3 papers
math.SG2024
Geodesic vector fields, induced contact structures and tightness in dimension three
Tilman Becker
In this paper, we provide new and simpler proofs of two theorems of Gluck and Harrison on contact structures induced by great circle or line fibrations. Furthermore, we prove that…
math.SG2022
Geodesic and conformally Reeb vector fields on flat 3-manifolds
Tilman Becker
A unit vector field on a Riemannian manifold is called geodesic if all of its integral curves are geodesics. We show, in the case of being a flat 3-manifold not equal to $\…
math.SG2019
The contact structure induced by a line fibration of R^3 is standard
Tilman Becker, Hansjörg Geiges
Building on the work of and answering a question by Michael Harrison, we show that any contact structure on Euclidean 3-space induced by a line fibration is diffeomorphic to the st…