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arXiv · 1204.2224

Dirac operators on foliations: the Lichnerowicz inequality

Weiping Zhang
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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.

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Weiping Zhang. 2012-04-10. Dirac operators on foliations: the Lichnerowicz inequality. https://arxiv.org/abs/1204.2224

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