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arXiv:1204.2224 [math.DG]AbstractReferencesReviewsResources

Dirac operators on foliations: the Lichnerowicz inequality

Weiping Zhang

Published 2012-04-10, updated 2015-02-12Version 5

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.

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
Categories: math.DG
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