## Tohoku Mathematical Journal

### 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.

#### Article information

Source
Tohoku Math. J. (2), Volume 66, Number 3 (2014), 321-353.

Dates
First available in Project Euclid: 8 October 2014

https://projecteuclid.org/euclid.tmj/1412783202

Digital Object Identifier
doi:10.2748/tmj/1412783202

Mathematical Reviews number (MathSciNet)
MR3266736

Zentralblatt MATH identifier
1318.53081

#### Citation

Sabau, Sorin V.; Shibuya, Kazuhiro; Pitiş, Gheorghe. Generalized Finsler structures on closed 3-manifolds. Tohoku Math. J. (2) 66 (2014), no. 3, 321--353. doi:10.2748/tmj/1412783202. https://projecteuclid.org/euclid.tmj/1412783202

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