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 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 . 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.
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}
}