Dirac operators on foliations: the Lichnerowicz inequality
Differential Geometry
2015-02-13 v5
Abstract
We construct Dirac operators on foliations by applying the Bismut-Lebeau analytic localization technique to the Connes fibration over a foliation. The Laplacian of the resulting Dirac operators has better lower bound than that obtained by using the usual adiabatic limit arguments on the original foliation. As a consequence, we prove an extension of the Lichnerowicz-Hitchin vanishing theorem to the case of foliations.
Keywords
Cite
@article{arxiv.1204.2224,
title = {Dirac operators on foliations: the Lichnerowicz inequality},
author = {Weiping Zhang},
journal= {arXiv preprint arXiv:1204.2224},
year = {2015}
}
Comments
53 pages. Title, abstract and the main results changed. The vanishing consequence is not as strong as originally claimed. The originally claimed vanishing results will be dealt with in a separate paper