Open Access
2008 Geodesible contact structures on $3$–manifolds
Patrick Massot
Geom. Topol. 12(3): 1729-1776 (2008). DOI: 10.2140/gt.2008.12.1729


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.


Download Citation

Patrick Massot. "Geodesible contact structures on $3$–manifolds." Geom. Topol. 12 (3) 1729 - 1776, 2008.


Received: 14 December 2007; Revised: 21 May 2008; Accepted: 25 April 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1152.57017
MathSciNet: MR2421139
Digital Object Identifier: 10.2140/gt.2008.12.1729

Primary: 57M50
Secondary: 57R17

Keywords: contact structures , Seifert manifolds , totally geodesic , twisting number

Rights: Copyright © 2008 Mathematical Sciences Publishers

Vol.12 • No. 3 • 2008
Back to Top