Year: 2009
Type: article
Abstract: In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation (M, 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.
DOI: 10.1112/blms/bdp042
Authors: Georges Habib, Ken Richardson
Institutions: Lebanese University, Texas Christian University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2048335342