Communications in Analysis and Geometry
Volume 21 (2013)
Adiabatic limit and connections in Finsler geometry
Pages: 607 – 624
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 , 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.