\right) =0$ if $X=\xi$.

Theorems & Definitions (26)

  • Lemma \oldthetheorem
  • Lemma \oldthetheorem
  • proof
  • Lemma \oldthetheorem
  • Lemma \oldthetheorem
  • proof
  • Remark \oldthetheorem
  • Lemma \oldthetheorem
  • Proposition \oldthetheorem
  • proof
  • ...and 16 more