Geodesible contact structures on 3–manifolds

Massot, Patrick

doi:10.2140/gt.2008.12.1729

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Geodesible contact structures on $3$–manifolds

Patrick Massot

Geometry & Topology 12 (2008) 1729–1776

DOI: 10.2140/gt.2008.12.1729

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/

Volume 12, issue 3 (2008)