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arXiv · 0809.2406

A brief note on the spectrum of the basic Dirac operator

Georges Habib·Ken Richardson
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Abstract

In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation $(M,\mathcal{F})$ 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 $M$. 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.

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Georges Habib, Ken Richardson. 2008-09-14. A brief note on the spectrum of the basic Dirac operator. https://doi.org/10.1112/blms%2Fbdp042

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