Generalized Finsler structures on closed 3-manifolds

Abstract

An $(I,J,K)$-generalized Finsler structure on a 3-manifold is a generalization of a Finslerian structure, introduced by R. Bryant in order to separate and clarify the local and global aspects in Finsler geometry making use of Cartan's method of exterior differential systems. In this paper, we show that there is a close relation between $(I,J,1)$-generalized Finsler structures and a class of contact circles, namely the so-called Cartan structures.This correspondence allows us to determine the topology of 3-manifolds that admit $(I,J,1)$-generalized Finsler structures and to single out classes of $(I,J,1)$-generalized Finsler structures induced by standard Cartan structures.