Geodesible contact structures on 3--manifolds

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.

49 pages, 6 figures. v2 includes referee's suggestions, adds some references and discussions, corrects small inaccuracies, minor exposition improvements. this is almost the published version

References in corpus (3)

• Transverse contact structures on Seifert 3-manifolds
• Strongly fillable contact 3-manifolds without Stein fillings
• Tight contact structures on Seifert manifolds over T^2 with one singular fibre

Cited by in corpus (7)

• Weak and strong fillability of higher dimensional contact manifolds
• On the contact mapping class group of Legendrian circle bundles
• Tight small Seifert fibered manifolds with $e_0=-2$
• Exactly fillable contact structures without Stein fillings
• Rectangular diagrams of surfaces: representability
• Contact structures, deformations and taut foliations
• Ricci Curvature, Reeb Flows and Contact 3-Manifolds