Generalized Finsler structures on closed 3-manifolds

TL;DR

This paper explores generalized Finsler structures on closed 3-manifolds, establishing a link with contact circle structures, which helps classify the topology of manifolds admitting such structures.

Contribution

It introduces a relation between (I,J,1)-generalized Finsler structures and Cartan contact structures, clarifying their global properties and topological implications.

Findings

Relation between (I,J,1)-generalized Finsler structures and Cartan contact structures

Topological classification of 3-manifolds admitting these structures

Identification of structures induced by standard Cartan structures

Abstract

An (I,J,K)-generalized Finsler structure on a 3-manifold is a generalization of a Finslerian structure, introduced in order to separate and clarify the local and global aspects in Finsler geometry making use of the 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.