Skip Navigation


Bulletin of the London Mathematical Society Advance Access originally published online on June 3, 2009
Bulletin of the London Mathematical Society 2009 41(4):683-690; doi:10.1112/blms/bdp042
This Article
Right arrow FREE Full Text (PDF) Freely available
Right arrow All Versions of this Article:
41/4/683    most recent
bdp042v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Habib, G.
Right arrow Articles by Richardson, K.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2009 London Mathematical Society

A brief note on the spectrum of the basic Dirac operator

Georges Habib

Mathematics Department
Faculty of Sciences II
Lebanese University
P.O. Box 90656
Fanar-Matn
Lebanon
ghabib@ul.edu.lb

Ken Richardson

Department of Mathematics
Texas Christian University
TCU Box 298900
Fort Worth, TX 76180
USA

Received 21 September 2008.

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.

2000 Mathematics Subject Classification 53C12 (primary), 53C21, 58J50, 58J60 (secondary).


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.