Geodesible contact structures on 3–manifolds

Massot, Patrick¹

¹ École Normale Supérieure de Lyon 69364 LYON Cedex 07, France

Geometry & topology, Tome 12 (2008) no. 3, pp. 1729-1776.

Résumé

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.

Détail

DOI : 10.2140/gt.2008.12.1729

Keywords: contact structures, totally geodesic, Seifert manifolds, twisting number

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