Tohoku Mathematical Journal
2014
September
SECOND SERIES VOL. 66, NO. 3

Tohoku Math. J.
66 (2014), 321-353

Title GENERALIZED FINSLER STRUCTURES ON CLOSED 3-MANIFOLDS

In memory of Professor Dr. Stere Ianus
Author Sorin V. Sabau, Kazuhiro Shibuya and Gheorghe Pitiş

(Received June 27, 2012)
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.

Mathematics Subject Classification. Primary 53C60; Secondary 53D35.
Key words and phrases. Generalized Finsler manifolds, taut contact circles, contact topology.

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