English

A brief note on the spectrum of the basic Dirac operator

Differential Geometry 2014-02-26 v1

Abstract

In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation (M,F)(M,\mathcal{F}) with respect to a change of bundle-like metric. We then establish new estimates for its eigenvalues on spin flows in terms of the O'Neill tensor and the first eigenvalue of the Dirac operator on MM. We discuss examples and also define a new version of the basic Laplacian whose spectrum does not depend on the choice of bundle-like metric.

Keywords

Cite

@article{arxiv.0809.2406,
  title  = {A brief note on the spectrum of the basic Dirac operator},
  author = {Georges Habib and Ken Richardson},
  journal= {arXiv preprint arXiv:0809.2406},
  year   = {2014}
}
R2 v1 2026-06-21T11:20:05.683Z