GENERALIZED FINSLER STRUCTURES ON CLOSED 3-MANIFOLDS

• SABAU SORIN V.

  School of Science, Department of Mathematics, Tokai University

• SHIBUYA KAZUHIRO

  Graduate School of Science, Hiroshima University

• PITIŞ GHEORGHE

  Department of Mathematics and Informatics, University Transilvania of Brasov

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.

Journal

• Tohoku Mathematical Journal, Second Series

  Tohoku Mathematical Journal, Second Series 66 (3), 321-353, 2014-09-30

  Mathematical Institute, Tohoku University

Keywords

• Generalized Finsler manifolds
• taut contact circles
• contact topology

Details

• CRID: 1391131406288722048
• NII Article ID: 130007953678
• DOI: 10.2748/tmj/1412783202
• ISSN: 2186585X
• ISSN: 00408735
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed