Adiabatic Limits and Foliations

Details Adiabatic Limits and Foliations Adiabatic Limits and Foliations

1999-12-29

arxiv.org/abs/math/9912223v1

Mathematics

Differential Geometry

Scientific paper

We use adiabatic limits to study foliated manifolds. The Bott connection naturally shows up as the adiabatic limit of Levi-Civita connections. As an application, we then construct certain natural elliptic operators associated to the foliation and present a direct geometric proof of a vanshing theorem of Connes[Co], which extends the Lichnerowicz vanishing theorem [L] to foliated manifolds with spin leaves, for what we call almost Riemannian foliations. Several new vanishing theorems are also proved by using our method.

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