Adiabatic limit and connections in Finsler geometry

Huitao Feng, Ming Li
2013 Communications in analysis and geometry  
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 [9], 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.
doi:10.4310/cag.2013.v21.n3.a6 fatcat:bcf6c5vpkvdqfoqavenbyc7uuu