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Adiabatic limits and foliations

Kefeng Liu Weiping Zhang

Differential Geometry mathscidoc:1912.43072

arXiv preprint math/9912223, 1999.12
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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@inproceedings{kefeng1999adiabatic,
  title={Adiabatic limits and foliations},
  author={Kefeng Liu, and Weiping Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111400542258632},
  booktitle={arXiv preprint math/9912223},
  year={1999},
}
Kefeng Liu, and Weiping Zhang. Adiabatic limits and foliations. 1999. In arXiv preprint math/9912223. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111400542258632.
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