Geometry & Topology
- Geom. Topol.
- Volume 12, Number 3 (2008), 1729-1776.
Geodesible contact structures on $3$–manifolds
In this paper, we study and almost completely classify contact structures on closed 3–manifolds which are totally geodesic for some Riemannian metric. Due to previously known results, this amounts to classifying contact structures on Seifert manifolds which are transverse to the fibers. Actually, we obtain the complete classification of contact structures with negative (maximal) twisting number (which includes the transverse ones) on Seifert manifolds whose base is not a sphere, as well as partial results in the spherical case.
Geom. Topol., Volume 12, Number 3 (2008), 1729-1776.
Received: 14 December 2007
Revised: 21 May 2008
Accepted: 25 April 2008
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57R17: Symplectic and contact topology
Massot, Patrick. Geodesible contact structures on $3$–manifolds. Geom. Topol. 12 (2008), no. 3, 1729--1776. doi:10.2140/gt.2008.12.1729. https://projecteuclid.org/euclid.gt/1513800108