Communications in Analysis and Geometry

Volume 21 (2013)

Number 3

Adiabatic limit and connections in Finsler geometry

Pages: 607 – 624

DOI: http://dx.doi.org/10.4310/CAG.2013.v21.n3.a6

Authors

Huitao Feng (Nankai University, China)

Ming Li (School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, China)

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 [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.

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