Volume 12, issue 3 (2008)

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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
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 57R17
References
Publication
Received: 14 December 2007
Revised: 21 May 2008
Accepted: 25 April 2008
Published: 4 July 2008
Proposed: Peter Ozsváth
Seconded: Yasha Eliashberg, Ron Stern
Authors
Patrick Massot
École Normale Supérieure de Lyon 69364 LYON Cedex 07
France
http://www.umpa.ens-lyon.fr/~pmassot/