#### Volume 12, issue 3 (2008)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Geodesible contact structures on $3$–manifolds

### Patrick Massot

Geometry & Topology 12 (2008) 1729–1776
##### Abstract

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.

##### Keywords
contact structures, totally geodesic, Seifert manifolds, twisting number
Primary: 57M50
Secondary: 57R17