English

Great Circle Fibrations and Contact Structures on Odd-Dimensional Spheres

Differential Geometry 2024-07-26 v2 Geometric Topology

Abstract

It is known that for every smooth great circle fibration of the 3-sphere, the distribution of tangent 2-planes orthogonal to the fibres is a contact structure, in fact a tight one, but we show here that, beginning with the 5-sphere, there exist smooth great circle fibrations of all odd-dimensional spheres for which the hyperplane distribution orthogonal to the fibres is not a contact structure.

Keywords

Cite

@article{arxiv.1901.06370,
  title  = {Great Circle Fibrations and Contact Structures on Odd-Dimensional Spheres},
  author = {Herman Gluck and Jingye Yang},
  journal= {arXiv preprint arXiv:1901.06370},
  year   = {2024}
}
R2 v1 2026-06-23T07:16:02.409Z