Geometry & Topology

Geodesible contact structures on $3$–manifolds

Patrick Massot

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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.

Article information

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57R17: Symplectic and contact topology

contact structures totally geodesic Seifert manifolds twisting number


Massot, Patrick. Geodesible contact structures on $3$–manifolds. Geom. Topol. 12 (2008), no. 3, 1729--1776. doi:10.2140/gt.2008.12.1729.

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