Adiabatic Limits and Foliations
Differential Geometry
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/9912223,
title = {Adiabatic Limits and Foliations},
author = {Kefeng Liu and Weiping Zhang},
journal= {arXiv preprint arXiv:math/9912223},
year = {2007}
}