Adiabatic limit and connections in Finsler Geometry
Differential Geometry
2012-10-31 v3
Abstract
In this paper, we identify the Bott connection on the natural foliation of the projective sphere bundle of a Finsler manifold to the Chern connection of this manifold. As a consequence, the symmetrization of the Bott connection turns out to be the Cartan connection of the Finsler manifold. Following Liu-Zhang \cite{LiuZ}, the Cartan connection can also be obtained through an adiabatic limit process. Furthermore, a Chern-Simons type form is defined and its conformal properties are discussed.
Keywords
Cite
@article{arxiv.1207.1552,
title = {Adiabatic limit and connections in Finsler Geometry},
author = {Huitao Feng and Ming Li},
journal= {arXiv preprint arXiv:1207.1552},
year = {2012}
}
Comments
In this new version, we give a simpler proof of our main result